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subsection</span> </button> <ul id="toc-Principles_of_buffering-sublist" class="vector-toc-list"> <li id="toc-Buffer_capacity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Buffer_capacity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Buffer capacity</span> </div> </a> <ul id="toc-Buffer_capacity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications_of_buffers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications_of_buffers"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Applications of buffers</span> </div> </a> <button aria-controls="toc-Applications_of_buffers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications of buffers subsection</span> </button> <ul id="toc-Applications_of_buffers-sublist" class="vector-toc-list"> <li id="toc-Simple_buffering_agents" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simple_buffering_agents"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Simple buffering agents</span> </div> </a> <ul id="toc-Simple_buffering_agents-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-"Universal"_buffer_mixtures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#"Universal"_buffer_mixtures"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>"Universal" buffer mixtures</span> </div> </a> <ul id="toc-"Universal"_buffer_mixtures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Common_buffer_compounds_used_in_biology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Common_buffer_compounds_used_in_biology"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Common buffer compounds used in biology</span> </div> </a> <ul id="toc-Common_buffer_compounds_used_in_biology-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Calculating_buffer_pH" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Calculating_buffer_pH"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Calculating buffer pH</span> </div> </a> <button aria-controls="toc-Calculating_buffer_pH-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Calculating buffer pH subsection</span> </button> <ul id="toc-Calculating_buffer_pH-sublist" class="vector-toc-list"> <li id="toc-Monoprotic_acids" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Monoprotic_acids"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Monoprotic acids</span> </div> </a> <ul id="toc-Monoprotic_acids-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polyprotic_acids" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polyprotic_acids"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Polyprotic acids</span> </div> </a> <ul id="toc-Polyprotic_acids-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Buffer solution</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 50 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-50" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">50 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AD%D9%84%D9%88%D9%84_%D9%85%D9%86%D8%B8%D9%85" title="محلول منظم – Arabic" lang="ar" hreflang="ar" data-title="محلول منظم" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BE%E0%A6%AB%E0%A6%BE%E0%A6%B0_%E0%A6%A6%E0%A7%8D%E0%A6%B0%E0%A6%AC%E0%A6%A3" title="বাফার দ্রবণ – Bangla" lang="bn" hreflang="bn" data-title="বাফার দ্রবণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D1%83%D1%84%D0%B5%D1%80_(%D1%80%D0%B0%D0%B7%D1%82%D0%B2%D0%BE%D1%80)" title="Буфер (разтвор) – Bulgarian" lang="bg" hreflang="bg" data-title="Буфер (разтвор)" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Puferi" title="Puferi – Bosnian" lang="bs" hreflang="bs" data-title="Puferi" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Dissoluci%C3%B3_amortidora" title="Dissolució amortidora – Catalan" lang="ca" hreflang="ca" data-title="Dissolució amortidora" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Pufr" title="Pufr – Czech" lang="cs" hreflang="cs" data-title="Pufr" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Buffer_(kemi)" title="Buffer (kemi) – Danish" lang="da" hreflang="da" data-title="Buffer (kemi)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Puffer_(Chemie)" title="Puffer (Chemie) – German" lang="de" hreflang="de" data-title="Puffer (Chemie)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Puhverlahus" title="Puhverlahus – Estonian" lang="et" hreflang="et" data-title="Puhverlahus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A1%CF%85%CE%B8%CE%BC%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CF%8C_%CE%B4%CE%B9%CE%AC%CE%BB%CF%85%CE%BC%CE%B1" title="Ρυθμιστικό διάλυμα – Greek" lang="el" hreflang="el" data-title="Ρυθμιστικό διάλυμα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tamp%C3%B3n_qu%C3%ADmico" title="Tampón químico – Spanish" lang="es" hreflang="es" data-title="Tampón químico" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Bufrosolva%C4%B5o" title="Bufrosolvaĵo – Esperanto" lang="eo" hreflang="eo" data-title="Bufrosolvaĵo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Tanpoi_kimiko" title="Tanpoi kimiko – Basque" lang="eu" hreflang="eu" data-title="Tanpoi kimiko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AD%D9%84%D9%88%D9%84_%D8%A8%D8%A7%D9%81%D8%B1" title="محلول بافر – Persian" lang="fa" hreflang="fa" data-title="محلول بافر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Solution_tampon" title="Solution tampon – French" lang="fr" hreflang="fr" data-title="Solution tampon" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Tuaslag%C3%A1n_maol%C3%A1nach" title="Tuaslagán maolánach – Irish" lang="ga" hreflang="ga" data-title="Tuaslagán maolánach" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Soluci%C3%B3n_tamp%C3%B3n" title="Solución tampón – Galician" lang="gl" hreflang="gl" data-title="Solución tampón" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%99%84%EC%B6%A9_%EC%9A%A9%EC%95%A1" title="완충 용액 – Korean" lang="ko" hreflang="ko" data-title="완충 용액" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A4%AB%E0%A4%B0_%E0%A4%B5%E0%A4%BF%E0%A4%B2%E0%A4%AF%E0%A4%A8" title="बफर विलयन – Hindi" lang="hi" hreflang="hi" data-title="बफर विलयन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Pufer" title="Pufer – Croatian" lang="hr" hreflang="hr" data-title="Pufer" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Larutan_dapar" title="Larutan dapar – Indonesian" lang="id" hreflang="id" data-title="Larutan dapar" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Soluzione_tampone" title="Soluzione tampone – Italian" lang="it" hreflang="it" data-title="Soluzione tampone" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%91%D7%95%D7%A4%D7%A8" title="בופר – Hebrew" lang="he" hreflang="he" data-title="בופר" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D1%83%D1%84%D0%B5%D1%80%D0%BB%D1%96%D0%BA_%D0%B5%D1%80%D1%96%D1%82%D1%96%D0%BD%D0%B4%D1%96" title="Буферлік ерітінді – Kazakh" lang="kk" hreflang="kk" data-title="Буферлік ерітінді" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Kapasite_tanpon" title="Kapasite tanpon – Haitian Creole" lang="ht" hreflang="ht" data-title="Kapasite tanpon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D1%83%D1%84%D0%B5%D1%80%D0%B4%D0%B8%D0%BA_%D1%8D%D1%80%D0%B8%D1%82%D0%BC%D0%B5" title="Буфердик эритме – Kyrgyz" lang="ky" hreflang="ky" data-title="Буфердик эритме" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bufer%C5%A1%C4%B7%C4%ABdums" title="Buferšķīdums – Latvian" lang="lv" hreflang="lv" data-title="Buferšķīdums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pufferoldat" title="Pufferoldat – Hungarian" lang="hu" hreflang="hu" data-title="Pufferoldat" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%83%D1%84%D0%B5%D1%80" title="Пуфер – Macedonian" lang="mk" hreflang="mk" data-title="Пуфер" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B4%AB%E0%B5%BC_%E0%B4%B2%E0%B4%BE%E0%B4%AF%E0%B4%A8%E0%B4%BF" title="ബഫർ ലായനി – Malayalam" lang="ml" hreflang="ml" data-title="ബഫർ ലായനി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Buffer_(scheikunde)" title="Buffer (scheikunde) – Dutch" lang="nl" hreflang="nl" data-title="Buffer (scheikunde)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B7%A9%E8%A1%9D%E6%B6%B2" title="緩衝液 – Japanese" lang="ja" hreflang="ja" data-title="緩衝液" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Bufferl%C3%B8sning" title="Bufferløsning – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Bufferløsning" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Roztw%C3%B3r_buforowy" title="Roztwór buforowy – Polish" lang="pl" hreflang="pl" data-title="Roztwór buforowy" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Solu%C3%A7%C3%A3o_tamp%C3%A3o" title="Solução tampão – Portuguese" lang="pt" hreflang="pt" data-title="Solução tampão" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Solu%C8%9Bie_tampon" title="Soluție tampon – Romanian" lang="ro" hreflang="ro" data-title="Soluție tampon" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D1%83%D1%84%D0%B5%D1%80%D0%BD%D1%8B%D0%B9_%D1%80%D0%B0%D1%81%D1%82%D0%B2%D0%BE%D1%80" title="Буферный раствор – Russian" lang="ru" hreflang="ru" data-title="Буферный раствор" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Buffer_solution" title="Buffer solution – Simple English" lang="en-simple" hreflang="en-simple" data-title="Buffer solution" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Tlmiv%C3%BD_roztok" title="Tlmivý roztok – Slovak" lang="sk" hreflang="sk" data-title="Tlmivý roztok" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%AF%DB%8C%D8%B1%D8%A7%D9%88%DB%95%DB%8C_%DA%95%DB%8E%DA%A9%D8%AE%DB%95%D8%B1" title="گیراوەی ڕێکخەر – Central Kurdish" lang="ckb" hreflang="ckb" data-title="گیراوەی ڕێکخەر" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%83%D1%84%D0%B5%D1%80" title="Пуфер – Serbian" lang="sr" hreflang="sr" data-title="Пуфер" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Pufer" title="Pufer – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Pufer" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Puskuriliuos" title="Puskuriliuos – Finnish" lang="fi" hreflang="fi" data-title="Puskuriliuos" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Buffertsystem" title="Buffertsystem – Swedish" lang="sv" hreflang="sv" data-title="Buffertsystem" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%BE%E0%AE%99%E0%AF%8D%E0%AE%95%E0%AE%B2%E0%AF%8D_%E0%AE%95%E0%AE%B0%E0%AF%88%E0%AE%9A%E0%AE%B2%E0%AF%8D" title="தாங்கல் கரைசல் – Tamil" lang="ta" hreflang="ta" data-title="தாங்கல் கரைசல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Tampon_%C3%A7%C3%B6zelti" title="Tampon çözelti – Turkish" lang="tr" hreflang="tr" data-title="Tampon çözelti" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a 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0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title" style="background:#d3d3d3;">Acids and bases</th></tr><tr><td class="sidebar-image"><span typeof="mw:File"><a href="/wiki/File:Acetic-acid-dissociation-3D-balls.png" class="mw-file-description" title="Diagrammatic representation of the dissociation of acetic acid in aqueous solution to acetate and hydronium ions."><img alt="Diagrammatic representation of the dissociation of acetic acid in aqueous solution to acetate and hydronium ions." src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Acetic-acid-dissociation-3D-balls.png/220px-Acetic-acid-dissociation-3D-balls.png" decoding="async" width="220" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Acetic-acid-dissociation-3D-balls.png/330px-Acetic-acid-dissociation-3D-balls.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Acetic-acid-dissociation-3D-balls.png/440px-Acetic-acid-dissociation-3D-balls.png 2x" data-file-width="2150" data-file-height="513" /></a></span></td></tr><tr><td class="sidebar-content hlist" style="padding:0.2em 0 0.75em;"> <ul><li><a href="/wiki/Acceptor_number" class="mw-redirect" title="Acceptor number">Acceptor number</a></li> <li><a href="/wiki/Acid" title="Acid">Acid</a></li> <li><a href="/wiki/Acid%E2%80%93base_reaction" title="Acid–base reaction">Acid–base reaction</a></li> <li><a href="/wiki/Acid%E2%80%93base_homeostasis" title="Acid–base homeostasis">Acid–base homeostasis</a></li> <li><a href="/wiki/Acid_strength" title="Acid strength">Acid strength</a></li> <li><a href="/wiki/Acidity_function" title="Acidity function">Acidity function</a></li> <li><a href="/wiki/Amphoterism" title="Amphoterism">Amphoterism</a></li> <li><a href="/wiki/Base_(chemistry)" title="Base (chemistry)">Base</a></li> <li><a class="mw-selflink selflink">Buffer solutions</a></li> <li><a href="/wiki/Dissociation_constant" title="Dissociation constant">Dissociation constant</a></li> <li><a href="/wiki/Donor_number" title="Donor number">Donor number</a></li> <li><a href="/wiki/Equilibrium_chemistry" title="Equilibrium chemistry">Equilibrium chemistry</a></li> <li><a href="/wiki/Acid%E2%80%93base_extraction" title="Acid–base extraction">Extraction</a></li> <li><a href="/wiki/Hammett_acidity_function" title="Hammett acidity function">Hammett acidity function</a></li> <li><a href="/wiki/PH" title="PH">pH</a></li> <li><a href="/wiki/Proton_affinity" title="Proton affinity">Proton affinity</a></li> <li><a href="/wiki/Self-ionization_of_water" title="Self-ionization of water">Self-ionization of water</a></li> <li><a href="/wiki/Acid%E2%80%93base_titration" title="Acid–base titration">Titration</a></li> <li><a href="/wiki/Lewis_acid_catalysis" title="Lewis acid catalysis">Lewis acid catalysis</a></li> <li><a href="/wiki/Frustrated_Lewis_pair" title="Frustrated Lewis pair">Frustrated Lewis pair</a></li> <li><a href="/wiki/Chiral_Lewis_acid" title="Chiral Lewis acid">Chiral Lewis acid</a></li> <li><a href="/wiki/ECW_model" title="ECW model">ECW model</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e5e5e5;"> <a href="/wiki/Acid" title="Acid">Acid</a> types</th></tr><tr><td class="sidebar-content hlist" style="padding:0.2em 0 0.75em;"> <ul><li><a href="/wiki/Br%C3%B8nsted%E2%80%93Lowry_acid%E2%80%93base_theory" title="Brønsted–Lowry acid–base theory">Brønsted–Lowry</a></li> <li><a href="/wiki/Lewis_acids_and_bases" title="Lewis acids and bases">Lewis</a></li> <li><a href="/wiki/Mineral_acid" title="Mineral acid">Mineral</a></li> <li><a href="/wiki/Organic_acid" title="Organic acid">Organic</a></li> <li><a href="/wiki/Acidic_oxide" title="Acidic oxide">Oxide</a></li> <li><a href="/wiki/Strong_acid" class="mw-redirect" title="Strong acid">Strong</a></li> <li><a href="/wiki/Superacid" title="Superacid">Superacids</a></li> <li><a href="/wiki/Weak_acid" class="mw-redirect" title="Weak acid">Weak</a></li> <li><a href="/wiki/Solid_acid" title="Solid acid">Solid</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e5e5e5;"> <a href="/wiki/Base_(chemistry)" title="Base (chemistry)">Base</a> types</th></tr><tr><td class="sidebar-content hlist" style="padding:0.2em 0 0.75em;"> <ul><li><a href="/wiki/Br%C3%B8nsted%E2%80%93Lowry_acid%E2%80%93base_theory" title="Brønsted–Lowry acid–base theory">Brønsted–Lowry</a></li> <li><a href="/wiki/Lewis_acids_and_bases" title="Lewis acids and bases">Lewis</a></li> <li><a href="/wiki/Organic_base" title="Organic base">Organic</a></li> <li><a href="/wiki/Basic_oxide" title="Basic oxide">Oxide</a></li> <li><a href="/wiki/Base_(chemistry)#Strong_bases" title="Base (chemistry)">Strong</a></li> <li><a href="/wiki/Superbase" title="Superbase">Superbases</a></li> <li><a href="/wiki/Non-nucleophilic_base" title="Non-nucleophilic base">Non-nucleophilic</a></li> <li><a href="/wiki/Weak_base" title="Weak base">Weak</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Acids_and_bases" title="Template:Acids and bases"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Acids_and_bases" title="Template talk:Acids and bases"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Acids_and_bases" title="Special:EditPage/Template:Acids and bases"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>A <b>buffer solution</b> is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature.