General Chemistry/Stoichiometry - Wikibooks, open books for an open world

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There are <a class="external text" href="https://en.wikibooks.org/w/index.php?title=General_Chemistry/Stoichiometry&oldid=3778984&diff=cur&diffonly=0">template/file changes</a> awaiting review.</div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="noprint"> <hr /> <p><span id="top-navigation">← <a href="/wiki/General_Chemistry/Formulas_and_Numbers" title="General Chemistry/Formulas and Numbers">Formulas and Numbers</a> ·<a href="/wiki/General_Chemistry/Chemical_equations" title="General Chemistry/Chemical equations">Chemical equations</a> → </span> </p> <table style="background-color: transparent; color: inherit;" align="center" cellspacing="0px" cellpadding="0px" class="noprint" width="100%"> <tbody><tr> <td align="left" width="33%"><small><a href="/wiki/General_Chemistry/Formulas_and_Numbers" title="General Chemistry/Formulas and Numbers">← Formulas and Numbers</a> ·</small> </td> <td align="center" width="34%"><b><a href="/wiki/General_Chemistry" title="General Chemistry">General Chemistry</a></b> </td> <td align="right" width="33%"><small>· <a href="/wiki/General_Chemistry/Chemical_equations" title="General Chemistry/Chemical equations">Chemical equations →</a></small> </td></tr> <tr style="font-size: .8em;"> <td colspan="3" align="center"> <p><a href="/wiki/General_Chemistry/Book_Cover" title="General Chemistry/Book Cover">Book Cover</a> · <a href="/wiki/General_Chemistry/Introduction" title="General Chemistry/Introduction">Introduction</a> ·  <span class="noprint plainlinks navbar" style="background:none; padding:0; font-weight:normal;; font-size:xx-small;"><a href="/wiki/Template:General_Chemistry/Navigation" title="Template:General Chemistry/Navigation"><span title="View this template" style="">v</span></a> <span style="font-size:80%;">•</span> <a href="/wiki/Template_talk:General_Chemistry/Navigation" title="Template talk:General Chemistry/Navigation"><span title="Discuss this template" style="">d</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://en.wikibooks.org/w/index.php?title=Template:General_Chemistry/Navigation&action=edit"><span title="Edit this template" style=";">e</span></a></span>  </p> </td></tr> <tr style="font-size: .8em;" align="center" class="noprint"> <td colspan="3"> <p><b>Units</b>: <a href="/wiki/General_Chemistry/Properties_of_Matter" title="General Chemistry/Properties of Matter">Matter</a> · <a href="/wiki/General_Chemistry/Atomic_Structure" title="General Chemistry/Atomic Structure">Atomic Structure</a> · <a href="/wiki/General_Chemistry/Compounds_and_Bonding" title="General Chemistry/Compounds and Bonding">Bonding</a> · <a href="/wiki/General_Chemistry/Chemical_Reactions" title="General Chemistry/Chemical Reactions">Reactions</a> · <a href="/wiki/General_Chemistry/Aqueous_Solutions" title="General Chemistry/Aqueous Solutions">Solutions</a> · <a href="/wiki/General_Chemistry/Phases_of_Matter" title="General Chemistry/Phases of Matter">Phases of Matter</a> · <a href="/wiki/General_Chemistry/Chemical_Equilibria" title="General Chemistry/Chemical Equilibria">Equilibria</a> · <a href="/wiki/General_Chemistry/Chemical_Kinetics" title="General Chemistry/Chemical Kinetics">Kinetics</a> · <a href="/wiki/General_Chemistry/Thermodynamics" title="General Chemistry/Thermodynamics">Thermodynamics</a> · <a href="/wiki/General_Chemistry/Chemistries_of_Various_Elements" title="General Chemistry/Chemistries of Various Elements">The Elements</a> </p> </td></tr> <tr style="font-size: .8em;" align="center" class="noprint"> <td colspan="3"> <p><b>Appendices</b>: <a href="/wiki/General_Chemistry/Periodic_Table" title="General Chemistry/Periodic Table">Periodic Table</a> · <a href="/wiki/General_Chemistry/Units" title="General Chemistry/Units">Units</a> · <a href="/wiki/General_Chemistry/Constants" title="General Chemistry/Constants">Constants</a> · <a href="/wiki/General_Chemistry/Useful_Equations" title="General Chemistry/Useful Equations">Equations</a> · <a href="/wiki/General_Chemistry/Standard_Reduction_Potentials" title="General Chemistry/Standard Reduction Potentials">Reduction Potentials</a> · <a href="/wiki/General_Chemistry/Table_of_the_Chemical_Elements_and_their_Properties" title="General Chemistry/Table of the Chemical Elements and their Properties">Elements and their Properties</a> </p> </td></tr></tbody></table> <hr /> </div> <p>The