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Factors Affecting Alpha

Which of the ...

Question

Which of the following relation is correct regarding $p H$ of salt of amphiprotic ion, $H_{2} P O_{4}^{-}$ :
Given: $K_{a_{1}}$ is first acid dissociation constant of $H_{3} P O_{4}$ and $K_{a_{2}}$ is second acid dissociation constant of $H_{3} P O_{4}$ .

A

p H = \frac{p K_{a_{1}}}{2 \times p K_{a_{2}}}

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B

p H = \frac{1}{2} [p K_{a_{1}} \times p K_{a_{2}}]

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C

p H = \frac{1}{2} [p K_{a_{1}} - p K_{a_{2}}]

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D

p H = \frac{1}{2} [p K_{a_{1}} + p K_{a_{2}}]

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Solution

The correct option is D $p H = \frac{1}{2} [p K_{a_{1}} + p K_{a_{2}}]$
Salts of amphiprotic ions :
Consider the following salts each with concentration C
Salt 1- $N a_{3} P O_{4}$
Salt 2- $N a H_{2} P O_{4}$

To calculate the pH, when $N a_{3} P O_{4}$ is dissolved in water, we can say that only $P O_{4}^{3 -}$ ion is hydrolyzed but in $N a H_{2} P O_{4}$ , the ions hydrolysed are $H_{2} P O_{4}^{-}$ . It is an amphiprotic ion.
$H_{2} P O_{4}^{-} (a q) + H_{2} O (l) ⇌ H_{3} P O_{4} (a q) + O H^{-} (a q) \to K_{h} = \frac{K_{w}}{K_{a_{1}}}$
$H_{2} P O_{4}^{-} (a q) + H_{2} O (l) ⇌ H P O_{4}^{2 -} (a q) + H_{3} O^{+} (a q) \to K_{h} = \frac{K_{w}}{K_{a_{2}}}$

Calculation of pH can be done with the relation:
$p H = \frac{1}{2} [p K_{a_{1}} + p K_{a_{2}}]$

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