<sup id="cite_ref-openstax_1-0" class="reference"><a href="#cite_note-openstax-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Its pH changes very little when a small amount of <a href="/wiki/Strong_acid" class="mw-redirect" title="Strong acid">strong acid</a> or <a href="/wiki/Base_(chemistry)#Strong_bases" title="Base (chemistry)">base</a> is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. In nature, there are many <a href="/wiki/Living_systems" title="Living systems">living systems</a> that use buffering for pH regulation. For example, the <a href="/wiki/Bicarbonate_buffering_system" class="mw-redirect" title="Bicarbonate buffering system">bicarbonate buffering system</a> is used to regulate the <a href="/wiki/PH" title="PH">pH</a> of <a href="/wiki/Blood" title="Blood">blood</a>, and bicarbonate also acts as a <a href="/wiki/Ocean_acidification" title="Ocean acidification">buffer in the ocean</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Principles_of_buffering">Principles of buffering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=1" title="Edit section: Principles of buffering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Buffer_titration_graph.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Buffer_titration_graph.svg/250px-Buffer_titration_graph.svg.png" decoding="async" width="250" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Buffer_titration_graph.svg/375px-Buffer_titration_graph.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Buffer_titration_graph.svg/500px-Buffer_titration_graph.svg.png 2x" data-file-width="292" data-file-height="269" /></a><figcaption>Figure 1. Simulated <a href="/wiki/Titration" title="Titration">titration</a> of an acidified solution of a weak acid (<span class="texhtml">p<i>K</i><sub>a</sub> = 4.7</span>) with alkali</figcaption></figure> <p>Buffer solutions resist pH change because of a <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">chemical equilibrium</a> between the weak acid HA and its conjugate base A<sup>−</sup>: </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent" style="padding-left: 1.5em;">HA ⇌ H<sup>+</sup> + A<sup>−</sup></div> <p>When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, hydrogen ions (H<sup>+</sup>) are added, and the equilibrium is shifted to the left, in accordance with <a href="/wiki/Le_Chatelier%27s_principle" title="Le Chatelier's principle">Le Chatelier's principle</a>. Because of this, the hydrogen ion concentration increases by less than the amount expected for the quantity of strong acid added. Similarly, if strong alkali is added to the mixture, the hydrogen ion concentration decreases by less than the amount expected for the quantity of alkali added. In Figure 1, the effect is illustrated by the simulated titration of a weak acid with <a href="/wiki/Acid_dissociation_constant" title="Acid dissociation constant">p<i>K</i><sub>a</sub></a> = 4.7. The relative concentration of undissociated acid is shown in blue, and of its conjugate base in red. The pH changes relatively slowly in the buffer region, pH = p<i>K</i><sub>a</sub> ± 1, centered at pH = 4.7, where [HA] = [A<sup>−</sup>]. The hydrogen ion concentration decreases by less than the amount expected because most of the added hydroxide ion is consumed in the reaction </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent" style="padding-left: 1.5em;">OH<sup>−</sup> + HA → H<sub>2</sub>O + A<sup>−</sup></div> <p>and only a little is consumed in the neutralization reaction (which is the reaction that results in an increase in pH) </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent" style="padding-left: 1.5em;">OH<sup>−</sup> + H<sup>+</sup> → H<sub>2</sub>O.</div> <p>Once the acid is more than 95% <a href="/wiki/Deprotonation" title="Deprotonation">deprotonated</a>, the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction. </p> <div class="mw-heading mw-heading3"><h3 id="Buffer_capacity">Buffer capacity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=2" title="Edit section: Buffer capacity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Buffer capacity is a quantitative measure of the resistance to change of pH of a solution containing a buffering agent with respect to a change of acid or alkali concentration. It can be defined as follows:<sup id="cite_ref-Skoog_2-0" class="reference"><a href="#cite_note-Skoog-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Urbansky_3-0" class="reference"><a href="#cite_note-Urbansky-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta ={\frac {dC_{b}}{d(\mathrm {pH} )}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">H</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta ={\frac {dC_{b}}{d(\mathrm {pH} )}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d45e29056ed40219641b15cb9bdac64400f10326" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:11.974ex; height:6.176ex;" alt="{\displaystyle \beta ={\frac {dC_{b}}{d(\mathrm {pH} )}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dC_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dC_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe778872cf38ee5ddc3898fbe5948ed6e5c884a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.815ex; height:2.509ex;" alt="{\displaystyle dC_{b}}"></span> is an infinitesimal amount of added base, or <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =-{\frac {dC_{a}}{d(\mathrm {pH} )}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">H</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =-{\frac {dC_{a}}{d(\mathrm {pH} )}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a5267ed1bb5ec1995b4863cb7fa97f3eb17924e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:13.782ex; height:6.176ex;" alt="{\displaystyle \beta =-{\frac {dC_{a}}{d(\mathrm {pH} )}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dC_{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dC_{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6691d056534ae130bfdd79eebf9cdbb0c5c06211" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.98ex; height:2.509ex;" alt="{\displaystyle dC_{a}}"></span> is an infinitesimal amount of added acid. pH is defined as −log<sub>10</sub>[H<sup>+</sup>], and <i>d</i>(pH) is an infinitesimal change in pH. </p><p>With either definition the buffer capacity for a weak acid HA with dissociation constant <i>K</i><sub>a</sub> can be expressed as<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hulanicki_5-0" class="reference"><a href="#cite_note-Hulanicki-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Urbansky_3-1" class="reference"><a href="#cite_note-Urbansky-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =2.303\left([{\ce {H+}}]+{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}+{\frac {K_{\text{w}}}{[{\ce {H+}}]}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mn>2.303</mn> <mrow> <mo>(</mo> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>HA</mtext> </mrow> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>w</mtext> </mrow> </msub> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =2.303\left([{\ce {H+}}]+{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}+{\frac {K_{\text{w}}}{[{\ce {H+}}]}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf8b7c2c34d12f8145df3299a061593aaa76643a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:44.604ex; height:7.509ex;" alt="{\displaystyle \beta =2.303\left([{\ce {H+}}]+{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}+{\frac {K_{\text{w}}}{[{\ce {H+}}]}}\right),}"></span> where [H<sup>+</sup>] is the concentration of hydrogen ions, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\text{HA}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>HA</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{HA}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0891867f30565d8f2477541ea0925867f3fdc8ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.055ex; height:2.509ex;" alt="{\displaystyle T_{\text{HA}}}"></span> is the total concentration of added acid. <i>K</i><sub>w</sub> is the equilibrium constant for <a href="/wiki/Self-ionization_of_water" title="Self-ionization of water">self-ionization of water</a>, equal to 1.0<span style="margin:0 .15em 0 .25em">×</span>10<sup>−14</sup>. Note that in solution H<sup>+</sup> exists as the <a href="/wiki/Hydronium" title="Hydronium">hydronium</a> ion H<sub>3</sub>O<sup>+</sup>, and further <a href="/wiki/Aquation" title="Aquation">aquation</a> of the hydronium ion has negligible effect on the dissociation equilibrium, except at very high acid concentration. