Question

The equilibrium constant kc for the reaction hf(aq) + h2o(l) h3o+(aq) +f-(aq) is 3.5 x 10-4. what is the equilibrium concentration of h3o+ if the initial concentration of hf is 1.0 m?

Answer 1

According to the reaction equation:
          Hf(aq) + H2O (l)↔ H3O+ (aq) + F(aq)  

initial   1 m                       0           0
            -X                         +X          +X
          (1-x)                         X            X
We assumed that [H3O+] = X
so. at eqilibrium:
Kc = [H3O] [ F] / [Hf] when we have Kc so by substitution:
3.5x10^-4 = X^2 / (1-X)
∴X^2 = 3.5x10^-4 - 3.5x10^-4 X
X^2 + 3.5x10^-4 X - 3.5x10^-4= Zero
by solving this equation:
(X-1.9x10^-2)(X + 1.9x10^-2) = Zero 
∴X = 1.9x10^-2 
∴ the equilibrium constatnt of H3O = 1.9x10^-2 M