### Calculate Ksp from electrochemical data

Example #1: Calculate the solubility product of AgI at 25.0 °C, given the following data:

 Reduction half-reaction E° (V) AgI(s) + e¯ ---> Ag(s) + I¯ -0.15 I2(s) + 2e¯ ---> 2I¯ -0.54 Ag+ + e¯ ---> Ag(s) 0.80

Solution:

1) The chemical equation for AgI dissolving is:

AgI(s) ⇌ Ag+(aq) + I¯(aq)

and the Ksp expression is:

Ksp = [Ag+] [I¯]

2) The equations to use are:

 E° (V) AgI(s) + e¯ ---> Ag(s) + I¯ -0.15 Ag(s) ---> Ag+ + e¯ -0.80

Yielding E° = -0.95 V

3) Use the Nernst Equation:

Ecell = E° - (0.0591 / n) log K

0 = -0.95 - (0.0591 / 1) log K

0.95 / -0.0591 = log K

log K = -16.07

K = 8.51 x 10¯17

Note: some instructors might insist that you round the answer off to two significant figures. On this site, the Ksp is listed as 8.52 x 10¯17.

Note also that you never have to use the Ksp expression to calculate anything. The Ksp is determined directly from the electrochemical data.

Example #2: Using the following reduction potentials, calculate the solubility product for AgCN at 298 K:

 Ag+ + e¯ ---> Ag E = 0.80 V AgCN + e¯ ---> Ag + CN¯ E = -0.01 V

Solution:

1) Reverse first half-reaction:

 Ag ---> Ag+ + e¯ E = -0.80 V AgCN + e¯ --> Ag + CN¯ E = -0.01 V