[Big-Daddy]

1) What approximations need to be made to say that, for a salt with a monoprotic anion as the conjugate base (whose basic action has equilibrium constant K_b) and a monoprotic cation as the conjugate acid (whose acidic action has equilibrium constant K_a), the pH is independent of the concentration of this salt and obeys the relation:

[tex][H^+] = \sqrt{K_w \cdot \frac{K_a}{K_b}}[/tex]

2) Prove that, besides activity effects, no approximations need to be made to show that, for a salt such as the one above, where K_a=K_b, then

[tex][H^+] = \sqrt{K_w}[/tex]

In other words that if K_a=K_b the solution will always be perfectly neutral. (Whereas the formula derived in (1) requires some approximations.)

Comments:
Either way we'll have to start from the main equations. Let's take the anion as A^- and cation as NH₄⁺ and assume that the coefficients on both NH₄⁺ and A- in the salt are 1. (We could investigate later whether the neutrality holds even if the coefficients are not both 1.)

c₀(Salt) = [NH₄⁺] + [NH₃] = [HA] + [A^-]
[NH₄⁺] + [H⁺] = [A^-] + [OH^-]
K_a = [NH₃] [H⁺] / [NH₄⁺]
K_b = [HA] [OH^-] / [A^-]
K_w = [H⁺] [OH^-]

Now what good approximations can we make here, so as to reach that formula in (1)?

And as for (2), simply equating K_a and K_b doesn't seem to be doing it for me. What should I do once I have placed the expressions equal to each other?