Kaplan Topical Acids and Bases Q 14

[GeorgiadisMD]

Hello, I am having some trouble with this question. Here is what it states

If a buffer solution that contains 0.15 moles NaNO2
and 1.5 moles HNO2 has a pH of 2.4, what will be
the approximate pH after the addition of 0.7 moles
NaOH?

A . 5.4
B . 4.4
C . 3.4
D . 0.7

I understand how to get the pKa using the Henderson-Hasselbach equation, but what exactly are they doing after they have the pKa? Like the 1.5-0.7 and the 1.5+0.7?

Also, "After adding of 0.7 moles of sodium hydroxide, 0.7 moles of
nitrous acid is converted to 0.7 moles of nitrite ion." Is this true because Nitrous Acid only contains one Hydrogen? Like for instance, if it was H2SO4, would 1.4 moles of NaOH be needed to neutralize? I am just completely lost on this.

Below is the answer and explanation for question 14...

14 . The correct answer to question 14 is C. Calculations for the pH of a buffer solution may be made using
the Henderson-Hasselbach equation. The equation states that the pH of a buffer solution is approximately equal to the pKa of
the acid plus the log of the ratio of the amount of conjugate base to acid. The pKa of nitrous acid may be found by
substituting in the pH for the original solution, 2.4, and subtracting the log of 0.15 divided by 1.5. The pKa of HNO2 is
then found to be 3.4. This is a constant and never changes. After adding of 0.7 moles of sodium hydroxide, 0.7 moles of
nitrous acid is converted to 0.7 moles of nitrite ion. The new amounts of both of these species is then 1.5 – 0.7, or a total of
0.8 moles of nitrous acid, and 0.15 + 0.7, or 0.85 moles of nitrate ion. Substituting in these new values into the Henderson-
Hasselbach equation with the pKa of nitrous acid as 3.4 we solve for the new pH. The pH is equal to 3.4 plus the log of 0.85
over 0.80, or 3.4. You can see that when the concentrations of the weak acid and its conjugate base are approximately the
same, the pH is equal to the pKa. Thus answer C is correct.

Thanks for all your help! 🙂

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[GeorgiadisMD]

Okay I think I figured out why they subtracted 0.7 from Nitrous Acid, and added 0.7 to the Nitrate ion. I guess its because you are losing something, and its moving from one species to the other. I would have never figured this out intuitively though. Is there some sort of logical way of thinking this through?

Thanks again!

 

[justhanging]

Your adding a strong base that's going to accept all the protons it can, starting with the most acidic species. Obviously the acidic species it takes from it will convert it to the conjugate base.

pKa's are not constant as the explanation claims. They change with temperature.