Calculate the pH of a 0.30 M solution of NH₄Cl. (K_b for NH₃ = 1.8 × 10^-5) A) 3.33 B) 11.67 C) 4.89 D) 9.11 E) 7.00

Question

Quizplus · Accepted Answer

Since the given compound doesn't have any acidic or basic functional groups, it doesn't undergo any acid-base reaction. Hence, the pH of the solution only depends on the dissociation of water. The dissociation constant of water (Kw) is 1.0 × 10^-14. At 25°C, the pH of a neutral solution (where [H+] = [OH-]) is 7. Therefore, we can calculate the concentration of [H+] or [OH-] in the solution as follows:
Kw = [H+][OH-] = 1.0 × 10^-14
Let [H+] = [OH-] = x

[H+] x [OH-] x pH 
1×10^-7M 1×10^-7M 7 
x x 1.70×10^-4 M 3.77 
1.70×10^-4 M x 3.77

In the given solution, the concentration of [H+] is equal to [OH-], so we can substitute 0.30 for both [H+] and [OH-] in the expression for Kw. 
1.8 × 10^-5 = x^2
x = 1.34 × 10^-3 M
Using the definition of pH, pH = - log[H+]
pH = -log(1.34 × 10^-3) = 4.89
Therefore, the pH of the solution is 4.89, which corresponds to choice (C).

Calculate the PH of a 0