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Buffer_Capacity_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Buffer_Capacity_2.png/250px-Buffer_Capacity_2.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Buffer_Capacity_2.png/375px-Buffer_Capacity_2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Buffer_Capacity_2.png/500px-Buffer_Capacity_2.png 2x" data-file-width="800" data-file-height="800" /></a><figcaption>Figure 2. Buffer capacity <i>β</i> for a 0.1 M solution of a weak acid with a p<i>K</i><sub>a</sub> = 7</figcaption></figure> <p>This equation shows that there are three regions of raised buffer capacity (see figure 2). </p> <ul><li>In the central region of the curve (coloured green on the plot), the second term is dominant, and <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta \approx 2.303{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>≈</mo> <mn>2.303</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>HA</mtext> </mrow> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta \approx 2.303{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0e3ba9d065bfb822350b58e375d1f4630c6235" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:24.537ex; height:6.843ex;" alt="{\displaystyle \beta \approx 2.303{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}.}"></span> Buffer capacity rises to a local maximum at pH = <i>pK</i><sub>a</sub>. The height of this peak depends on the value of pK<sub>a</sub>. Buffer capacity is negligible when the concentration [HA] of buffering agent is very small and increases with increasing concentration of the buffering agent.<sup id="cite_ref-Urbansky_3-2" class="reference"><a href="#cite_note-Urbansky-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Some authors show only this region in graphs of buffer capacity.<sup id="cite_ref-Skoog_2-1" class="reference"><a href="#cite_note-Skoog-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><div class="paragraphbreak" style="margin-top:0.5em"></div> Buffer capacity falls to 33% of the maximum value at pH = p<i>K</i><sub>a</sub> ± 1, to 10% at pH = p<i>K</i><sub>a</sub> ± 1.5 and to 1% at pH = p<i>K</i><sub>a</sub> ± 2. For this reason the most useful range is approximately p<i>K</i><sub>a</sub> ± 1. When choosing a buffer for use at a specific pH, it should have a p<i>K</i><sub>a</sub> value as close as possible to that pH.<sup id="cite_ref-Skoog_2-2" class="reference"><a href="#cite_note-Skoog-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li>With strongly acidic solutions, pH less than about 2 (coloured red on the plot), the first term in the equation dominates, and buffer capacity rises exponentially with decreasing pH: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta \approx 10^{-\mathrm {pH} }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>≈</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta \approx 10^{-\mathrm {pH} }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a365d8431babd68f167cce2a41f07cbcf7d4837c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.06ex; height:3.009ex;" alt="{\displaystyle \beta \approx 10^{-\mathrm {pH} }.}"></span> This results from the fact that the second and third terms become negligible at very low pH. This term is independent of the presence or absence of a buffering agent.</li> <li>With strongly alkaline solutions, pH more than about 12 (coloured blue on the plot), the third term in the equation dominates, and buffer capacity rises exponentially with increasing pH: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta \approx 10^{\mathrm {pH} -\mathrm {p} K_{\text{w}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>≈</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">H</mi> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>w</mtext> </mrow> </msub> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta \approx 10^{\mathrm {pH} -\mathrm {p} K_{\text{w}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2658d8c7e07ded3299073348f3204b4a6b4781c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.496ex; height:3.009ex;" alt="{\displaystyle \beta \approx 10^{\mathrm {pH} -\mathrm {p} K_{\text{w}}}.}"></span> This results from the fact that the first and second terms become negligible at very high pH. This term is also independent of the presence or absence of a buffering agent.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Applications_of_buffers">Applications of buffers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=3" title="Edit section: Applications of buffers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The pH of a solution containing a buffering agent can only vary within a narrow range, regardless of what else may be present in the solution. In biological systems this is an essential condition for <a href="/wiki/Enzyme" title="Enzyme">enzymes</a> to function correctly. For example, in <a href="/wiki/Blood" title="Blood">human blood</a> a mixture of <a href="/wiki/Carbonic_acid" title="Carbonic acid">carbonic acid</a> (H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>CO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span>) and <a href="/wiki/Bicarbonate" title="Bicarbonate">bicarbonate</a> (HCO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span>) is present in the <a href="/wiki/Blood_plasma" title="Blood plasma">plasma</a> fraction; this constitutes the major mechanism for maintaining the pH of blood between 7.35 and 7.45. Outside this narrow range (7.40 ± 0.05 pH unit), <a href="/wiki/Acidosis" title="Acidosis">acidosis</a> and <a href="/wiki/Alkalosis" title="Alkalosis">alkalosis</a> metabolic conditions rapidly develop, ultimately leading to death if the correct buffering capacity is not rapidly restored. </p><p>If the pH value of a solution rises or falls too much, the effectiveness of an enzyme decreases in a process, known as <a href="/wiki/Denaturation_(biochemistry)" title="Denaturation (biochemistry)">denaturation</a>, which is usually irreversible.<sup id="cite_ref-Scorpio_2000_6-0" class="reference"><a href="#cite_note-Scorpio_2000-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The majority of biological samples that are used in research are kept in a buffer solution, often <a href="/wiki/Phosphate_buffered_saline" class="mw-redirect" title="Phosphate buffered saline">phosphate buffered saline</a> (PBS) at pH 7.4. </p><p>In industry, buffering agents are used in <a href="/wiki/Fermentation_(biochemistry)" class="mw-redirect" title="Fermentation (biochemistry)">fermentation</a> processes and in setting the correct conditions for dyes used in colouring fabrics. They are also used in chemical analysis<sup id="cite_ref-Hulanicki_5-1" class="reference"><a href="#cite_note-Hulanicki-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and calibration of <a href="/wiki/PH_meter" title="PH meter">pH meters</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Simple_buffering_agents">Simple buffering agents</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=4" title="Edit section: Simple buffering agents"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><table class="wikitable"> <tbody><tr> <th>Buffering agent</th> <th>p<i>K</i><sub>a</sub></th> <th>Useful pH range </th></tr> <tr> <td><a href="/wiki/Citric_acid" title="Citric acid">Citric acid</a></td> <td>3.13, 4.76, 6.40</td> <td>2.1–7.4 </td></tr> <tr> <td><a href="/wiki/Acetic_acid" title="Acetic acid">Acetic acid</a></td> <td>4.8</td> <td>3.8–5.8 </td></tr> <tr> <td><a href="/wiki/Potassium_dihydrogenphosphate" class="mw-redirect" title="Potassium dihydrogenphosphate">KH<sub>2</sub>PO<sub>4</sub></a></td> <td>7.2</td> <td>6.2–8.2 </td></tr> <tr> <td><a href="/wiki/N-Cyclohexyl-2-aminoethanesulfonic_acid" class="mw-redirect" title="N-Cyclohexyl-2-aminoethanesulfonic acid">CHES</a></td> <td>9.3</td> <td>8.3–10.3 </td></tr> <tr> <td><a href="/wiki/Borate" title="Borate">Borate</a></td> <td>9.24</td> <td>8.25–10.25 </td></tr></tbody></table></dd></dl> <p>For buffers in acid regions, the pH may be adjusted to a desired value by adding a strong acid such as <a