Query related to ionic equilibrium constant [duplicate]

Question

I know that [H+][OH-] = kw =10^-14 at 25 degree.But while calculating the pH of 10^-8 M HCl, this equation is used for total concentration of [H+] and [OH-] in the solution. Why is this equation valid in all kinds of aqueous solutions? I think that this equation should be valid only for the dissociation of water, and the amount of H+ and OH- released by water should be 10^-7 mol/l each in any situation.Can someone clear this confusion?

Answer 1

Why should be the equilibrium of water auto-dissociation the exception, compared to other equilibrium reactions? It is about coexistence of $\ce{H+}$ ($\ce{H3O+}$) and $\ce{OH-}$ ions. There is no rule their concentration must be equal.

The net rate of water dissociation/recombination in pure water or diluted solutions is

$$\frac{\mathrm{d}[\ce{H+}]}{\mathrm{d}t}=A - B \cdot [\ce{H+}] \cdot [\ce{OH-}].$$

So the condition for equilibrium, when both $\ce{[H+]}$ and $\ce{[OH-]}$ are constant, is not the equality of concentrations, but the product of concentrations being equal to $K_\mathrm{w}$.

$$\frac{\mathrm{d}[\ce{H+}]}{\mathrm{d}t}=A - B \cdot K_\mathrm{w}=0$$

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If $\ce{[H+][OH-]} > K_\mathrm{w}$, ion recombination is faster than water autoionization and the value of $\ce{[H+][OH-]}$ decreases ( and vice versa ), therefore $\ce{[H+][OH-]}$ converges to $K_\mathrm{w}$.

At different temperature, or at concentrated solutions the particular value $\pu{e-14}$ is not valid anymore, but the principle remains.