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<title>Problem: 03-02-1 | Toshiki's Note</title>
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data-v-1b9f5c6f><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="caret-icon" data-v-1b9f5c6f><path d="M9,19c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l5.3-5.3L8.3,6.7c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l6,6c0.4,0.4,0.4,1,0,1.4l-6,6C9.5,18.9,9.3,19,9,19z"></path></svg></div></div><div class="items" data-v-1b9f5c6f><!--[--><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/chemistry/problems/02-20" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>Problem: 02-20</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/chemistry/problems/03-02-1" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>Problem: 03-02-1</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/chemistry/problems/03-02-2" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>Problem: 03-02-2</p><!--]--></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-1b9f5c6f data-v-1b9f5c6f><div class="item" data-v-1b9f5c6f><div class="indicator" data-v-1b9f5c6f></div><a class="VPLink link link" href="/academic/chemistry/problems/03-02-3" data-v-1b9f5c6f><!--[--><p class="text" data-v-1b9f5c6f>Problem: 03-02-3</p><!--]--></a><!----></div><!----></div><!--]--></div></section></div><!--]--><!--[--><!--]--></nav></aside><div class="VPContent has-sidebar" id="VPContent" data-v-f6284a77 data-v-f3ed2c70><div class="VPDoc has-sidebar has-aside" data-v-f3ed2c70 data-v-39e6c32d><!--[--><!--]--><div 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vp-sponsor aside"><!--[--><section class="vp-sponsor-section"><!----><div class="VPSponsorsGrid vp-sponsor-grid medium"><!--[--><div class="vp-sponsor-grid-item"><a class="vp-sponsor-grid-link" target="_blank" rel="sponsored noopener"><article class="vp-sponsor-grid-box"><h4 class="visually-hidden"></h4><img class="vp-sponsor-grid-image" src="https://jsd.toshiki.dev/gh/andatoshiki/toshiki-notebook@master/assets/logo/sponsor/telegram.png"></article></a></div><!--]--></div></section><!--]--></div></div><!--]--><!--]--><!--]--><!--]--></div></div></div></div><div class="content" data-v-39e6c32d><div class="content-container" data-v-39e6c32d><!--[--><!--]--><!----><main class="main" data-v-39e6c32d><div style="position:relative;" class="vp-doc _academic_chemistry_problems_03-02-1" data-v-39e6c32d><div><h1 id="problem-03-02-1" tabindex="-1">Problem: 03-02-1 <a class="header-anchor" href="#problem-03-02-1" aria-label="Permalink to &quot;Problem: 03-02-1&quot;">​</a></h1><div><section class="border-b-1 border-[var(--vp-c-divider)] w-full border-b-solid mt-[24px] pb-[12px] flex gap-[12px] mb-[12px] flex-wrap max-w-[85%]"><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 16 16" width="1.2em" height="1.2em"><path fill="currentColor" d="M8 16A8 8 0 1 1 8 0a8 8 0 0 1 0 16Zm.847-8.145a2.502 2.502 0 1 0-1.694 0C5.471 8.261 4 9.775 4 11c0 .395.145.995 1 .995h6c.855 0 1-.6 1-.995c0-1.224-1.47-2.74-3.153-3.145Z"></path></svg> Author:<span>Anda Toshiki</span></div><!----><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 15 15" width="1.2em" height="1.2em"><path fill="currentColor" fill-rule="evenodd" d="M1.903 7.297c0 3.044 2.207 5.118 4.686 5.547a.521.521 0 1 1-.178 1.027C3.5 13.367.861 10.913.861 7.297c0-1.537.699-2.745 1.515-3.663c.585-.658 1.254-1.193 1.792-1.602H2.532a.5.5 0 0 1 0-1h3a.5.5 0 0 1 .5.5v3a.5.5 0 0 1-1 0V2.686l-.001.002c-.572.43-1.27.957-1.875 1.638c-.715.804-1.253 1.776-1.253 2.97Zm11.108.406c0-3.012-2.16-5.073-4.607-5.533a.521.521 0 1 1 .192-1.024c2.874.54 5.457 2.98 5.457 6.557c0 1.537-.699 2.744-1.515 3.663c-.585.658-1.254 1.193-1.792 1.602h1.636a.5.5 0 1 1 0 1h-3a.5.5 0 0 1-.5-.5v-3a.5.5 0 1 1 1 0v1.845h.002c.571-.432 1.27-.958 1.874-1.64c.715-.803 1.253-1.775 1.253-2.97Z" clip-rule="evenodd"></path></svg> Updated:<span>5 minutes ago</span></div><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 16 16" width="1.2em" height="1.2em"><path fill="currentColor" d="M9.293 0H4a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h8a2 2 0 0 0 2-2V4.707A1 1 0 0 0 13.707 4L10 .293A1 1 0 0 0 9.293 0zM9.5 3.5v-2l3 3h-2a1 1 0 0 1-1-1zM5.485 6.879l1.036 4.144l.997-3.655a.5.5 0 0 1 .964 0l.997 3.655l1.036-4.144a.5.5 0 0 1 .97.242l-1.5 6a.5.5 0 0 1-.967.01L8 9.402l-1.018 3.73a.5.5 0 0 1-.967-.01l-1.5-6a.5.5 0 1 1 .97-.242z"></path></svg> Words:<span>404</span></div><div class="flex gap-[4px] items-center"><svg style="display:inline-block;" viewBox="0 0 20 20" width="1.2em" height="1.2em"><path fill="currentColor" d="M10 0a10 10 0 1 0 10 10A10 10 0 0 0 10 0zm2.5 14.5L9 11V4h2v6l3 3z"></path></svg> Reading:<span>2 min</span></div></section></div><h2 id="question" tabindex="-1">Question <a class="header-anchor" href="#question" aria-label="Permalink to &quot;Question&quot;">​</a></h2><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><mn>2</mn><msub><mrow><mtext> </mtext><mi mathvariant="normal">N</mi></mrow><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo>→</mo><mn>4</mn><msub><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">O</mi></mrow><mn>2</mn></msub><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">2 \mathrm{~N}_2 \mathrm{O}_5(g) \rightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g) </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</span><span