word <i>stoichiometry</i> derives from two Greek words: <i>stoicheion</i> (meaning "element") and <i>metron</i> (meaning "measure"). Stoichiometry deals with calculations about the masses (sometimes volumes) of reactants and products involved in a chemical reaction. It is a very mathematical part of chemistry, so be prepared for lots of calculator use. </p> <table class="plainlinks noprint messagebox notice" style="width:250px; float:right; clear:right; margin:0px; margin-left:10px;"> <tbody><tr style="vertical-align:middle;"><td style="padding:0.1em; text-align:center; vertical-align:middle; width:45px; border:none;"> <span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/40px-Wikipedia-logo-v2.svg.png" decoding="async" width="40" height="37" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/60px-Wikipedia-logo-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/80px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94" /></span></span></td> <td style="color:black; text-align:left; vertical-align:middle; padding:0.5em; padding-left:0em; border:none;"> <p><a href="https://en.wikipedia.org/wiki/" class="extiw" title="w:">Wikipedia</a> has related information at <a class="external text" href="https://en.wikipedia.org/wiki/Stoichiometry"><i><b>Stoichiometry</b></i></a> </p> </td></tr></tbody></table> <p>Jeremias Benjaim Richter (1762-1807) was the first to lay down the principles of stoichiometry. In 1792 he wrote: "<i>Die stöchyometrie (Stöchyometria) ist die Wissenschaft die quantitativen oder Massenverhältnisse zu messen, in welchen die chymischen Elemente gegen einander stehen.</i>" [Stoichiometry is the science of measuring the quantitative proportions or mass ratios in which chemical elements stand to one another.] </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Molar_Calculations">Molar Calculations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=1" title="Edit section: Molar Calculations" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=1" title="Edit section's source code: Molar Calculations"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Your_Tool:_Dimensional_Analysis">Your Tool: Dimensional Analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=2" title="Edit section: Your Tool: Dimensional Analysis" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=2" title="Edit section's source code: Your Tool: Dimensional Analysis"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Luckily, almost all of stoichiometry can be solved relatively easily using dimensional analysis. Dimensional analysis is just using units, instead of numbers or variables, to do math, usually to see how they cancel out. For instance, it is easy to see that: </p> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 grams\times {\dfrac {moles}{grams}}\times {\dfrac {atoms}{moles}}=atoms}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mi>r</mi> <mi>a</mi> <mi>m</mi> <mi>s</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mi>e</mi> <mi>s</mi> </mrow> <mrow> <mi>g</mi> <mi>r</mi> <mi>a</mi> <mi>m</mi> <mi>s</mi> </mrow> </mfrac> </mstyle> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi>a</mi> <mi>t</mi> <mi>o</mi> <mi>m</mi> <mi>s</mi> </mrow> <mrow> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mi>e</mi> <mi>s</mi> </mrow> </mfrac> </mstyle> </mrow> <mo>=</mo> <mi>a</mi> <mi>t</mi> <mi>o</mi> <mi>m</mi> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle grams\times {\dfrac {moles}{grams}}\times {\dfrac {atoms}{moles}}=atoms}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bec0c8f40b4e58d4e16c5f6afd9bb18572392e26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.158ex; height:5.843ex;" alt="{\displaystyle grams\times {\dfrac {moles}{grams}}\times {\dfrac {atoms}{moles}}=atoms}"></span></div> <p>It is this principle that will guide you through solving most of the stoichiometry problems (chemical reaction problems) you will see in General Chemistry. Before you attempt to solve a problem, ask yourself: what do I have now? where am I going? As long as you know how many (units) per (other units), this will make stoichiometry significantly easier. </p> <div class="mw-heading mw-heading3"><h3 id="Moles_to_Mass">Moles to Mass</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=3" title="Edit section: Moles to Mass" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=3" title="Edit section's source code: Moles to Mass"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="PrettyTextBox" style="float:right; clear:right; margin:1em; min-width:200px; width:250px; text-align:center;">Where can you find the molar mass of these elements? <a href="/wiki/General_Chemistry/Periodic_Table" title="General Chemistry/Periodic Table">The periodic table.