# Query related to ionic equilibrium constant [duplicate]

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?

• Well I'll point out that $K_w$ is a pseudo constant. The value does depend on temperature, pressure and ionic strength among other factors. The gist is that $K_w$ is for the equilibrium when a water molecule splits as so: $$\ce{H2O <=> H+ + OH-}$$ The concentration of $\ce{H2O}$ is left out of the mathematical expression for the equilibrium since the molarity of water is assumed to be a constant for dilute solutions.
– MaxW
Jul 9, 2021 at 8:27

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 $$K_\mathrm{w}$$.

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

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.

• But Why then is the equation [H+][OH-] = kw =10^-14 valid in all kinds of aqueous solutions ( whether acids or bases)? Jul 9, 2021 at 7:06