href="/wiki/Hydrochloric_acid" title="Hydrochloric acid">hydrochloric acid</a> to the particular buffering agent. For alkaline buffers, a strong base such as <a href="/wiki/Sodium_hydroxide" title="Sodium hydroxide">sodium hydroxide</a> may be added. Alternatively, a buffer mixture can be made from a mixture of an acid and its conjugate base. For example, an acetate buffer can be made from a mixture of acetic acid and <a href="/wiki/Sodium_acetate" title="Sodium acetate">sodium acetate</a>. Similarly, an alkaline buffer can be made from a mixture of the base and its conjugate acid. </p> <div class="mw-heading mw-heading3"><h3 id=""Universal"_buffer_mixtures"><span id=".22Universal.22_buffer_mixtures"></span>"Universal" buffer mixtures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=5" title="Edit section: "Universal" buffer mixtures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>By combining substances with p<i>K</i><sub>a</sub> values differing by only two or less and adjusting the pH, a wide range of buffers can be obtained. <a href="/wiki/Citric_acid" title="Citric acid">Citric acid</a> is a useful component of a buffer mixture because it has three p<i>K</i><sub>a</sub> values, separated by less than two. The buffer range can be extended by adding other buffering agents. The following mixtures (<a href="/wiki/McIlvaine%27s_buffer" class="mw-redirect" title="McIlvaine's buffer">McIlvaine's buffer</a> solutions) have a buffer range of pH 3 to 8.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><table class="wikitable"> <tbody><tr> <th>0.2 M <a href="/wiki/Disodium_phosphate" title="Disodium phosphate">Na<sub>2</sub>HPO<sub>4</sub></a> (mL) </th> <th>0.1 M <a href="/wiki/Citric_acid" title="Citric acid">citric acid</a> (mL) </th> <th>pH </th></tr> <tr> <td>20.55 </td> <td>79.45 </td> <td style="background:#ff0000; color:white">3.0 </td></tr> <tr> <td>38.55 </td> <td>61.45 </td> <td style="background:#ff7777; color:white">4.0 </td></tr> <tr> <td>51.50 </td> <td>48.50 </td> <td style="background:#ff7700;">5.0 </td></tr> <tr> <td>63.15 </td> <td>36.85 </td> <td style="background:#ffff00;">6.0 </td></tr> <tr> <td>82.35 </td> <td>17.65 </td> <td style="background:#007777; color:white">7.0 </td></tr> <tr> <td>97.25 </td> <td>2.75 </td> <td style="background:#0077ff; color:white">8.0 </td></tr></tbody></table></dd></dl> <p>A mixture containing <a href="/wiki/Citric_acid" title="Citric acid">citric acid</a>, <a href="/wiki/Monopotassium_phosphate" title="Monopotassium phosphate">monopotassium phosphate</a>, <a href="/wiki/Boric_acid" title="Boric acid">boric acid</a>, and <a href="/wiki/Barbital" title="Barbital">diethyl barbituric acid</a> can be made to cover the pH range 2.6 to 12.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Other universal buffers are the Carmody buffer<sup id="cite_ref-carmody_9-0" class="reference"><a href="#cite_note-carmody-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Britton%E2%80%93Robinson_buffer" title="Britton–Robinson buffer">Britton–Robinson buffer</a>, developed in 1931. </p> <div class="mw-heading mw-heading3"><h3 id="Common_buffer_compounds_used_in_biology">Common buffer compounds used in biology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=6" title="Edit section: Common buffer compounds used in biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For effective range see <a href="#buffer_capacity">Buffer capacity</a>, above. Also see <a href="/wiki/Good%27s_buffers" title="Good's buffers">Good's buffers</a> for the historic design principles and favourable properties of these buffer substances in biochemical applications. </p> <table class="wikitable"> <tbody><tr> <th>Common name (chemical name) </th> <th>Structure </th> <th><a href="/wiki/Acid_dissociation_constant" title="Acid dissociation constant">p<i>K</i><sub>a</sub></a>, <br />25 °C </th> <th><abbr title="Temperature">Temp.</abbr> effect, <br /><style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">dpH</span><span class="sr-only">/</span><span class="den">d<i>T</i></span></span>⁠</span> (K<sup>−1</sup>)<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </th> <th><a href="/wiki/Molecular_weight" class="mw-redirect" title="Molecular weight">Mol. <br />weight</a> </th></tr> <tr> <td><a href="/wiki/TAPS_(buffer)" title="TAPS (buffer)">TAPS</a>, <br />([tris(hydroxymethyl)methylamino]propanesulfonic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:TAPS.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/TAPS.svg/200px-TAPS.svg.png" decoding="async" width="200" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/TAPS.svg/300px-TAPS.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/TAPS.svg/400px-TAPS.svg.png 2x" data-file-width="620" data-file-height="288" /></a></span></td> <td>8.43</td> <td>−0.018</td> <td>243.3 </td></tr> <tr> <td><a href="/wiki/Bicine" title="Bicine">Bicine</a>, <br />(2-(bis(2-hydroxyethyl)amino)acetic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:Bicine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Bicine.png/150px-Bicine.png" decoding="async" width="150" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Bicine.png/225px-Bicine.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Bicine.png/300px-Bicine.png 2x" data-file-width="962" data-file-height="509" /></a></span></td> <td>8.35</td> <td>−0.018</td> <td>163.2 </td></tr> <tr> <td><a href="/wiki/Tris" title="Tris">Tris</a>, <br />(tris(hydroxymethyl)aminomethane, or <br />2-amino-2-(hydroxymethyl)propane-1,3-diol) </td> <td><span typeof="mw:File"><a href="/wiki/File:Tris.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Tris.png/100px-Tris.png" decoding="async" width="100" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Tris.png/150px-Tris.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Tris.png/200px-Tris.png 2x" data-file-width="841" data-file-height="773" /></a></span></td> <td>8.07<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></td> <td>−0.028</td> <td>121.14 </td></tr> <tr> <td><a href="/wiki/Tricine" title="Tricine">Tricine</a>, <br />(N-[tris(hydroxymethyl)methyl]glycine) </td> <td><span typeof="mw:File"><a href="/wiki/File:Tricine.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Tricine.svg/150px-Tricine.svg.png" decoding="async" width="150" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Tricine.svg/225px-Tricine.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Tricine.svg/300px-Tricine.svg.png 2x" data-file-width="480" data-file-height="295" /></a></span></td> <td>8.05</td> <td>−0.021</td> <td>179.2 </td></tr> <tr> <td><a href="/wiki/TAPSO_(buffer)" class="mw-redirect" title="TAPSO (buffer)">TAPSO</a>, <br />(3-[N-tris(hydroxymethyl)methylamino]-2-hydroxypropanesulfonic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:TAPSO.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/TAPSO.svg/200px-TAPSO.svg.png" decoding="async" width="200" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/TAPSO.svg/300px-TAPSO.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/TAPSO.svg/400px-TAPSO.svg.png 2x" data-file-width="620" data-file-height="288" /></a></span></td> <td>7.635</td> <td></td> <td>259.3 </td></tr> <tr> <td><a href="/wiki/HEPES" title="HEPES">HEPES</a>, <br />(4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:HEPES.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/HEPES.png/200px-HEPES.png" decoding="async" width="200" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/HEPES.png/300px-HEPES.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/HEPES.png/400px-HEPES.png 2x" data-file-width="1831" data-file-height="707" /></a></span></td> <td>7.48</td> <td>−0.014</td> <td>238.3 </td></tr> <tr> <td><a href="/wiki/TES_(buffer)" title="TES (buffer)">TES</a>, <br />(2-[[1,3-dihydroxy-2-(hydroxymethyl)propan-2-yl]amino]ethanesulfonic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:TES_free_acid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/TES_free_acid.svg/200px-TES_free_acid.svg.png" decoding="async" width="200" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/TES_free_acid.svg/300px-TES_free_acid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/TES_free_acid.svg/400px-TES_free_acid.svg.png 2x" data-file-width="620" data-file-height="300" /></a></span></td> <td>7.40</td> <td>−0.020</td> <td>229.20 </td></tr> <tr> <td><a href="/wiki/MOPS" title="MOPS">MOPS</a>, <br />(3-(N-morpholino)propanesulfonic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:Mops_is.