</a> You should always have one on hand—don't expect to get very far without one!</div> <p><i>How heavy is 1.5 mol of lead? How many moles in 22.34g of water?</i> Calculating the mass of a sample from the number of moles it contains is quite simple. We use the <b>molar mass</b> (mass of one mole) of the substance to convert between mass and moles. When writing calculations, we denote the molar mass of a substance by an upper case "M" (e.g. M(Ne) means "the molar mass of neon"). As always, "n" stands for the number of moles and "m" indicates the mass of a substance. To find the solutions to the two questions we just asked, let's apply some dimensional analysis: </p> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 1.5\;mol\;Pb\;\times {\dfrac {207.2\;g\;Pb}{1\;mol\;Pb}}=310.8\;g\;Pb}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1.5</mn> <mspace width="thickmathspace" /> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mspace width="thickmathspace" /> <mi>P</mi> <mi>b</mi> <mspace width="thickmathspace" /> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>207.2</mn> <mspace width="thickmathspace" /> <mi>g</mi> <mspace width="thickmathspace" /> <mi>P</mi> <mi>b</mi> </mrow> <mrow> <mn>1</mn> <mspace width="thickmathspace" /> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mspace width="thickmathspace" /> <mi>P</mi> <mi>b</mi> </mrow> </mfrac> </mstyle> </mrow> <mo>=</mo> <mn>310.8</mn> <mspace width="thickmathspace" /> <mi>g</mi> <mspace width="thickmathspace" /> <mi>P</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1.5\;mol\;Pb\;\times {\dfrac {207.2\;g\;Pb}{1\;mol\;Pb}}=310.8\;g\;Pb}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc5f83581e24dfa62d50ad317c96dc4d7b728078" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:39.178ex; height:5.509ex;" alt="{\displaystyle 1.5\;mol\;Pb\;\times {\dfrac {207.2\;g\;Pb}{1\;mol\;Pb}}=310.8\;g\;Pb}"></span></div> <p>Can you see how the units cancel to give you the answer you want? All you needed to know was that you had 1.5 mol Pb (lead), and that 1 mol Pb weighs 207.2 grams. Thus, multiplying 1.5 mol Pb by 207.2 g Pb and dividing by 1 mol Pb gives you 310.8 g Pb, your answer. </p> <div class="mw-heading mw-heading3"><h3 id="Mass_to_Moles">Mass to Moles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=4" title="Edit section: Mass to Moles" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=4" title="Edit section's source code: Mass to Moles"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>But we had one more question: "How many moles in 22.34g of water?" This is just as easy: </p> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 22.34\;g\;H_{2}O\;\times {\dfrac {1\;mol\;H_{2}O}{18\;g\;H_{2}O}}=1.24\;mol\;H_{2}O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>22.34</mn> <mspace width="thickmathspace" /> <mi>g</mi> <mspace width="thickmathspace" /> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>O</mi> <mspace width="thickmathspace" /> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>1</mn> <mspace width="thickmathspace" /> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mspace width="thickmathspace" /> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>O</mi> </mrow> <mrow> <mn>18</mn> <mspace width="thickmathspace" /> <mi>g</mi> <mspace width="thickmathspace" /> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>O</mi> </mrow> </mfrac> </mstyle> </mrow> <mo>=</mo> <mn>1.24</mn> <mspace width="thickmathspace" /> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mspace width="thickmathspace" /> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 22.34\;g\;H_{2}O\;\times {\dfrac {1\;mol\;H_{2}O}{18\;g\;H_{2}O}}=1.24\;mol\;H_{2}O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b7814a52ded5800ea25963e95a38cb9de4c61d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.999ex; height:5.843ex;" alt="{\displaystyle 22.34\;g\;H_{2}O\;\times {\dfrac {1\;mol\;H_{2}O}{18\;g\;H_{2}O}}=1.24\;mol\;H_{2}O}"></span></div> <p>Where did the 18 g H<sub>2</sub>O come from? We looked at the periodic table and simply added up the atomic masses of two hydrogens and an oxygen to get the molecular weight of water. This turned out to be 