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<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">I received a couple of questions about how to calculate the pH for very small concentrations
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">of strong acid or base in water (conc. less than or around 10^-6 M). I also received a couple<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">of questions about a problem dealing with calculating the pH of a solution made by mixing<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">a strong acid and strong base (neutralization reaction). People said they couldn’t find either<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">of these in the book or end-of-chapter exercises. Here’s what I want to say about both of<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">these questions.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">I actually answered the first one, 16.106 (in the Additional Exercises in the EOC exercises)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">in an e-mail last Wed. night. Granted you may not have seen it since you had the midterm<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">earlier that day. Still, when you don’t read the e-mails right away file them away and try to<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">remember something was sent and take a quick look when you’re working on the material.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">You’ll find my explanation below.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">The other question about the pH after mixing a strong acid and strong base is 16.100<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">from the Additional Exercises. It may seem this one would make more sense in ch 17,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">since it is a neutralization rxn, which is what happens in titrations. However, you did SA-SB<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">neutralization rxns in Ch 4.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">How many of you are trying the Additional Exercises or Integrative Exercises? I know<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">some of you are as I’ve had questions about them during office hours and via e-mail. But<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">that’s coming from just a few people. Hopefully, everyone is trying these at some point.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">These questions aren’t all in Mastering yet so I can’t even assign them in the MC<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">homework. These are viable questions to be asked on quizzes and exams.</span><span style="font-family:"Arial",sans-serif"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">Dr. Zellmer<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b>From:</b> Zellmer, Robert <zellmer.1@osu.edu> <br>
<b>Sent:</b> Wednesday, June 30, 2021 9:13 PM<br>
<b>To:</b> cbc-chem1220@groups.asc.ohio-state.edu<br>
<b>Cc:</b> cbc-chem1220-ta@groups.asc.ohio-state.edu<br>
<b>Subject:</b> Ch 16 question from students<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">I often get the following question from students. How do I correctly calculate<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the pH for something like a 1 x 10^-8 M NaOH or 1 x 10^-7 M HCl solution<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">There’s actually a homework problem like this in the additional exercises.<br>
<br>
I'll give a little hint. While NaOH and HCl are strong acids and will completely
<br>
dissociate or ionize, these conc. are very small and close to the conc. of OH- <br>
or H+ from pure water. Normally, with conc. of 10^-5 M or greater for the strong
<br>
acids and bases we can ignore the conc. of H+ or OH- coming from the water. <br>
As a matter of fact, if you look at the autoionization rxn for H2O it goes back to
<br>
the left when H+ or OH- is added from an outside source (acid or base) so you <br>
get even less H+ or OH- from the autoionization rxn. This applies even for weak <br>
acids or bases, as long as their conc. are relatively high and they're not too weak.
<br>
Thus, for an acid, the conc. of H+ we normally consider is coming just from the <br>
acid and we ignore any H+ from the water itself (same for a base and OH-). <br>
<br>
However, with very small conc. of acid or base (whether strong or weak) you <br>
might not be able to ignore the H+ or OH- coming from the water. <br>
<br>
So here's the hint. Set this up as you would for the autoionization of H2O, <br>
<br>
H2O (l) <=> H+ (aq) + OH- (aq) <br>
<br>
Normally, the first line in the ICE table would have zero for both the H+ and <br>
OH- on the right. When you add strong acid or base and their conc. are really <br>
small (close to 10^-7), treat the above problem kind of like a common-ion problem</span><br>
<br>
<span style="font-size:12.0pt;font-family:"Arial",sans-serif">(i.e. the initial conc. of the H+ or OH- in the ICE table won't be zero).
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Lets say we have 1 x 10^-8 M HCl. This means conc. of H+ from the strong<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">acid is [H+] = 1 x 10^-8 M. Set up the autoionization equilibrium for H2O in<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the following way,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"> H2O (l) <=> H+ (aq) + OH- (aq)
<br>
10^-8 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"> -x +x +x<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"> -----------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"> ---- x + 10^-8 x<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Plug these into Kw and calculate “x”. You will need to solve a quadratic eqn.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">The “x” is the H+ and OH- coming from water. It will be less than that from<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">pure water. Then you add the “x” and the 10^-8 to get the total conc. of H+.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">The total [H+] will be a little greater than 10^-7 but not by much. You’ll see<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the pH will be close to 7 (a little less than 7), close to that of pure water.<br>
<br>
Dr. Zellmer<o:p></o:p></span></p>
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