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Q. Dissociation constants of $CH_3COOH$ and $NH_4OH$ in aqueous solution are $10^{-5}$. If $pH$ of a $CH_3COOH$ solution is $3$, What will be the $pH$ of $NH_4OH$?

Equilibrium

Solution:

$pH$ of $CH_3COOH = 3$
$\left[H^{+}\right]=10^{-3}\,M$ from $CH_{3}COOH$
$\left[NH_{4}OH\right]=\left[CH_{3}COOH\right]=10^{-3}\,M$
$\left[OH^{-}\right]=10^{-3}\,M$
$\left[H^{+}\right]\left[OH^{-}\right]=10^{-14}$
$\left[H^{+}\right]=\frac{10^{-14}}{10^{-3}}=10^{-11}$
$pH$ of $NH_{4}OH=-log\,\left(10^{-11}\right)$
$=11$