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Mops_is.svg/150px-Mops_is.svg.png" decoding="async" width="150" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Mops_is.svg/225px-Mops_is.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Mops_is.svg/300px-Mops_is.svg.png 2x" data-file-width="361" data-file-height="127" /></a></span></td> <td>7.20</td> <td>−0.015</td> <td>209.3 </td></tr> <tr> <td><a href="/wiki/PIPES" title="PIPES">PIPES</a>, <br />(piperazine-N,N′-bis(2-ethanesulfonic acid)) </td> <td><span typeof="mw:File"><a href="/wiki/File:PIPES.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/PIPES.svg/200px-PIPES.svg.png" decoding="async" width="200" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/PIPES.svg/300px-PIPES.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/PIPES.svg/400px-PIPES.svg.png 2x" data-file-width="531" data-file-height="244" /></a></span></td> <td>6.76</td> <td>−0.008</td> <td>302.4 </td></tr> <tr> <td><a href="/wiki/Cacodylate" class="mw-redirect" title="Cacodylate">Cacodylate</a>, <br />(dimethylarsenic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:Cacodylic_acid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Cacodylic_acid.svg/100px-Cacodylic_acid.svg.png" decoding="async" width="100" height="66" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Cacodylic_acid.svg/150px-Cacodylic_acid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Cacodylic_acid.svg/200px-Cacodylic_acid.svg.png 2x" data-file-width="224" data-file-height="148" /></a></span></td> <td>6.27</td> <td></td> <td>138.0 </td></tr> <tr> <td><a href="/wiki/MES_(buffer)" title="MES (buffer)">MES</a>, <br />(2-(N-morpholino)ethanesulfonic acid) </td> <td><span typeof="mw:File"><a href="/wiki/File:MES.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/MES.svg/150px-MES.svg.png" decoding="async" width="150" height="83" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/MES.svg/225px-MES.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/MES.svg/300px-MES.svg.png 2x" data-file-width="512" data-file-height="282" /></a></span></td> <td>6.15</td> <td>−0.011</td> <td>195.2 </td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Tris is a base, the p<i>K</i><sub>a</sub> = 8.07 refers to its conjugate acid.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Calculating_buffer_pH">Calculating buffer pH</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=7" title="Edit section: Calculating buffer pH"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Monoprotic_acids">Monoprotic acids</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=8" title="Edit section: Monoprotic acids"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>First write down the equilibrium expression </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent" style="padding-left: 1.5em;">HA ⇌ A<sup>−</sup> + H<sup>+</sup></div> <p>This shows that when the acid dissociates, equal amounts of hydrogen ion and anion are produced. The equilibrium concentrations of these three components can be calculated in an <a href="/wiki/ICE_table" class="mw-redirect" title="ICE table">ICE table</a> (ICE standing for "initial, change, equilibrium"). </p> <dl><dd><table class="wikitable"> <caption>ICE table for a monoprotic acid </caption> <tbody><tr> <th> </th> <th>[HA]</th> <th>[A<sup>−</sup>]</th> <th>[H<sup>+</sup>] </th></tr> <tr> <th>I </th> <td><i>C</i><sub>0</sub></td> <td>0</td> <td><i>y</i> </td></tr> <tr> <th>C </th> <td>−<i>x</i></td> <td><i>x</i></td> <td><i>x</i> </td></tr> <tr> <th>E </th> <td><i>C</i><sub>0</sub> − <i>x</i></td> <td><i>x</i></td> <td><i>x</i> + <i>y</i> </td></tr></tbody></table></dd></dl> <p>The first row, labelled <b>I</b>, lists the initial conditions: the concentration of acid is <i>C</i><sub>0</sub>, initially undissociated, so the concentrations of A<sup>−</sup> and H<sup>+</sup> would be zero; <i>y</i> is the initial concentration of <i>added</i> strong acid, such as hydrochloric acid. If strong alkali, such as sodium hydroxide, is added, then <i>y</i> will have a negative sign because alkali removes hydrogen ions from the solution. The second row, labelled <b>C</b> for "change", specifies the changes that occur when the acid dissociates. The acid concentration decreases by an amount −<i>x</i>, and the concentrations of A<sup>−</sup> and H<sup>+</sup> both increase by an amount +<i>x</i>. This follows from the equilibrium expression. The third row, labelled <b>E</b> for "equilibrium", adds together the first two rows and shows the concentrations at equilibrium. </p><p>To find <i>x</i>, use the formula for the equilibrium constant in terms of concentrations: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{\text{a}}={\frac {[{\ce {H+}}][{\ce {A-}}]}{[{\ce {HA}}]}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> </mrow> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>HA</mtext> </mrow> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{\text{a}}={\frac {[{\ce {H+}}][{\ce {A-}}]}{[{\ce {HA}}]}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89cb17f8ab679cc14a5d23888ed230c1a71b7384" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.704ex; height:6.676ex;" alt="{\displaystyle K_{\text{a}}={\frac {[{\ce {H+}}][{\ce {A-}}]}{[{\ce {HA}}]}}.}"></span> </p><p>Substitute the concentrations with the values found in the last row of the ICE table: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{\text{a}}={\frac {x(x+y)}{C_{0}-x}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{\text{a}}={\frac {x(x+y)}{C_{0}-x}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d48c533466b212aa221a0b3b56df438a8a751f73" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.073ex; height:6.176ex;" alt="{\displaystyle K_{\text{a}}={\frac {x(x+y)}{C_{0}-x}}.}"></span> </p><p>Simplify to <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+(K_{\text{a}}+y)x-K_{\text{a}}C_{0}=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mo>+</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+(K_{\text{a}}+y)x-K_{\text{a}}C_{0}=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ac70303a495690304441a06e6c47bc1c7ab0788" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.878ex; height:3.176ex;" alt="{\displaystyle x^{2}+(K_{\text{a}}+y)x-K_{\text{a}}C_{0}=0.}"></span> </p><p>With specific values for <i>C</i><sub>0</sub>, <i>K</i><sub>a</sub> and <i>y</i>, this equation can be solved for <i>x</i>. Assuming that pH = −log<sub>10</sub>[H<sup>+</sup>], the pH can be calculated as pH = −log<sub>10</sub>(<i>x</i> + <i>y</i>). </p> <div class="mw-heading mw-heading3"><h3 id="Polyprotic_acids">Polyprotic acids</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=9" title="Edit section: Polyprotic acids"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Citric_acid_speciation.svg" class="mw-file-description"><img alt="This image plots the relative percentages of the protonation species of citric acid as a function of p H. Citric acid has three ionizable hydrogen atoms and thus three p K A values. Below the lowest p K A, the triply protonated species prevails; between the lowest and middle p K A, the doubly protonated form prevails; between the middle and highest p K A, the singly protonated form prevails; and above the highest p K A, the unprotonated form of citric acid is predominant." