Question

If 1.0 mole of ammonium cyanide, NH4CN, was dissolved in 1.0 liter of water, the pH of the solution would be ____________ at 25°C. For NH3: Kb = 1.8 x 10–5 and for HCN: Ka = 4.0 x 10–10.

a) 5.0
b) 7.0
c) 9.0
d) 11.0

Answer 1

To determine the pH of a 1.0 molar solution of NH4CN, considering NH4+ as acidic and CN- as basic, and the ionization constants of ammonium and cyanide, the solution is basic with a pH around 9.25. Hence, the most plausible answer is (c) pH 9.0.

Step-by-step explanation:

To determine the pH of a 1.0 molar solution of ammonium cyanide, NH4CN, you must consider the ionization constants of the components of the salt, and the resulting equilibrium in solution. Ammonium ion (NH4+) is acidic, while cyanide ion (CN−) is basic. Given the parameters, NH4CN behaves as a buffer system.

First, we assess the predominant reaction. The cyanide ion is the base of a weak acid (HCN), and it will react with water to produce hydroxide ions (OH−). The basic dissociation constant (Kb) for CN− is calculated using the provided acid dissociation constant (Ka of HCN) and the water dissociation constant (Kw):

Kb (CN−) = Kw / Ka (HCN) = (1.0 × 10−14) / (4.0 × 10−10)

However, NH4+ will also dissociate slightly, producing H+ ions, which would lower the pH. To calculate the exact pH, we should consider the equilibria established by both NH4+ and CN− in water.

Using the Kb of NH3 and the Henderson-Hasselbalch equation, the pH is found to be higher than 7, making the solution basic. For the exact pH value, more complex calculations involving equilibrium concentrations are required, which are not provided herein. Therefore, based on the nature of the components, the pH is likely close to the pKa of NH4+, which is around 9.25, thus making option (c) pH 9.0 the most plausible answer without exact calculations.