If 1 mM solution of ethylamine produces $\mathrm{pH}=9$, then the ionization constant $\left(\mathrm{K}_{\mathrm{b}}\right)$ 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.]

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Equilibrium

If 1 mM solution of ethylamine produces

pH = 9

, then the ionization constant

(K_{b})

of ethylamine is

1 0^{- x}

. The value of

x

is ____ (nearest integer). [The degree of ionization of ethylamine can be neglected with respect to unity.]

Answer: 7

For the weak base ethylamine,

pH = 9

gives

pOH = 5

, so

[O H^{-}] = 1 0^{- 5} M

.

With initial concentration

C = 1 0^{- 3} M

and degree of ionisation

α ≪ 1

so that

1 - α \approx 1

K_{b} = \frac{( C α ) ( C α )}{C ( 1 - α )} \approx \frac{[ O H ^{-} ] ^{2}}{C} = \frac{( 1 0 ^{- 5} ) ^{2}}{1 0 ^{- 3}} = 1 0^{- 7}

Comparing with

K_{b} = 1 0^{- x}

x = 7

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Integer answer