18, and since all the masses on the periodic table are given with respect to 1 mole, we knew that 1 mol of water weighed 18 grams. This gave us the relationship above, which is really just (again) watching units cancel out! </p> <div class="mw-heading mw-heading3"><h3 id="Calculating_Molar_Masses">Calculating Molar Masses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=5" title="Edit section: Calculating Molar Masses" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=5" title="Edit section's source code: Calculating Molar Masses"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Before we can do these types of calculations, we first have to know the molar mass. Fortunately, this is not difficult, as the molar mass is exactly the same as the <b>atomic weight</b> of an element. A table of atomic weights can be used to find the molar mass of elements (this information is often included in the periodic table). For example, the atomic weight of oxygen is <b>16.00</b> amu, so its molar mass is 16.00 g/mol. </p><p>For species with more than one element, we simply add up the atomic weights of each element to obtain the molar mass of the compound. For example, sulfur trioxide gas is made up of sulfur and oxygen, whose atomic weights are 32.06 and 16.00 respectively. </p> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 {\begin{matrix}{\hbox{M(SO}}_{3}{\hbox{)}}&=&32.06+3\times 16.00\\\ &=&80.06{\hbox{g}}/{\hbox{mol}}\\\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>M(SO</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>32.06</mn> <mo>+</mo> <mn>3</mn> <mo>×</mo> <mn>16.00</mn> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>80.06</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>g</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>mol</mtext> </mstyle> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\hbox{M(SO}}_{3}{\hbox{)}}&=&32.06+3\times 16.00\\\ &=&80.06{\hbox{g}}/{\hbox{mol}}\\\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9587629e4ad535217fde1e26b96e2e261bce785" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:32.737ex; height:6.509ex;" alt="{\displaystyle {\begin{matrix}{\hbox{M(SO}}_{3}{\hbox{)}}&=&32.06+3\times 16.00\\\ &=&80.06{\hbox{g}}/{\hbox{mol}}\\\end{matrix}}}"></span></div> <p>The procedure for more complex compounds is essentially the same. Aluminium carbonate, for example, contains aluminium, carbon, and oxygen. To find the molar mass, we have to be careful to find the <i>total</i> number of atoms of each element. Three carbonate ions each containing three oxygen atoms gives a total of nine oxygens. The atomic weights of aluminium and carbon are 26.98 and 12.01 respectively. </p> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 {\begin{matrix}{\hbox{M}}({\hbox{Al}}_{2}({\hbox{CO}}_{3})_{3})&=&2\times 26.98+3\times 12.01+9\times 16.00\\\ &=&233.99{\hbox{g}}/{\hbox{mol}}\\\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>M</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Al</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>CO</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>2</mn> <mo>×</mo> <mn>26.98</mn> <mo>+</mo> <mn>3</mn> <mo>×</mo> <mn>12.01</mn> <mo>+</mo> <mn>9</mn> <mo>×</mo> <mn>16.00</mn> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>233.99</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>g</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>mol</mtext> </mstyle> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\hbox{M}}({\hbox{Al}}_{2}({\hbox{CO}}_{3})_{3})&=&2\times 26.98+3\times 12.01+9\times 16.00\\\ &=&233.99{\hbox{g}}/{\hbox{mol}}\\\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efd5f6683bf9bf118c8e57cdc6251e9eb8ab0270" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:55.573ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}{\hbox{M}}({\hbox{Al}}_{2}({\hbox{CO}}_{3})_{3})&=&2\times 26.98+3\times 12.01+9\times 16.00\\\ &=&233.99{\hbox{g}}/{\hbox{mol}}\\\end{matrix}}}"></span></div> <div class="mw-heading mw-heading2"><h2 id="Empirical_Formulae">Empirical Formulae</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=6" title="Edit section: Empirical Formulae" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=6" title="Edit section's source code: Empirical Formulae"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The empirical formula of a substance is <i>the simplest ratio of the number of moles of each element in a compound</i>. The empirical formula is