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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";color:black">I got the following question from a fellow student today.<span style="mso-spacerun:yes">
</span>It deals with the Nernst eqn.<span style="mso-spacerun:yes"> </span>I got another question<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";color:black">a short while ago about this eqn.<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";color:black">“I was working on the mastering for 20.6 and I have a question. For some background info, I used the
<span class="SpellE">lnQ</span> form of the Nernst equation for a question under nonstandard state conditions and got the question right. The next question was under standard
<span class="GramE">state</span> and I still used <span class="SpellE">lnQ</span>. I got it wrong because I had the wrong amount of e- transferred, but the hint said to use the log form which I understand is used for standard conditions. However, upon correcting
my e- error I tried both <span class="SpellE">lnQ</span> and <span class="SpellE">
logQ</span> and there was a 0.00001 difference between the two answers. So based on the sig figs for the problem they would come out to be the same. So that leads to my question... does it really matter whether you used
<span class="SpellE">lnQ</span> or <span class="SpellE">logQ</span>?”<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;mso-fareast-font-family:"Times New Roman";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">The Nernst
<span class="SpellE">eqn</span> is used to relate cell potential under non-standard conditions, E, to<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">cell potential under standard conditions,
<span class="SpellE">E^o</span>, the reaction quotient, Q, the temp<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">and moles of electrons transferred during the reaction.<span style="mso-spacerun:yes">
</span>It comes from the <span class="SpellE">eqn</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">in Ch 19 that relates delta(G) to delta(<span class="SpellE">G^o</span>), temp and Q.<span style="mso-spacerun:yes">
</span>It can be written in<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">a couple of ways,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">E =
<span class="SpellE">E^<span class="GramE">o</span></span><span class="GramE"> <span style="mso-spacerun:yes">
</span>-</span> (RT/<span class="SpellE">nF</span>)*ln(Q)<span style="mso-tab-count:3">
</span><span style="mso-tab-count:1"> </span><span style="mso-tab-count:1">
</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">R = 8.314 J/mol*K<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">T = temp in kelvin<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">n = number of moles of electrons transferred<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">F = Faraday constant (96,485 Coulombs/mol e-, to 5 sig. fig.)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">or<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">E =
<span class="SpellE">E^<span class="GramE">o</span></span><span class="GramE"> <span style="mso-spacerun:yes">
</span>-</span> 2.303*(RT/<span class="SpellE">nF</span>)*log(Q)<span style="mso-spacerun:yes">
</span>(base 10 log – not much reason to use this)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">The 2.303 comes from the relationship between natural log and base 10 log.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">The ln(10) = 2.302585093.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">The log(10) = 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">To convert from ln(10) to base 10 log you need to multiply log(10) by<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">ln(10) which we generally round to 2.303.<span style="mso-spacerun:yes">
</span>So, that number is even a<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">rounded number.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">At our normal REFERENCE temp of exactly 25 C (298.15 K) (this is NOT<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">part of the standard state definition), using base 10 log,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">E =
<span class="SpellE">E^<span class="GramE">o</span></span><span class="GramE"> <span style="mso-spacerun:yes">
</span>-</span> (0.0592 V/n)*log(Q)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">The 0.0592 Volts is to 3 sig. fig. enough in most cases for what we do.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">The “n” is the same as above.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">This last
<span class="SpellE">eqn</span> is often how we use the Nernst <span class="SpellE">
eqn</span> since we do most of <span class="GramE">our</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">work at the reference temp of 25 C.<span style="mso-spacerun:yes">
</span>We’ve discussed this very often in<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">class.<span style="mso-spacerun:yes">
</span>The tables at the back of the book for the thermodynamic quantities<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">we deal with, such as
<span class="SpellE">equil</span>, constants, delta(<span class="SpellE">H^o</span> of formation),
<span class="SpellE">S^o,</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">delta(<span class="SpellE">G^o</span> of formation) and
<span class="SpellE">E^o</span> values, are at 25 C (298.15 K).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">If you see a question in the book, Mastering,
<span class="GramE">quiz</span> or exam that requires a<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">temp and it’s not given assume 25 C.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Using the different equations should give the same results, with perhaps<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">slight differences in the last sig. fig. due to what you use for the constants,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">(<span class="GramE">i.e.</span> how many sig. fig.).<span style="mso-spacerun:yes">
</span>I showed how this can affect things in class.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">I used an
<span class="SpellE">E^o</span> value and then delta(<span class="SpellE">G^o</span>) = -
<span class="SpellE">nFE^o</span> and delta(<span class="SpellE">G^o</span>) = - RT*ln(K)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">to calculate K.<span style="mso-spacerun:yes">
</span>I showed what happens to the final answer when carrying<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">several extra digits, one extra digit or the correct sig. fig. from one step to<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">the next.<span style="mso-spacerun:yes">
</span>I showed that even using 298 K compared to 298.15 K can make<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">a difference (although this difference is much less than rounding in each<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">step rather than carrying extra digits).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">It really shouldn’t matter which
<span class="SpellE">eqn</span> you use <span class="GramE">as long as</span> you use the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">constants given on the info sheet and carry extra digits from one step to<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">the next in a multi-step calculation.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Most people rarely use the 2<sup>nd</sup>
<span class="SpellE">eqn</span> above anymore since we have<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">calculators that can do natural logs for us.<span style="mso-spacerun:yes">
</span>Back before calc. there<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">were easier ways to do base 10 logs w/o a calculator than natural<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">logs.<span style="mso-spacerun:yes">
</span>It’s sort of still stuck around.<span style="mso-spacerun:yes"> </span>The last
<span class="SpellE">eqn</span> is still extensively<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">used because we do most of our work at 298.15 K.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">If you want to use the Nernst
<span class="SpellE">eqn</span> at a different <span class="GramE">temp</span> you can’t use the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">one with the 0.0592 V.<span style="mso-spacerun:yes">
</span>You need to use the first or second <span class="SpellE">eqn</span> given<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">above.<span style="mso-spacerun:yes">
</span>This has nothing to do with non-standard state conditions.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Standard state conditions are not related to a particular temp.<span style="mso-spacerun:yes">
</span>It<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">means what the standard physical state something is in at a<o:p></o:p></span></p>
<p class="MsoNormal"><span class="GramE"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">particular temp</span></span><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""> of interest.<span style="mso-spacerun:yes">
</span>For things in solution the standard conc.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">is 1 M.<span style="mso-spacerun:yes">
</span>For gases, the std. <span class="SpellE">st.</span> is a partial pressure of 1 atm (technically<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">behaving ideally).<span style="mso-spacerun:yes">
</span>For solids or liquids, it’s the pure substance.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">That means we can do things that aren’t under std.
<span class="SpellE">st.</span> conditions at<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">25 C (298.15 K).<span style="mso-spacerun:yes">
</span>We can use any of the <span class="SpellE">eqns</span> above for this.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">If you also want to do this at a temp other than 25 C you would need<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">to use the first or second eqn.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">I hope this helps.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Dr. Zellmer<o:p></o:p></span></p>
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