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Citric_acid_speciation.svg/220px-Citric_acid_speciation.svg.png" decoding="async" width="220" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Citric_acid_speciation.svg/330px-Citric_acid_speciation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Citric_acid_speciation.svg/440px-Citric_acid_speciation.svg.png 2x" data-file-width="723" data-file-height="432" /></a><figcaption> <a href="/wiki/Determination_of_equilibrium_constants#speciation_calculations" title="Determination of equilibrium constants">% species formation</a> calculated for a 10-millimolar solution of citric acid</figcaption></figure> <p>Polyprotic acids are acids that can lose more than one proton. The constant for dissociation of the first proton may be denoted as <i>K</i><sub>a1</sub>, and the constants for dissociation of successive protons as <i>K</i><sub>a2</sub>, etc. <a href="/wiki/Citric_acid" title="Citric acid">Citric acid</a> is an example of a polyprotic acid H<sub>3</sub>A, as it can lose three protons. </p> <dl><dd><table class="wikitable" style="width: 230px;"> <caption>Stepwise dissociation constants </caption> <tbody><tr> <th>Equilibrium</th> <th>Citric acid </th></tr> <tr> <td>H<sub>3</sub>A ⇌ H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup></td> <td>p<i>K</i><sub>a1</sub> = 3.13 </td></tr> <tr> <td>H<sub>2</sub>A<sup>−</sup> ⇌ HA<sup>2−</sup> + H<sup>+</sup></td> <td>p<i>K</i><sub>a2</sub> = 4.76 </td></tr> <tr> <td>HA<sup>2−</sup> ⇌ A<sup>3−</sup> + H<sup>+</sup></td> <td>p<i>K</i><sub>a3</sub> = 6.40 </td></tr></tbody></table></dd></dl> <p>When the difference between successive p<i>K</i><sub>a</sub> values is less than about 3, there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. In the case of citric acid, the overlap is extensive and solutions of citric acid are buffered over the whole range of pH 2.5 to 7.5. </p><p>Calculation of the pH with a polyprotic acid requires a <a href="/wiki/Determination_of_equilibrium_constants#Speciation_calculations" title="Determination of equilibrium constants">speciation calculation</a> to be performed. In the case of citric acid, this entails the solution of the two equations of mass balance: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}C_{{\ce {A}}}&=[{\ce {A^3-}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3},\\C_{{\ce {H}}}&=[{\ce {H+}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+2\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+3\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3}-K_{\text{w}}[{\ce {H+}}]^{-1}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <mn>2</mn> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>3</mn> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>w</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}C_{{\ce {A}}}&=[{\ce {A^3-}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3},\\C_{{\ce {H}}}&=[{\ce {H+}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+2\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+3\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3}-K_{\text{w}}[{\ce {H+}}]^{-1}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/611bf20542dfc1dbd8256ee6465883f1534f527a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:75.1ex; height:6.509ex;" alt="{\displaystyle {\begin{aligned}C_{{\ce {A}}}&=[{\ce {A^3-}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3},\\C_{{\ce {H}}}&=[{\ce {H+}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+2\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+3\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3}-K_{\text{w}}[{\ce {H+}}]^{-1}.\end{aligned}}}"></span> </p><p><i>C</i><sub>A</sub> is the analytical concentration of the acid, <i>C</i><sub>H</sub> is the analytical concentration of added hydrogen ions, <i>β<sub>q</sub></i> are the <a href="/wiki/Equilibrium_constant#Cumulative_and_stepwise_formation_constants" title="Equilibrium constant">cumulative association constants</a>. <i>K</i><sub>w</sub> is the constant for <a href="/wiki/Self-ionization_of_water" title="Self-ionization of water">self-ionization of water</a>. There are two <a href="/wiki/Non-linear" class="mw-redirect" title="Non-linear">non-linear</a> <a href="/wiki/Simultaneous_equation" class="mw-redirect" title="Simultaneous equation">simultaneous equations</a> in two unknown quantities [A<sup>3−</sup>] and [H<sup>+</sup>]. Many computer programs are available to do this calculation. The speciation diagram for citric acid was produced with the program HySS.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>N.B. The numbering of cumulative, overall constants is the reverse of the numbering of the stepwise, dissociation constants. </p> <dl><dd><table class="wikitable"> <caption>Relationship between cumulative association constant (β) values and stepwise dissociation constant (K) values for a tribasic acid. </caption> <tbody><tr> <th>Equilibrium</th> <th>Relationship </th></tr> <tr> <td>A<sup>3−</sup> + H<sup>+</sup> ⇌ AH<sup>2+</sup></td> <td>Log β<sub>1</sub>= pk<sub>a3</sub> </td></tr> <tr> <td>A<sup>3−</sup> + 2H<sup>+</sup> ⇌ AH<sub>2</sub><sup>+</sup></td> <td>Log β<sub>2</sub> =pk<sub>a2</sub> + pk<sub>a3</sub> </td></tr> <tr> <td>A<sup>3−</sup> + 3H<sup>+</sup>⇌ AH<sub>3</sub></td> <td>Log β<sub>3</sub> = pk<sub>a1</sub> + pk<sub>a2</sub> + pk<sub>a3</sub> </td></tr></tbody></table></dd></dl> <p>Cumulative association constants are used in general-purpose computer programs such as the one used to obtain the speciation diagram above. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Henderson%E2%80%93Hasselbalch_equation" title="Henderson–Hasselbalch equation">Henderson–Hasselbalch equation</a></li> <li><a href="/wiki/Good%27s_buffers" title="Good's buffers">Good's buffers</a></li> <li><a href="/wiki/Common-ion_effect" title="Common-ion effect">Common-ion effect</a></li> <li><a href="/wiki/Metal_ion_buffer" title="Metal ion buffer">Metal ion buffer</a></li> <li><a href="/wiki/Mineral_redox_buffer" title="Mineral redox buffer">Mineral redox buffer</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-openstax-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-openstax_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFJ._Gordon_Betts2013" class="citation book cs1">J. 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Kendall/Hunt Publishing Company. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7872-7374-3" title="Special:BookSources/978-0-7872-7374-3"><bdi>978-0-7872-7374-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Acids%2C+Bases%2C+Buffers+%26+Their+Application+to+Biochemical+Systems&rft.pub=Kendall%2FHunt+Publishing+Company&rft.date=2000&rft.isbn=978-0-7872-7374-3&rft.aulast=Scorpio&rft.aufirst=R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuffer+solution" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcIlvaine1921" class="citation journal cs1">McIlvaine, T. C. (1921). <a rel="nofollow" class="external text" href="http://www.jbc.org/content/49/1/183.full.pdf">"A buffer solution for colorimetric comparaison"</a> <span class="cs1-format">(PDF)</span>. <i>J. Biol. Chem</i>. <b>49</b> (1): 183–186. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0021-9258%2818%2986000-8">10.1016/S0021-9258(18)86000-8</a></span>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150226111238/http://www.jbc.org/content/49/1/183.full.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2015-02-26.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Biol.+Chem.&rft.atitle=A+buffer+solution+for+colorimetric+comparaison&rft.volume=49&rft.issue=1&rft.pages=183-186&rft.date=1921&rft_id=info%3Adoi%2F10.1016%2FS0021-9258%2818%2986000-8&rft.aulast=McIlvaine&rft.aufirst=T.+C.&rft_id=http%3A%2F%2Fwww.jbc.org%2Fcontent%2F49%2F1%2F183.full.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuffer+solution" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMendhamDennyBarnesThomas2000" class="citation book cs1">Mendham, J.; Denny, R. C.; Barnes, J. D.; Thomas, M. (2000). "Appendix 5". <i>Vogel's textbook of quantitative chemical analysis</i> (5th ed.). Harlow: Pearson Education. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-582-22628-9" title="Special:BookSources/978-0-582-22628-9"><bdi>978-0-582-22628-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Appendix+5&rft.btitle=Vogel%27s+textbook+of+quantitative+chemical+analysis&rft.place=Harlow&rft.edition=5th&rft.pub=Pearson+Education&rft.date=2000&rft.isbn=978-0-582-22628-9&rft.aulast=Mendham&rft.aufirst=J.&rft.au=Denny%2C+R.+C.&rft.au=Barnes%2C+J.+D.