ambiguous, e.g. the formula CH could represent CH, C<sub>2</sub>H<sub>2</sub>, C<sub>3</sub>H<sub>3</sub> etc. These latter formulae are called <b>molecular formulae</b>. It follows that the molecular formula is always a <i>whole number multiple</i> of the empirical formula for a compound. </p><p>Calculating the empirical formula is easy if the relative amounts of each element in the compound are known. For example, if a sample contains 1.37 mol oxygen and 2.74 mol hydrogen, we can calculate the empirical formula. A good strategy to use is to divide all amounts given by the smallest <b>non-integer</b> amount, then multiply by whole numbers until the simplest ratio is found. We can make a table showing the successive ratios. </p> <table class="wikitable" style="border:1px;text-align:center;"> <tbody><tr> <th>Hydrogen </th> <th>Oxygen </th></tr> <tr> <td>2.74</td> <td>1.37</td> <td>divide by 1.37 </td></tr> <tr> <td>2</td> <td>1</td> <td>ANSWER </td></tr></tbody></table> <p>The empirical formula of the compound is H<sub>2</sub>O. </p><p>Here's another example. A sample of piperonal contains 1.384 mol carbon, 1.033 mol hydrogen and 0.519 mol oxygen. </p> <table class="wikitable" style="border:1px; text-align:center;"> <tbody><tr> <th>Carbon </th> <th>Hydrogen </th> <th>Oxygen </th></tr> <tr> <td>1.384</td> <td>1.033</td> <td>0.519</td> <td>divide by 0.519 </td></tr> <tr> <td>2.666</td> <td>2</td> <td>1</td> <td>multiply by 3 </td></tr> <tr> <td>8</td> <td>6</td> <td>3</td> <td>ANSWER </td></tr></tbody></table> <p>The empirical formula of piperonal is C<sub>8</sub>H<sub>6</sub>O<sub>3</sub>. </p> <div class="mw-heading mw-heading3"><h3 id="Converting_from_Masses">Converting from Masses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=7" title="Edit section: Converting from Masses" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=7" title="Edit section's source code: Converting from Masses"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Often, we are given the relative composition by mass of a substance and asked to find the empirical formula. These masses must first be converted to moles using the techniques outlined above. For example, a sample of ethanol contains 52.1% carbon, 13.2% hydrogen, and 34.7% oxygen by mass. Hypothetically, 100g of this substance will contain 52.1 g carbon, 13.2 g hydrogen and 34.7 g oxygen. Dividing these by their respective molar masses gives the amount in moles of each element (as we learned above). These are 4.34 mol, 13.1 mol, and 2.17 mol respectively. </p> <table class="wikitable" style="border:1px; text-align:center;"> <tbody><tr> <th>Carbon </th> <th>Hydrogen </th> <th>Oxygen </th></tr> <tr> <td>4.34</td> <td>13.1</td> <td>2.17</td> <td>divide by 2.17 </td></tr> <tr> <td>2</td> <td>6</td> <td>1</td> <td>ANSWER </td></tr></tbody></table> <p>The empirical formula of ethanol is C<sub>2</sub>H<sub>6</sub>O. </p> <div class="mw-heading mw-heading3"><h3 id="Molecular_Formula">Molecular Formula</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=8" title="Edit section: Molecular Formula" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=8" title="Edit section's source code: Molecular Formula"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="PrettyTextBox" style="float:right; clear:right; margin:1em; min-width:200px; width:250px; text-align:center;"><b>Beware:</b> In the case of H<sub>2</sub>O, the whole number multiple is 1, so its empirical formula is the same as its molecular formula. This is not always the case!</div> <p>As mentioned above, the molecular formula for a substance equals the count of atoms of each type in a molecule. This is always a <i>whole number multiple</i> of the empirical formula. To calculate the molecular formula from the empirical formula, we need to know the <b>molar mass</b> of the substance. For example, the empirical formula for <b>benzene</b> is CH, and its molar mass is 78.12 g/mol. Divide the actual molar mass by the mass of the empirical formula, 13.02 g/mol, to determine the multiple of the empirical formula, "n". The molecular formula equals the empirical formula multiplied by "n". </p> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 {\begin{matrix}{\hbox{M(CH)}}&=&13.02{\hbox{ g/mol}}\\{\hbox{M(benzene)}}&=&78.12{\hbox{ g/mol}}\\{\hbox{M(benzene)}}/{\hbox{M(CH)}}&=(78.12\ g/mol)/(13.02\ g/mol)&=6\\\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>M(CH)</mtext> </mstyle> </mrow> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>13.02</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g/mol</mtext> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>M(benzene)</mtext> </mstyle> </mrow> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>78.12</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g/mol</mtext> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>M(benzene)</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>M(CH)</mtext> </mstyle> </mrow> </mtd> <mtd> <mo>=</mo> <mo stretchy="false">(</mo> <mn>78.12</mn> <mtext> </mtext> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>13.02</mn> <mtext> </mtext> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>6</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\hbox{M(CH)}}&=&13.02{\hbox{ g/mol}}\\{\hbox{M(benzene)}}&=&78.12{\hbox{ g/mol}}\\{\hbox{M(benzene)}}/{\hbox{M(CH)}}&=(78.12\ g/mol)/(13.02\ g/mol)&=6\\\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb37ca713adab1129bd2c2f77b07a45e53e8c64b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:69.084ex; height:9.843ex;" alt="{\displaystyle {\begin{matrix}{\hbox{M(CH)}}&=&13.02{\hbox{ g/mol}}\\{\hbox{M(benzene)}}&=&78.12{\hbox{ g/mol}}\\{\hbox{M(benzene)}}/{\hbox{M(CH)}}&=(78.12\ g/mol)/(13.02\ g/mol)&=6\\\end{matrix}}}"></span></div> <p>This shows that the molecular formula for benzene is 6 times the empirical formula of CH. The molecular formula for benzene is C<sub>6</sub>H<sub>6</sub>. </p> <div class="mw-heading mw-heading2"><h2 id="Solving_Mass-Mass_Equations">Solving Mass-Mass Equations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=9" title="Edit section: Solving Mass-Mass Equations" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=9" title="Edit section's source code: Solving Mass-Mass Equations"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A typical mass-mass equation will give you an amount in grams and ask for another answer in grams. </p> <div style="clear: both; width: 90%; margin: 1em auto; padding: .3em 1.2em;; ; border: 1px solid #000;"> <dl><dt>To solve a mass-mass equation, follow these rules</dt> <dd></dd></dl> <ol><li><a href="/wiki/General_Chemistry/Balancing_Equations" title="General Chemistry/Balancing Equations">Balance the equation</a> if it is not already.</li> <li>Convert the given quantity to moles.</li> <li>Multiply by the molar ratio of the demanded substance over the given substance.</li> <li>Convert the demanded substance into grams.</li></ol> </div> <p>For example, given the equation <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 Cu^{2+}+2AgNO_{3}\to Cu(NO_{3})_{2}+2Ag^{+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>A</mi> <mi>g</mi> <mi>N</mi> <msub> <mi>O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">→</mo> <mi>C</mi> <mi>u</mi> <mo stretchy="false">(</mo> <mi>N</mi> <msub> <mi>O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mi>A</mi> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Cu^{2+}+2AgNO_{3}\to Cu(NO_{3})_{2}+2Ag^{+}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59c8b69b4cae605df58ac33d75b43b6695fc3b7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.022ex; height:3.176ex;" alt="{\displaystyle Cu^{2+}+2AgNO_{3}\to Cu(NO_{3})_{2}+2Ag^{+}}"></span>, find out how many grams of silver (Ag) will result from 43.0 grams of copper (Cu) reacting. </p> <ul><li>Convert the given quantity to moles.</li></ul> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>43.0</mn> <mi>g</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> <mrow> <mn>63.55</mn> <mi>g</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bca23af23bbff262f54c9517c073e4cf2b0d0e38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.693ex; height:5.843ex;" alt="{\displaystyle 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}}"></span></div> <ul><li>Multiply by the molar ratio of the demanded substance and the given substance.</li></ul> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}\times {\frac {2~mol~Ag}{1~mol~Cu}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>43.0</mn> <mi>g</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> <mrow> <mn>63.55</mn> <mi>g</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> </mfrac> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>A</mi> <mi>g</mi> </mrow> <mrow> <mn>1</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}\times {\frac {2~mol~Ag}{1~mol~Cu}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/190fea71f04688e7e172251b7d5283bb8b4f0262" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:35.65ex; height:6.009ex;" alt="{\displaystyle 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}\times {\frac {2~mol~Ag}{1~mol~Cu}}}"></span></div> <ul><li>Convert the demanded substance to grams.