[vickca86]

This question is irritating the hell out of me and my tutor had no idea how to solve it.

One liter of a buffer solution is prepared by dissolving 0.115 mol of NaNO₂ and 0.070 mol of HCl in water. What is the pH of this solution? If the solution is diluted twofold with water, what is the pH?

The thought just occurred to me that this may be a trick question in some regard since HCl is a strong acid and NaNO₂ is a salt of a weak acid, but I haven't came across a trick question in the previous 19 chapters so I'm banking on a typo?

The only other way I could possibly think to solve this is:

NaNO₂ + H₂O ----> NaOH + HNO₂ then
HNO₂ + H₂O ----> H₃O⁺ + NO₂^- and then
HCl + H₂O -----> H₃O⁺ + Cl^-

add the [] of H₃O⁺ and use the pH = pKa+log[CB/A] formula, but then my problem is what pKa value do I use?

I keep going back to the answer being whatever the pH of HCl calculates out to be and then for the second part dividing the [HCl] by half and using that pH value.

I know I'm over thinking this, I just don't understand why the text book would give a question like this when it doesn't fall into the normal way the book gives chapter questions.

[Borek]

Nothing tricky about this problem.

NO₂^- is a base, it gets protonated by the strong acid, producing HNO₂.

Change the tutor.

[Babcock_Hall]

@OP, Once the HCl is consumed by the base, what are the final concentrations of the acid and the base?

[vickca86]

Well, there is more base than acid so HCl = 0 and NaNO₂ = 0.045

[Borek]

And HNO₂?

I wonder what is the level at which this question is asked. If you are expected just to use Henderson-Hasselbalch equation you are already done - just plug and chug. But if you are expected to do the full analysis, you should calculate exact equilibrium concentrations using ICE table. Definitely more elaborate.

[opsomath]

Yeah, the only real red flag here is that the tutor couldn't solve it. The solution winds up being a straight mixture of nitrous acid and sodium nitrite, enabling you to solve it with whatever method you are taught for calculating the pH of a mixture of a weak acid and its conjugate base.