class="mord"><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">N</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mclose">)</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:1em;vertical-align:-0.25em;"></span><span class="mord">4</span><span class="mord"><span class="mord"><span class="mord mathrm">NO</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mclose">)</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"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mclose">)</span></span></span></span></span></p><p>The decomposition of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5(g)</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"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mclose">)</span></span></span></span> is represented by the equation above. A sample of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5(g)</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"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mclose">)</span></span></span></span> is monitored as it decomposes, and the concentration of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> as a function of time is recorded. The results are shown in the table below.</p><table><thead><tr><th>Time (s)</th><th><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\mathrm{[N_2O_5]}</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"><span class="mopen">[</span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span></span></th></tr></thead><tbody><tr><td>0</td><td>1.000</td></tr><tr><td>25.0</td><td>0.801</td></tr><tr><td>50.0</td><td>0.642</td></tr><tr><td>75.0</td><td>0.515</td></tr></tbody></table><p>Calculate the average rate of the reaction between <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50.0</mn></mrow><annotation encoding="application/x-tex">50.0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">50.0</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>75.0</mn></mrow><annotation encoding="application/x-tex">75.0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">75.0</span></span></span></span> seconds.</p><h2 id="solution" tabindex="-1">Solution <a class="header-anchor" href="#solution" aria-label="Permalink to &quot;Solution&quot;">​</a></h2><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>a</mi><mrow><mtext> </mtext><mi mathvariant="normal">A</mi></mrow><mo>+</mo><mi>b</mi><mrow><mtext> </mtext><mi mathvariant="normal">B</mi></mrow><mo>→</mo><mi>c</mi><mi mathvariant="normal">C</mi><mo>+</mo><mi>d</mi><mi mathvariant="normal">D</mi></mrow><annotation encoding="application/x-tex">a \mathrm{~A}+b \mathrm{~B} \rightarrow c \mathrm{C}+d \mathrm{D} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">a</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">A</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:0.6944em;"></span><span class="mord mathnormal">b</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">B</span></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:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">c</span><span class="mord mathrm">C</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:0.6944em;"></span><span class="mord mathnormal">d</span><span class="mord mathrm">D</span></span></span></span></span></p><p>the rate of reaction is defined as</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><mstyle mathcolor="cyan"><mtext> rate </mtext><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><mfrac><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">[</mo><mi mathvariant="normal">A</mi><mo stretchy="false">]</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mi>b</mi></mfrac><mfrac><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">[</mo><mi mathvariant="normal">B</mi><mo stretchy="false">]</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mo>+</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mfrac><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">[</mo><mi mathvariant="normal">C</mi><mo stretchy="false">]</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mo>+</mo><mfrac><mn>1</mn><mi>d</mi></mfrac><mfrac><mrow><mi mathvariant="normal">Δ</mi><mo stretchy="false">[</mo><mi mathvariant="normal">D</mi><mo stretchy="false">]</mo></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\color{cyan}\text { rate }=-\frac{1}{a} \frac{\Delta[\mathrm{A}]}{\Delta t}=-\frac{1}{b} \frac{\Delta[\mathrm{B}]}{\Delta t}=+\frac{1}{c} \frac{\Delta[\mathrm{C}]}{\Delta t}=+\frac{1}{d} \frac{\Delta[\mathrm{D}]}{\Delta t} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord text" style="color:cyan;"><span class="mord" style="color:cyan;"> rate </span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel" style="color:cyan;">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em;"></span><span class="mord" style="color:cyan;">−</span><span class="mord" style="color:cyan;"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord mathnormal" style="color:cyan;">a</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord" style="color:cyan;"><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" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mord mathnormal" style="color:cyan;">t</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mopen" style="color:cyan;">[</span><span class="mord