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Acids and Bases in Water

The pH of amm...

Question

The $p H$ of ammonium phosphate solution, if $p K_{a}$ of phosphoric acid and $p K_{b}$ of ammonium hydroxide are 5.23 and 4.75 respectively, is

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Solution

Ammonium acetate is a salt of weak acid, phosphoric acid and weak base, ammonium hydroxide.
$(N H_{4})_{3} P O_{4} ⇋ 3 N H_{4}^{+} + P O_{4}^{3 -}$

$[H^{+}] = K_{a} \times \sqrt{\frac{K_{w}}{K_{a} \times K_{b}}}$

$p H = p K_{a} + 1 / 2$ { $p K_{w} - p K_{a} - p K_{b}$ }

$p H = 5.23 + 1 / 2$ { $14 - 5.23 - 4.75$ }

$p H = 5.23 + 1 / 2 \times (4.02) = 7.24 \approx 7$ (Nearest integer)

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