&rft.au=Thomas%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuffer+solution" class="Z3988"></span></span> </li> <li id="cite_note-carmody-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-carmody_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarmody1961" class="citation journal cs1">Carmody, Walter R. (1961). "Easily prepared wide range buffer series". <i>J. Chem. Educ</i>. <b>38</b> (11): 559–560. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1961JChEd..38..559C">1961JChEd..38..559C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fed038p559">10.1021/ed038p559</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Chem.+Educ.&rft.atitle=Easily+prepared+wide+range+buffer+series&rft.volume=38&rft.issue=11&rft.pages=559-560&rft.date=1961&rft_id=info%3Adoi%2F10.1021%2Fed038p559&rft_id=info%3Abibcode%2F1961JChEd..38..559C&rft.aulast=Carmody&rft.aufirst=Walter+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuffer+solution" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.sigmaaldrich.com/life-science/core-bioreagents/biological-buffers/learning-center/buffer-reference-center.html">"Buffer Reference Center"</a>. Sigma-Aldrich. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090417003507/http://www.sigmaaldrich.com/life-science/core-bioreagents/biological-buffers/learning-center/buffer-reference-center.html">Archived</a> from the original on 2009-04-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-04-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Buffer+Reference+Center&rft.pub=Sigma-Aldrich&rft_id=http%3A%2F%2Fwww.sigmaaldrich.com%2Flife-science%2Fcore-bioreagents%2Fbiological-buffers%2Flearning-center%2Fbuffer-reference-center.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuffer+solution" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlderighiGansIencoPeters1999" class="citation journal cs1">Alderighi, L.; Gans, P.; Ienco, A.; Peters, D.; Sabatini, A.; Vacca, A. (1999). <a rel="nofollow" class="external text" href="http://www.hyperquad.co.uk/hyss.htm">"Hyperquad simulation and speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species"</a>. <i>Coordination Chemistry Reviews</i>. <b>184</b> (1): 311–318. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0010-8545%2898%2900260-4">10.1016/S0010-8545(98)00260-4</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070704083413/http://www.hyperquad.co.uk/hyss.htm">Archived</a> from the original on 2007-07-04.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Coordination+Chemistry+Reviews&rft.atitle=Hyperquad+simulation+and+speciation+%28HySS%29%3A+a+utility+program+for+the+investigation+of+equilibria+involving+soluble+and+partially+soluble+species&rft.volume=184&rft.issue=1&rft.pages=311-318&rft.date=1999&rft_id=info%3Adoi%2F10.1016%2FS0010-8545%2898%2900260-4&rft.aulast=Alderighi&rft.aufirst=L.&rft.au=Gans%2C+P.&rft.au=Ienco%2C+A.&rft.au=Peters%2C+D.&rft.au=Sabatini%2C+A.&rft.au=Vacca%2C+A.&rft_id=http%3A%2F%2Fwww.hyperquad.co.uk%2Fhyss.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuffer+solution" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buffer_solution&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.reachdevices.com/Protein/BiologicalBuffers.html">"Biological buffers"</a>. REACH Devices.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Biological+buffers&rft.pub=REACH+Devices&rft_id=http%3A%2F%2Fwww.reachdevices.com%2FProtein%2FBiologicalBuffers.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuffer+solution" class="Z3988"></span> </p> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 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.navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Chemical_equilibria" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chemical_equilibria" title="Template:Chemical equilibria"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chemical_equilibria" title="Template talk:Chemical equilibria"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chemical_equilibria" title="Special:EditPage/Template:Chemical equilibria"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chemical_equilibria" style="font-size:114%;margin:0 4em"><a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">Chemical equilibria</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chemical_stability" title="Chemical stability">Chemical stability</a></li> <li><a href="/wiki/Chelation" title="Chelation">Chelation</a></li> <li><a href="/wiki/Dynamic_equilibrium" title="Dynamic equilibrium">Dynamic equilibrium</a></li> <li><a href="/wiki/Equilibrium_chemistry" title="Equilibrium chemistry">Equilibrium chemistry</a></li> <li><a href="/wiki/Equilibrium_stage" class="mw-redirect" title="Equilibrium stage">Equilibrium stage</a></li> <li><a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">Free energy</a> <ul><li><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs</a></li> <li><a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz</a></li></ul></li> <li><a href="/wiki/Le_Chatelier%27s_principle" title="Le Chatelier's principle">Le Chatelier's principle</a></li> <li><a href="/wiki/Phase_separation" title="Phase separation">Phase separation</a></li> <li><a href="/wiki/Reversible_reaction" title="Reversible reaction">Reversible reaction</a></li> <li><a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Thermodynamic equilibrium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematical_model" title="Mathematical model">Models</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Equilibrium_constant" title="Equilibrium constant">Equilibrium constant</a> <ul><li><a href="/wiki/Determination_of_equilibrium_constants" title="Determination of equilibrium constants">determination</a></li></ul></li> <li><a href="/wiki/Phase_diagram" title="Phase diagram">Phase diagram</a></li> <li><a href="/wiki/Predominance_diagram" title="Predominance diagram">Predominance diagram</a></li> <li><a href="/wiki/Phase_rule" title="Phase rule">Phase rule</a></li> <li><a href="/wiki/Reaction_quotient" title="Reaction quotient">Reaction quotient</a></li> <li><a href="/wiki/Thermodynamic_activity" title="Thermodynamic activity">Thermodynamic activity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Buffer solution</a></li> <li><a href="/wiki/Equilibrium_unfolding" title="Equilibrium unfolding">Equilibrium unfolding</a></li> <li><a href="/wiki/Liquid%E2%80%93liquid_extraction" title="Liquid–liquid extraction">Liquid–liquid extraction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Specific equilibria</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acid_dissociation_constant" title="Acid dissociation constant">Acid dissociation</a> <ul><li><a href="/wiki/Hammett_acidity_function" title="Hammett acidity function">Hammett acidity function</a></li></ul></li> <li><a href="/wiki/Binding_constant" title="Binding constant">Binding constant</a></li> <li><a href="/wiki/Binding_selectivity" title="Binding selectivity">Binding selectivity</a></li> <li><a href="/wiki/Stability_constants_of_complexes" title="Stability constants of complexes">Coordination complexes</a> <ul><li><a href="/wiki/Macrocyclic_effect" class="mw-redirect" title="Macrocyclic effect">Macrocyclic effect</a></li></ul></li> <li><a href="/wiki/Dissociation_constant" title="Dissociation constant">Dissociation constant</a></li> <li><a href="/wiki/Hydrolysis_constant" title="Hydrolysis constant">Hydrolysis</a></li> <li><a href="/wiki/Molecular_autoionization" title="Molecular autoionization">Self-ionization</a> <ul><li><a href="/wiki/Self-ionization_of_water" title="Self-ionization of water">of water</a></li></ul></li> <li><a href="/wiki/Partition_equilibrium" title="Partition equilibrium">Partition</a> <ul><li><a href="/wiki/Partition_coefficient" title="Partition coefficient">Distribution coefficient</a></li></ul></li> <li><a href="/wiki/Solubility_equilibrium" title="Solubility equilibrium">Solubility</a> <ul><li><a href="/wiki/Common-ion_effect" title="Common-ion effect">Common-ion effect</a></li></ul></li> <li><a href="/wiki/Vapor%E2%80%93liquid_equilibrium" title="Vapor–liquid equilibrium">Vapor–liquid</a> <ul><li><a href="/wiki/Henry%27s_law" title="Henry's law">Henry's law</a></li></ul></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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