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<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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