Given the following standard reduction potentials, calculate the solubility product of AgCN at 25°C.

Question

Given the following standard reduction potentials,  calculate the solubility product of AgCN at 25°C.

Quizplus · Accepted Answer

The balanced equation for the dissolution of AgCN is:

AgCN(s) ⇌ Ag+(aq) + CN-(aq)

The half-reactions involved are:

Ag+(aq) + e- ⇌ Ag(s)          E° = 0.80 V
CN-(aq) ⇌ CNO-(aq) + e-     E° = 0.49 V

To calculate the solubility product constant (Ksp) of AgCN, we need to write the overall equation and calculate its standard potential (E°):

AgCN(s) ⇌ Ag+(aq) + CN-(aq)     E° = E°(Ag+) - E°(CN-) = 0.80 V - 0.49 V = 0.31 V

The value of E° is positive, which means that the dissolution of AgCN is not spontaneous, and therefore Ksp will be small.

To calculate Ksp, we can use the Nernst equation:

E = E° - (RT/nF) ln Q

where Q is the reaction quotient, R is the gas constant, T is the temperature in Kelvin, F is the Faraday constant, and n is the number of electrons transferred in the half-reaction.

For the dissolution reaction, the reaction quotient is:

Q = [Ag+][CN-]

At equilibrium, Q = Ksp, so we can write:

Ksp = [Ag+][CN-] = exp[(E° - E)/(RT/nF)]

Substituting the values given in the problem:

E° = 0.31 V
R = 8.314 J/(mol*K)
T = 25°C = 298 K
F = 96,485 C/mol
n = 1

We get:

Ksp = exp[(0.31 V)/(0.0257 V/K)] = 2.1 × 10^-14

Therefore, the answer is C.

Given the Following Standard Reduction Potentials, Calculate the Solubility