Given pK_b values at 298 K: NH3 4.75, CH3NH2 3.38, (CH3)2NH 3.27, (CH3)3N 4.22, C6H5NH2 9.38. Which statements are correct? (Use 10^1.37 = 23.4 and 10^4.63 = 4.27 x 10^4.)

K_b of CH3NH2 is more than 20 times K_b of NH3.

K_b of (CH3)2NH is greater than K_b of CH3NH2.

K_b of NH3 is more than 10^4 times K_b of C6H5NH2.

K_b of CH3NH2 is more than 20 times K_b of NH3.

K_b of (CH3)2NH is greater than K_b of CH3NH2.

K_b of NH3 is more than 10^4 times K_b of C6H5NH2.

K_b of (CH3)3N is greater than K_b of CH3NH2.

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3nc032

Given $p K_{b}$ values at 298 K: $NH X_{3}$ 4.75, $CH X_{3} NH X_{2}$ 3.38, $(CH X_{3}) X_{2} NH$ 3.27, $(CH X_{3}) X_{3} N$ 4.22, $C X_{6} H X_{5} NH X_{2}$ 9.38. Which statements are correct? (Use $1 0^{1.37} = 23.4$ and $1 0^{4.63} = 4.27 \times 1 0^{4}$ .)

A $K_{b}$ of $CH X_{3} NH X_{2}$ is more than 20 times $K_{b}$ of $NH X_{3}$ .
B $K_{b}$ of $(CH X_{3}) X_{2} NH$ is greater than $K_{b}$ of $CH X_{3} NH X_{2}$ .
C $K_{b}$ of $NH X_{3}$ is more than $1 0^{4}$ times $K_{b}$ of $C X_{6} H X_{5} NH X_{2}$ .
D $K_{b}$ of $(CH X_{3}) X_{3} N$ is greater than $K_{b}$ of $CH X_{3} NH X_{2}$ .

A smaller

p K_{b}

means a larger

K_{b}

, so

(CH X_{3}) X_{2} NH

(3.27) beats

CH X_{3} NH X_{2}

(3.38). The ratio

K_{b} (CH X_{3} NH X_{2}) / K_{b} (NH X_{3}) = 1 0^{4.75 - 3.38} = 1 0^{1.37} = 23.4

. The ratio

K_{b} (NH X_{3}) / K_{b} (C X_{6} H X_{5} NH X_{2}) = 1 0^{9.38 - 4.75} = 1 0^{4.63} = 4.27 \times 1 0^{4}

. For

(CH X_{3}) X_{3} N

the

p K_{b}

of 4.22 is larger than 3.38, so it is the weaker base.