If 1 mM solution of ethylamine produces pH = 9, then the ionization constant of ethylamine is . The value of is ______ (nearest integer). [The degree of ionization of ethylamine can be neglected with respect to unity.] [2025]

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Solution

Q.
If 1 mM solution of ethylamine produces pH = 9, then the ionization constant $(K_{b})$ of ethylamine is $10^{- x}$ . The value of $x$ is ______ (nearest integer).

[The degree of ionization of ethylamine can be neglected with respect to unity.] [2025]

Ans.
(7)

$\begin{matrix} C_{2} H_{5} {NH}_{2} (a q) & + & H_{2} O & ⇌ & C_{2} H_{5} {NH}_{3}^{+} (a q) & + & O H^{-} (a q) \\ t = 0 & 10^{- 3} M & excess & 0 & 0 \\ t = \infty & 10^{- 3} (1 - α) & 10^{- 3} α M & 10^{- 3} α M \\ ≃ 10^{- 3} M \end{matrix}$

$pOH = 14 - pH = 14 - 9 = 5$

Thus ${[O H]}^{-} = 10^{- 5} M$

Also, $[C_{2} H_{5} {NH}_{3}^{+}] = {[O H]}^{-} = 10^{- 5} M$

$K_{b} = \frac{{[O H]}^{-} [C_{2} H_{5} {NH}_{3}^{+}]}{[C_{2} H_{5} {NH}_{2}]} = \frac{10^{- 5} \times 10^{- 5}}{10^{- 3}} = 10^{- 7}$

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