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data-v-c5936a1e><div class="content-container" data-v-c5936a1e><!--[--><!--]--><main class="main" data-v-c5936a1e><div style="position:relative;" class="vp-doc _academic_chemistry_problems_03-02-2" data-v-c5936a1e><div><h1 id="problem-03-02-2" tabindex="-1">Problem: 03-02-2 <a class="header-anchor" href="#problem-03-02-2" aria-hidden="true">#</a></h1><h2 id="question" tabindex="-1">Question <a class="header-anchor" href="#question" aria-hidden="true">#</a></h2><p>The rate law for a particular reaction is rate <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mi>k</mi><mo stretchy="false">[</mo><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">Y</mi></mrow><msup><mo stretchy="false">]</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">=k[\mathrm{XY}]^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mopen">[</span><span class="mord"><span class="mord mathrm" style="margin-right:0.025em;">XY</span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. In an experiment, the initial rate of the reaction is determined to be <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.16</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mi mathvariant="normal">L</mi><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0.16</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">mol</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord mathrm">L</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span> when the initial concentration of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">Y</mi></mrow><annotation encoding="application/x-tex">\mathrm{XY}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord"><span class="mord mathrm" style="margin-right:0.025em;">XY</span></span></span></span></span> is <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.40</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mi mathvariant="normal">/</mi><mi mathvariant="normal">L</mi></mrow><annotation encoding="application/x-tex">0.40 \mathrm{~mol} / \mathrm{L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0.40</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">mol</span></span><span class="mord">/</span><span class="mord mathrm">L</span></span></span></span>.</p><ul><li>What is the value of the rate constant, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span>, for the reaction? <ul><li>[ ] <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.10</mn><mrow><mtext> </mtext><mi mathvariant="normal">L</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">0.10 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0.10</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">L</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathrm">mol</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span></li><li>[ ] <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.40</mn><mrow><mtext> </mtext><mi mathvariant="normal">L</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">0.40 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0.40</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">L</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathrm">mol</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span></li><li>[x] <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.0</mn><mrow><mtext> </mtext><mi mathvariant="normal">L</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1.0</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">L</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathrm">mol</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span></li><li>[ ] <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.5</mn><mrow><mtext> </mtext><mi mathvariant="normal">L</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">2.5 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2.5</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">L</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathrm">mol</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span></li></ul></li></ul><h2 id="solution" tabindex="-1">Solution <a class="header-anchor" href="#solution" aria-hidden="true">#</a></h2><p>lo tind the value of the rate constant for the reaction, let's first solve the rate law for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span> :</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>k</mi><mo>=</mo><mfrac><mtext> rate </mtext><mrow><mo stretchy="false">[</mo><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">Y</mi></mrow><msup><mo stretchy="false">]</mo><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">k=\frac{\text { rate }}{[\mathrm{XY}]^2} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2281em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2921em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">[</span><span class="mord"><span class="mord mathrm" style="margin-right:0.025em;">XY</span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord"> rate </span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p>Next, let's plug in the initial rate and concentration given in the text:</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>k</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mfrac><mrow><mn>0.16</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mi mathvariant="normal">L</mi><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mn>0.40</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mi mathvariant="normal">/</mi><mi mathvariant="normal">L</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mfrac><mrow><mn>0.16</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mi mathvariant="normal">L</mi><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><mrow><mn>0.16</mn><msup><mrow><mtext> </mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mn>2</mn></msup><mi mathvariant="normal">/</mi><msup><mi mathvariant="normal">L</mi><mn>2</mn></msup></mrow></mfrac></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>1.0</mn><mrow><mtext> </mtext><mi mathvariant="normal">L</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned} k & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{(0.40 \mathrm{~mol} / \mathrm{L})^2} \\ & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{0.16 \mathrm{~mol}^2 / \mathrm{L}^2} \\ & =1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s}) \end{aligned} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.9284em;vertical-align:-3.2142em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.7142em;"><span style="top:-5.7142em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span><span style="top:-3.0512em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"></span></span><span style="top:-0.8728em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:3.2142em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.7142em;"><span style="top:-5.7142em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">0.40</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">mol</span></span><span class="mord">/</span><span class="mord mathrm">L</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.16</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">mol</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord mathrm">L</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.0512em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.2116em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.16</span><span class="mord"><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">mol</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8984em;"><span style="top:-3.1473em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord">/</span><span class="mord"><span class="mord mathrm">L</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.16</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">mol</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord mathrm">L</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.0384em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-0.8728em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1.0</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">L</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathrm">mol</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:3.2142em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p>So, the value of the rate constant for the reaction is <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.0</mn><mrow><mtext> </mtext><mi mathvariant="normal">L</mi></mrow><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mo>⋅</mo><mi mathvariant="normal">s</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1.0</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">L</span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathrm">mol</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathrm">s</span><span class="mclose">)</span></span></span></span></p></div></div></main><!--[--><!--[--><!--[--><!----><!--]--><!--]--><!--]--><footer class="VPDocFooter" data-v-c5936a1e data-v-e033cd21><div class="edit-info" data-v-e033cd21><div 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