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<div class="moz-cite-prefix">On 6/30/20 6:33 PM, <br>
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cite="mid:8101b061b6fe401e995dbdb336179790@BN3PR01MB1969.prod.exchangelabs.com">
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<div>How do I determine if a reaction is second or first order
by looking at the rate law? <br>
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<p>So for a reaction with ONE COMPONENT, the order is the exponent
to which the concentration is raised.</p>
<p><img alt="$rate=k [A]$" style="vertical-align: middle;"
src="cid:part1.0A4F24D7.1CD55058@mercer.edu"></p>
<p>would be a first order reaction and <br>
</p>
<p><img alt="$rate=k[A]^2$" style="vertical-align: middle;"
src="cid:part2.433AB3AF.F6C46AE2@mercer.edu"></p>
<p>would be a second order reaction.<br>
</p>
<p><br>
</p>
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cite="mid:8101b061b6fe401e995dbdb336179790@BN3PR01MB1969.prod.exchangelabs.com">
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<div> Also could you explain finding the k constant through
half life? I was too busy writing to catch everything. </div>
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<p>So when HALF of the compound is gone, the concentration is equal
to <img alt="$[A]/2$" style="vertical-align: middle;"
src="cid:part4.1383949F.B14F8E39@mercer.edu">, Referring to
page 142 from the lecture slides, we are considering a first order
reaction and are using the FIRST ORDER INTEGRATED RATE LAW, e.g
---</p>
<p><img alt="$[A] = [A_0] e^{-kt}$" style="vertical-align: middle;"
src="cid:part5.4413831B.3D74965C@mercer.edu"></p>
<p>so at the HALF LIFE (when half of the original compound is gone)
<br>
</p>
<p><img alt="$\frac{[A_0]}{2} = [A_0] e^{-kt_{\frac{1}{2}}}$"
style="vertical-align: middle;"
src="cid:part6.13B9EEB0.8A95AAF3@mercer.edu"></p>
<p>this simplifies to <br>
</p>
<p> <img alt="$\frac{1}{2} = e^{-kt_{\frac{1}{2}}}$"
style="vertical-align: middle;"
src="cid:part7.65B1D987.32ABC7CF@mercer.edu"></p>
<p>I take the natural log of both sides to arrive at</p>
<p><img alt="$\ln{\frac{1}{2}} = -kt_{\frac{1}{2}}$"
style="vertical-align: middle;"
src="cid:part8.A573ABBF.FAD983D1@mercer.edu"></p>
<p><img alt="$-0.6931=-kt_{\frac{1}{2}}$" style="vertical-align:
middle;" src="cid:part9.305BE725.F6B139E0@mercer.edu"></p>
<p>or...</p>
<p><img alt="$\frac{0.6931}{k}=t_{\frac{1}{2}}$"
style="vertical-align: middle;"
src="cid:part10.2B81F765.3285EF4C@mercer.edu"></p>
<p>or</p>
<p><img alt="$\frac{0.6931}{t_{\frac{1}{2}}}=k$"
style="vertical-align: middle;"
src="cid:part11.DCC96E2F.11087A29@mercer.edu"></p>
<p><br>
</p>
<p>For first order reactions if you are given the half life you can
easily find <img alt="$k$" style="vertical-align: middle;"
src="cid:part12.6FB672A9.BADB52ED@mercer.edu"><br>
</p>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Director of the Computational Science Program
Mercer University, Macon, GA 31207 (478) 301-5627
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