[neon]

A solution contains 0.09 M HCl, 0.09M CHCl₂COOH and 0.1M CH₃COOH. The pH of the solution is 1. If Ka for acetic acid is 10^-5, then find Ka for CHCl₂COOH.

I am trying to use the formula
[itex][H+] = \sqrt{K_1C_1+K_2C_2+C_3} [/itex]

If the above equation is incorrect then please give me some hints to solve the problem.

[Borek]

Formula doesn't look reasonable to me - it would mean in the case of just HCl concentration of H⁺ would equal square root of the acid concentration, which is clearly wrong.

Assume HCl is fully dissociated. If so, concentration of H⁺ is a sum of three H⁺ concentrations - 0.09 from HCl, x from acetic acid and y from dichloroacetic acid. That gives first equation:

[tex]x + y + 0.09 = 10^{-1}[/tex]

You can get two more equations using ICE tables for acetic acid and dichloroacetic acid dissociations (construct ICE tables using x and y).

That will give three equations in three unknowns. Solve.

And remember: I never said it will be easy to solve. Most likely it will be quite difficult without some approximations or numerical treatment.