mathrm" style="color:cyan;">A</span><span class="mclose" style="color:cyan;">]</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel" style="color:cyan;">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em;"></span><span class="mord" style="color:cyan;">−</span><span class="mord" style="color:cyan;"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord mathnormal" style="color:cyan;">b</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord" style="color:cyan;"><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" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mord mathnormal" style="color:cyan;">t</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mopen" style="color:cyan;">[</span><span class="mord mathrm" style="color:cyan;">B</span><span class="mclose" style="color:cyan;">]</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel" style="color:cyan;">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em;"></span><span class="mord" style="color:cyan;">+</span><span class="mord" style="color:cyan;"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord mathnormal" style="color:cyan;">c</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord" style="color:cyan;"><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" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mord mathnormal" style="color:cyan;">t</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mopen" style="color:cyan;">[</span><span class="mord mathrm" style="color:cyan;">C</span><span class="mclose" style="color:cyan;">]</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel" style="color:cyan;">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em;"></span><span class="mord" style="color:cyan;">+</span><span class="mord" style="color:cyan;"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord mathnormal" style="color:cyan;">d</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord" style="color:cyan;"><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" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mord mathnormal" style="color:cyan;">t</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="color:cyan;border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan;"><span class="mord" style="color:cyan;">Δ</span><span class="mopen" style="color:cyan;">[</span><span class="mord mathrm" style="color:cyan;">D</span><span class="mclose" style="color:cyan;">]</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p>Notice that the rate of change in concentration of each species is divided by its coefficient from the balanced chemical equation ( <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi><mo separator="true">,</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">b, c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">b</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span></span></span></span>, or <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</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">d</span></span></span></span> ). This ensures that the calculated reaction rate is the same no matter which reactant or product is monitored for changes in concentration. In this case, the monitored species was <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>. With that in mind, let&#39;s write the reaction rate in terms of the rate of change in concentration of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></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><mtext> rate </mtext><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfrac><mrow><mi mathvariant="normal">Δ</mi><mrow><mo fence="true">[</mo><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub><mo fence="true">]</mo></mrow></mrow><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\text { rate }=-\frac{1}{2} \frac{\Delta\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\Delta t} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord text"><span class="mord"> rate </span></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:2.113em;vertical-align:-0.686em;"></span><span class="mord">−</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:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</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">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></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="mord">Δ</span><span class="mord mathnormal">t</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">Δ</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">[</span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">]</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p>Since the coefficient for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> in the balanced equation is 2 , we divided the rate of change in concentration of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> by 2 . Additionally, since <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>5</mn></msub></mrow><annotation encoding="application/x-tex">\mathrm{N}_2 \mathrm{O}_5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathrm">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;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 class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathrm">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> is being consumed in the reaction, we included a negative sign in front of the expression.