An ammonia solution has a pH of 8.30, what is the [H₃O⁺] in this solution? A) 5.0 × 10^-23 M B) 2.0 × 10^-6 M C) 5.0 × 10^-9 M D) 2.0 × 10⁸ M

Question

Quizplus · Accepted Answer

The pH of 8.30 indicates that this is a basic solution. Ammonia (NH3) is a weak base and can be written as NH3 + H2O ⇌ NH4+ + OH-. Therefore, [OH-] can be calculated using the equation: pOH = 14 - pH = 14 - 8.30 = 5.70. Then, [OH-] = 10^-pOH = 2.0 × 10^-6 M. Since NH4+ is the conjugate acid of a weak base, it is a weak acid and can be written as NH4+ ⇌ H+ + NH3. The Ka expression for this equilibrium is Ka = [H+][NH3]/[NH4+]. At equilibrium, [H+] = [NH4+], so Ka = [H+]^2/[NH3] = [H+]^2/(Kb[NH4+]), where Kb is the base dissociation constant for NH3. Kb = Kw/Ka = 1.0 × 10^-14/1.8 × 10^-5 = 5.6 × 10^-10. Therefore, [H+]^2 = KaKb[NH3] = 5.6 × 10^-10 × 2.0 × 10^-6 = 1.1 × 10^-15. Thus, [H+] = 1.0 × 10^-7. Finally, [HSO4-] = [H+] = 1.0 × 10^-7 M, and [SO42-] = [OH-] = 2.0 × 10^-6 M. Therefore, [HSO4-][SO42-]/[H2SO4] = (1.0 × 10^-7)(2.0 × 10^-6)/(1.0 × 10^-2) = 2.0 × 10^-12 M. Since [H+] = [HSO4-], [HSO4-]/[H2SO4] = 1.0 × 10^-7/1.0 × 10^-2 = 1.0 × 10^-5. Therefore, [HSO4-][SO42-]/[H2SO4] = (1.0 × 10^-5)(2.0 × 10^-6) = 2.0 × 10^-11 M. This is not one of the answer choices, so we must choose the closest answer, which is C (5.0 × 10^-9 M).

An Ammonia Solution Has a PH of 8