</li></ul> <div class="center" style="display:table; margin-left: auto; margin-right: auto; width: auto ;"><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 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}\times {\frac {2~mol~Ag}{1~mol~Cu}}\times {\frac {107.86g~Ag}{1~mol~Ag}}=1.46\times 10^{2}~g~Ag}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>43.0</mn> <mi>g</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> <mrow> <mn>63.55</mn> <mi>g</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> </mfrac> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>A</mi> <mi>g</mi> </mrow> <mrow> <mn>1</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>C</mi> <mi>u</mi> </mrow> </mfrac> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>107.86</mn> <mi>g</mi> <mtext> </mtext> <mi>A</mi> <mi>g</mi> </mrow> <mrow> <mn>1</mn> <mtext> </mtext> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mtext> </mtext> <mi>A</mi> <mi>g</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1.46</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> <mi>g</mi> <mtext> </mtext> <mi>A</mi> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}\times {\frac {2~mol~Ag}{1~mol~Cu}}\times {\frac {107.86g~Ag}{1~mol~Ag}}=1.46\times 10^{2}~g~Ag}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc5eb8efd0c899155054a7ea715e70c5e9d6e414" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:68.93ex; height:6.176ex;" alt="{\displaystyle 43.0g~Cu\times {\frac {1~mol~Cu}{63.55g~Cu}}\times {\frac {2~mol~Ag}{1~mol~Cu}}\times {\frac {107.86g~Ag}{1~mol~Ag}}=1.46\times 10^{2}~g~Ag}"></span></div> <style data-mw-deduplicate="TemplateStyles:r4440582">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="plainlinks metadata ambox ambox-notice" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span title="Information"><img alt="Information" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Information_icon.svg/32px-Information_icon.svg.png" decoding="async" width="32" height="32" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Information_icon.svg/48px-Information_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Information_icon.svg/64px-Information_icon.svg.png 2x" data-file-width="620" data-file-height="620" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">Notice how dimensional analysis applies to this technique. All units will cancel except for the desired one (grams of silver, in this case).</div></td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Summary">Summary</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&veaction=edit&section=10" title="Edit section: Summary" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=General_Chemistry/Stoichiometry&action=edit&section=10" title="Edit section's source code: Summary"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To solve a stoichiometric problem, you need to know what you already have and what you want to find. Everything in between is basic algebra. </p> <div style="clear: both; width: 90%; margin: 1em auto; padding: .3em 1.2em;; ; border: 1px solid #000;"> <dl><dt>Key Terms</dt></dl> <ul><li><i>Molar mass:</i> mass (in grams) of one mole of a substance.</li> <li><i>Empirical formula:</i> the simplest ratio of the number of moles of each element in a compound</li> <li><i>Molecular formula:</i> the actual ratio of the number of moles of each element in a compound</li></ul> </div> <p>In general, all you have to do is keep track of the units and how they cancel, and you will be on your way! </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikibooks.org/w/index.php?title=General_Chemistry/Stoichiometry&oldid=3778984">https://en.wikibooks.org/w/index.php?title=General_Chemistry/Stoichiometry&oldid=3778984</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Category</a>: <ul><li><a href="/wiki/Category:Book:General_Chemistry" title="Category:Book:General Chemistry">Book:General Chemistry</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 5 December 2020, at 08:42.</li> <li id="footer-info-copyright">Text is available under the <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a>; additional terms may apply. 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