</p><p>Now, let&#39;s plug in the information from the table to calculate the average reaction rate between <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50.0</mn></mrow><annotation encoding="application/x-tex">50.0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">50.0</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>75.0</mn></mrow><annotation encoding="application/x-tex">75.0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">75.0</span></span></span></span> seconds:</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"><mtext> rate </mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfrac><mrow><mo stretchy="false">(</mo><mn>0.515</mn><mi>M</mi><mo>−</mo><mn>0.642</mn><mi>M</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mn>75.0</mn><mrow><mtext> </mtext><mi mathvariant="normal">s</mi></mrow><mo>−</mo><mn>50.0</mn><mrow><mtext> </mtext><mi mathvariant="normal">s</mi></mrow><mo stretchy="false">)</mo></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>2.54</mn><mo>×</mo><mn>1</mn><msup><mn>0</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mi>M</mi><msup><mrow><mtext> </mtext><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned} \text { rate } &amp; =-\frac{1}{2} \frac{(0.515 M-0.642 M)}{(75.0 \mathrm{~s}-50.0 \mathrm{~s})} \\ &amp; =2.54 \times 10^{-3} M \mathrm{~s}^{-1} \end{aligned} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.1871em;vertical-align:-1.8436em;"></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:2.3436em;"><span style="top:-4.3436em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mord text"><span class="mord"> rate </span></span></span></span><span style="top:-2.2434em;"><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:1.8436em;"><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:2.3436em;"><span style="top:-4.3436em;"><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><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:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</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">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></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">75.0</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">s</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">50.0</span><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">s</span></span><span class="mclose">)</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="mopen">(</span><span class="mord">0.515</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</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">0.642</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</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:-2.2434em;"><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">2.54</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">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord"><span class="mord"><span class="mspace nobreak"> </span><span class="mord mathrm">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8436em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p>So, the average rate of the reaction between <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50.0</mn></mrow><annotation encoding="application/x-tex">50.0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">50.0</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>75.0</mn></mrow><annotation encoding="application/x-tex">75.0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">75.0</span></span></span></span> seconds is <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn mathvariant="bold">2.54</mn><mo>×</mo><mn mathvariant="bold">1</mn><msup><mn mathvariant="bold">0</mn><mrow><mo>−</mo><mn mathvariant="bold">3</mn></mrow></msup><mi mathvariant="normal">M</mi><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn mathvariant="bold">1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\bold{2.54 \times 10^{-3} \mathrm{M} \mathrm{s}^{-1}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8974em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord mathbf">2.54</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 mathbf">1</span><span class="mord"><span class="mord mathbf">0</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"><span class="mord mtight">−</span><span class="mord mathbf mtight">3</span></span></span></span></span></span></span></span></span><span class="mord mathrm">M</span><span class="mord"><span class="mord mathrm">s</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"><span class="mord mtight">−</span><span class="mord mathbf mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span>.</p></div></div></main><footer class="VPDocFooter" data-v-39e6c32d data-v-bae355c8><!--[--><!--[--><!--[--><!--[--><!----><!--]--><!--]--><!--]--><!--]--><div class="edit-info" data-v-bae355c8><div class="edit-link" data-v-bae355c8><a class="VPLink link vp-external-link-icon no-icon edit-link-button" href="https://github.com/andatoshiki/toshiki-notebook/edit/master/docs/academic/chemistry/problems/03-02-1.md" target="_blank" rel="noreferrer" data-v-bae355c8><!--[--><svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 24 24" class="edit-link-icon" aria-label="edit icon" data-v-bae355c8><path 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