The trimethylammonium ion, [(CH₃)₃NH]⁺, is a weak acid - HSC - SSCE Chemistry - Question 20 - 2021 - Paper 1

Assuming that the dissociation of trimethylammonium ion is small, we can use the fact that:

K_a = rac{[H_3O^+][(CH_3)_3N]}{[(CH_3)_3NH^+]}

Let $x$ be the concentration of trimethylammonium ions that dissociate. Thus, at equilibrium, we can write:

$[H_3O^+] ext{ is } 3.47 imes 10^{-5} ext{ M}$ $[(CH_3)_3N] = x$ $[(CH_3)_3NH^+] = C - x ext{ (where C is the initial concentration)}$

Since trimethylammonium chloride is a strong electrolyte, we consider the initial concentration to be the same as the equilibrium concentration of the salt. This leads to:

$K_a = 1.55 imes 10^{-10}$ Since Kᵨ is related to Kₐ by:

Kᵨ = rac{K_w}{K_a} Here, $K_w = 1.0 imes 10^{-14}$ at 25°C. Thus:

Kᵨ = rac{1.0 imes 10^{-14}}{1.55 imes 10^{-10}} = 6.45 imes 10^{−5}

Given the calculated Kᵨ, the closest answer option is:

C. 60.2