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<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">I’ve been asked the following about 17.18(b), a common-ion (CI) problem.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">It’s followed by my answer.<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-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">“I just had a question regarding one of the EOC problems for chapter 17, specifically<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">18b. The question asks to calculate the percent ionization of 0.125M Lactic acid solution<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">in a solution containing 0.0075M Sodium Lactate. When setting up the Acid-Dissociation<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">constant equation, I noticed that the answer key ignores the x's in (0.0075+x) and (0.125-x).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">This makes the equation =
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">(0.0075)(x)/(0.125) = 1.4*10^-4, instead of (0.0075+x)(x)/(0.125-x) = 1.4*10^-4.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">Wouldn't it be incorrect to omit the x's in this equation? By taking the acid disassociation<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">constant divided by the concentration of Lactic acid or
<span class="GramE">Lactate,</span> you get a value well above<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-fareast-font-family:"Times New Roman";color:black;background:yellow;mso-highlight:yellow">the general rule you described of <1.0*10^-3. “</span><span style="font-family:"Arial",sans-serif;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-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-fareast-font-family:"Times New Roman";color:red">The following was my response:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;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"">Before I go into the stuff below about the question, I gave a process in class to check<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">whether ignoring “x” in a weak acid problem would be okay before even going through<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">the ICE table.<span style="mso-spacerun:yes">
</span>Take the Ka and divide it by the original conc. of acid. If that ratio is less<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">than about 10^-3 it will okay to ignore “x” in the resulting expression for Ka obtained<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">from the ICE table.<span style="mso-spacerun:yes">
</span>The same applies to a weak base problem (using <span class="SpellE">Kb</span> and the original<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">conc. of base).<span style="mso-spacerun:yes">
</span>Strictly speaking, this was for when you start with only weak acid or only<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">weak base, not a common-ion (CI) problem.<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""><span style="mso-spacerun:yes">
</span>Ka <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"><<span style="mso-spacerun:yes"> </span>~</span> 10^-3<span style="mso-tab-count:2">
</span>Okay to ignore “x” in the expression for Ka.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">[HA]o<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"">(You can do the same thing for weak bases,
<span class="SpellE">Kb</span>/[base]o < 10^-3).<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"">How about for a CI problem?<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"">Let’s start by looking at something simpler,<span style="mso-spacerun:yes">
</span>just 0.125 M lactic acid (HL for short).<span style="mso-spacerun:yes"> </span>
If you<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">set up the ICE table for 0.125 M HL you get,<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""><span style="mso-spacerun:yes">
</span>x^2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ka = ----------------- = 1.4 x 10^-4<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes">
</span>(0.125 – x)<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"">You can ignore the “x” in the denominator in this case<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""><span style="mso-spacerun:yes">
</span>x^2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ka = ----------------- = 1.4 x 10^-4<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes">
</span>(0.125)<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"">and get only a 3.3% error.<span style="mso-spacerun:yes">
</span>Note, in this case Ka/[HL]_o = 1.4 x 10^-3/0.125 = 1.12 x 10^-3<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">(which is close to what I have above) and ignoring “x” with respect to the 0.125 M is okay.<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"">For the CI problem you have<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""><span style="mso-tab-count:1">
</span><span class="GramE">HL<span style="mso-spacerun:yes"> </span><</span>==><span style="mso-spacerun:yes">
</span>H^+<span style="mso-spacerun:yes"> </span>+<span style="mso-spacerun:yes">
</span>L^-<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes">
</span>0.125<span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>0<span style="mso-spacerun:yes">
</span>0.0075<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""><span style="mso-spacerun:yes">
</span>y (0.0075 + y)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ka = ---------------------- = 1.4 x 10^-4<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes">
</span>(0.125 – y)<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"">Since you’re starting with one of the products this rxn won’t go as far to the right as<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">it did with just the lactic acid.<span style="mso-spacerun:yes">
</span>That means this “y” will be smaller than the “x” above<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">with just 0.125 M HL (lactic acid).<span style="mso-spacerun:yes">
</span>That means ignoring “y” with respect to 0.125 is<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">a better approx. than above when ignoring the “x” w/<span class="SpellE">rsp</span> to 0.125 when you start with<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">only the lactic acid.<span style="mso-spacerun:yes">
</span>Thus, you only need to worry about the 0.0075.<span style="mso-spacerun:yes">
</span>Ignoring the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">“y” in both the numerator and denominator gives the following for “y”,<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"">y = 2.33 x 10^-3 M<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 % error with respect to the 0.125 is only 1.87%, less than 3.3% from above<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">when starting with only 0.125 M HL (lactic acid).<span style="mso-spacerun:yes">
</span>However, the % error w/<span class="SpellE">rsp</span> to the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">0.0075 is 31%.<span style="mso-spacerun:yes">
</span>That means you really shouldn’t ignore the “y” w/<span class="SpellE">rsp</span> to the 0.0075,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">as is done in the solutions manual.<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"">You can see the error by using this “y” value in the expression for Ka and see if<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">you get the Ka.<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""><span style="mso-spacerun:yes">
</span>(2.33 x 10^-3) (0.0075 + 2.33 x 10^-3)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ka = ------------------------------------------------------ = 1.87 x 10^-4<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes">
</span><span style="mso-spacerun:yes"> </span>(0.125 – 2.33 x 10^-3)<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"">Comparing this to the actual Ka of 1.4 x 10^-4 gives a 34% error.<span style="mso-spacerun:yes">
</span>Not good!<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""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">You can solve a quadratic or do the following, just ignore “y” w/<span class="SpellE">rsp</span> to the 0.125<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">but not the 0.0075.<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""><span style="mso-spacerun:yes">
</span>y (0.0075 + y)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ka = ---------------------- = 1.4 x 10^-4<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes">
</span>(0.125)<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 is still going to be a quadratic equation but one that’s easier to set up.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">You could also solve it by using the method of successive approximations<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">as I did in class.<span style="mso-spacerun:yes">
</span>Doing this I get the following for ‘y’,<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"">y = 1.868 x 10^-3<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 is a better value for the [H+] that comes from this CI problem.<span style="mso-spacerun:yes">
</span>Using<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">this value for “y” to calculate Ka you get the following:<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""><span style="mso-spacerun:yes">
</span>(1. 868 x 10^-3) (0.0075 + 1. 868 x 10^-3)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ka = ----------------------------------------------------------- = 1.42 x 10^-4<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes">
</span>(0.125 – 1. 868 x 10^-3)<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"">Comparing this to the actual Ka of 1.4 x 10^-4 gives a 1.5% error.<span style="mso-spacerun:yes">
</span>This<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">is less than 5% so this is fine.<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 gives the following for % ionization,<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"">% ionization = (1.868 x 10^-3)/0.125 * 100 = 1.49 %
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><span style="mso-spacerun:yes"> </span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">This is a better answer compared to 1.87% ionization you get by ignoring<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">the “y” w/<span class="SpellE">rsp</span> to both 0.125 and 0.0075 as was done in the solutions manual.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">The 1.87% is about a 26% error.<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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