Calculate [H^{+}] of a 0.01 M A^{+}B^{-} sal | vedclass

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(D) The salt $A^{+}B^{-}$ is a salt of a strong base and a weak acid $HB$.Hydrolysis reaction: $B^{-} + H_2O \leftrightarrow HB + OH^{-}$.Hydrolysis c

Vedclass · Accepted Answer

$1.6 	imes 10^{-12} \ M$

Vedclass · Answer

(D) The salt $A^{+}B^{-}$ is a salt of a strong base and a weak acid $HB$.Hydrolysis reaction: $B^{-} + H_2O \leftrightarrow HB + OH^{-}$.Hydrolysis constant $K_h = \frac{K_w}{K_a} = \frac{10^{-14}}{10^{-12}} = 10^{-2}$.For a salt of a weak acid and strong base,$K_h = \frac{C\alpha^2}{1-\alpha}$.Given $C = 0.01 \ M$,we have $\frac{0.01 \alpha^2}{1-\alpha} = 10^{-2}$,which simplifies to $\alpha^2 = 1 - \alpha$ or $\alpha^2 + \alpha - 1 = 0$.Solving for $\alpha$ using the quadratic formula: $\alpha = \frac{-1 + \sqrt{1 + 4}}{2} = \frac{\sqrt{5}-1}{2} \approx 0.618$.$[OH^{-}] = C\alpha = 0.01 	imes 0.618 = 6.18 	imes 10^{-3} \ M$.$[H^{+}] = \frac{K_w}{[OH^{-}]} = \frac{10^{-14}}{6.18 	imes 10^{-3}} \approx 1.6 	imes 10^{-12} \ M$.

Calculate $[H^{+}]$ of a $0.01 \ M$ $A^{+}B^{-}$ salt solution if the $K_a$ of $HB$ is $10^{-12}$.

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