At 298 K, a certain buffer solution contains equal concentrations of X⁻ and HX , K_b for X⁻ is 10⁻¹⁰ . What is the pH of this buffer solution ?

Step-by-step solution

Given K_b for X⁻ = 10⁻¹⁰ . For a conjugate acid-base pair at 298 K, K_a K_b = K_w = 10⁻¹⁴ . K_a = 10⁻¹⁴ 10⁻¹⁰ = 10⁻⁴ The pK_a of the weak acid HX is: pK_a = - (K_a) = - (10⁻⁴) = 4 Using the Henderson-Hasselbalch equation for an acidic buffer: pH = pK_a + ( [X⁻] [HX] ) Since the concentrations of X⁻ and HX are equal, [X⁻] = [HX] . pH = 4 + (1) = 4 + 0 = 4 Answer: 4