# Why does the pH of a weak acid not increase by 1 when diluted by a factor of 10? [closed]

Strong acid pH increases by one unit when diluted by a factor of 10, but why do weak acids not?

• HINT - What is the difference between a strong acid and a weak acid? – MaxW Jan 12 at 19:08
• Why does the pH of water not increase by 1 when diluted by a factor of 10? Oh, and BTW, how come pure water has a pH? – Ivan Neretin Jan 12 at 19:22
• Because 10*10/10 <> 1*1/1 – Poutnik Jan 12 at 19:32

In a weak acid $$\ce{HB}$$ solution, with a nominal concentration $$c$$, a tiny amount of its molecules are dissociated into $$\ce{H^+}$$ and $$\ce{B^-}$$. Let's call this concentration $$[\ce{H^+}]$$ = $$\ce{[B^-]}$$ = $$x <, so that the following approximation can be made : $$c - x$$= $$c$$. The dissociation equilibrium constant $$K_a$$ of this weak acid $$\ce{HB}$$ can be approximated by$$K_a\ce{= \frac {[H^+][B^-]}{c - x} = \frac{x^2}{c-x} = \frac{x^2}{c}}$$ $$\ce{[H^+] = x = \sqrt{K_ac}}$$ $$\ce{pH = \frac{1}{2} (logK_a - log c)}$$ Look at the coefficient $$1/2$$ before the logarithm. If the concentration $$c$$ is multiplied by $$10$$, the log c increases by $$1$$, but the $$p$$H changes by $$1/2$$.