At 298 K, a basic buffer solution contains equal concentrations of a weak base B and its conjugate acid BH⁺ . If the acid dissociation constant ( K_a ) for BH⁺ is 10⁻⁹ , what is the pH of this buffer solution?

Step-by-step solution

Given K_a for the conjugate acid BH⁺ = 10⁻⁹ . For a conjugate acid-base pair at 298 K, K_a K_b = K_w = 10⁻¹⁴ . The base dissociation constant ( K_b ) for the weak base B is: K_b = 10⁻¹⁴ 10⁻⁹ = 10⁻⁵ The pK_b of the weak base is: pK_b = - (K_b) = - (10⁻⁵) = 5 Using the Henderson-Hasselbalch equation for a basic buffer: pOH = pK_b + ( [BH⁺] [B] ) Since the concentrations of B and BH⁺ are equal, [BH⁺] = [B] . pOH = 5 + (1) = 5 + 0 = 5 The pH of the solution is calculated as: pH = 14 - pOH = 14 - 5 = 9 Answer: 9