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Q.
pH of a solution of a strong acid is $5.0.$ What will be the pH of the solution obtained after diluting the given solution 100 times?
Equilibrium
Solution:
$pH = 5, [H^+] = 10^{-5}\, mol\, L^{-1}$
On 100 times dilution, $[H^+] = 10^{-7}\, mol\, L^{-1}$
$∴ pH = 7$
It is not possible. This indicates that solution is very dilute. Hence,
Total hydrogen ion concentration, [$H^+]$
$=\begin{bmatrix}Contribution\, of\\ H_{3}O^{+}\,ion\\ concentration\\ of \,acid\end{bmatrix}+\begin{bmatrix}Contribution\, of\\ H_{3}O^{+}\,ion\\ concentration\\ of \,water\end{bmatrix}$
$=10^{-7}+10^{-7}.$
$pH=2\times10^{-7}=7-log\,2=7-0.3010=6.6990$