What is the correct pH in a reaction between hydrogen sulfate ion and ammonia?

[Qube]

Homework Statement

http://i.minus.com/jfUXIXvQJw8hw.png

Homework Equations

Ka of hydrogen sulfate ion will be taken as 1.2x10^-2.

Ka of ammonium ion will be taken as 5.6x10^-10

Kb of ammonia will be taken as 1.8x10^-5

Kb of sulfate ion will be taken as something very tiny (Kw/Ka of hydrogen sulfate ion).

These values are consistent throughout the literature.

The Attempt at a Solution

The reaction of hydrogen sulfate ion and bubbled in ammonia is a large extent reaction. We'll take it as going to completion. Also the pH controlling species here is obviously hydrogen sulfate ion since the magnitude of its Ka is far beyond that of ammonium or ammonia.

The problem is that with 0.25 moles of hydrogen sulfate ion left in the system there is NO way there can be a pH of 2.40. A pH of 1.3, yes. It seems that my teacher may have used the natural log instead of the base ten log because taking the natural log of the hydronium ion concentration yields a 2.90 (which may look like 2.40). The pH can easily be ascertained through a simple x^2/Mi = Ka calculation.

So am I wrong or is my teacher wrong?

 

[Borek]

pH of the 1M NH₄HSO₄ solution is around 1.0, pH of the 1M (NH₄)₂SO₄ solution is around 5.47, 2.40 is definitely between these two values.

 

[epenguin]

It's a salt of a strong acid and weak base essentially. You have already hit on an essential simplifying fact - the ammonia is essentially all protonated in the problem. So it is no different than if you replaced NH₄⁺ everywhere by Na⁺, a fairly ordinary problem.

 

[Qube]

No, that's not quite right either; I know what I did wrong. I forgot to realize this was a buffer solution. We have an ammonia/ammonium buffer and a hydrogen sulfate ion/sulfate ion buffer. We use the Henderson-Hasselbach equation then to estimate pH. I should also have realized that with the sheer amount of sulfate ion in the system relative to hydrogen sulfate ion (ratio of 3:1 or 0.75 moles to 0.25 moles) should, by Le Chatlier's principle, reduce the production of hydronium ion (relative to if there were only hydrogen sulfate ion in the system, as I had erroneously supposed).

 

[Borek]

To some extent it is a buffer solution, but using HH equation is quite dangerous. HSO₄^- is too strong for that. HH equation requires use of the equilibrium concentrations, you can't be sure typical assumption about the neutralization ("went to completion") is justified.

I agree with epenguin, ammonia dissociation can be safely ignored.

IOW equivalent question is "How much NaOH has to be added to 1M NaHSO₄ to produce pH 2.4 solution". I would try to approach it with some variant of the ICE table.