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Salt of Weak Acid and Strong Base

Hydrazine is ...

Question

Hydrazine is a weak base that dissociates in water as:
$N_{2} H_{2} + H_{2} O ⇌ N_{2} H_{5}^{+} + {O H}^{-}$ .
The equilibrium constant for dissociation at $25^{o} C$ is $2 \times 10^{- 6}$ . Nearest integer to $p H$ of the solution wil be_______ if initial conc. of $N_{2} H_{4}$ is $0.01 M$ .

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Solution

$N_{2} H_{4}$
$N_{2} H_{5}^{+}$ $O H^{-}$
Equilibrium concentration (M)
$0.01 - x$ $x$ $x$
The expression for the equilibrium constant K is $K = \frac{[N_{2} H_{5}^{+}] [O H^{-}]}{[N_{2} H_{4}]}$
Substitute values in the above expression.
$\frac{x \times x}{0.01 - x} = 2 \times 10^{- 6}$
$x^{2} = 2 \times 10^{- 8}$
$x = 1.414 \times 10^{- 4}$
$p O H = - l o g [O H^{-}] = - l o g 1.414 \times 10^{- 4} = 3.85$
$p H = 14 - p O H = 14 - 3.85 = 10.15 ≃ 10$

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	$N_{2} H_{4}$	$N_{2} H_{5}^{+}$	$O H^{-}$
Equilibrium concentration (M)	$0.01 - x$	$x$	$x$