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

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    $\begingroup$ HINT - What is the difference between a strong acid and a weak acid? $\endgroup$ – MaxW Jan 12 at 19:08
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    $\begingroup$ 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? $\endgroup$ – Ivan Neretin Jan 12 at 19:22
  • $\begingroup$ Because 10*10/10 <> 1*1/1 $\endgroup$ – Poutnik Jan 12 at 19:32
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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 $[\ce{H^+}]$ = $\ce{[B^-]}$ = $x <<c$, 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$$K_a\ce{= \frac {[H^+][B^-]}{$c - x$} = \frac{$x$^2}{$c-x$} = \frac{$x$^2}{$c$}}$$ $$\ce{[H^+] = x = \sqrt{K_ac}}$$ $$\ce{$p$H = \frac{1}{2} (log$K$_a - log $c$)}$$ 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 $1/2$.

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