Calculate Ksp from electrochemical data

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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¯ ---> AgE = 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

2) Add:

AgCN ---> Ag+ + CN¯    E = -0.81 V

3) Use -RT ln K = -nFE

(8.314) (298) ln K = (1) (96485) (-0.81)

ln K = -31.544

Ksp = 2.0 x 10-14


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