Question

When trying to find the solubility product of a salt in a metal - metal insoluble salt electrode, I find that I am getting a different answer if I consider the cell to be a concentration cell and if I do not.

For example, to find Ksp of PbSO4 in the cell: Pb(s) | PbSO4(s) | Na2SO4(aq)(0.01M) || Pb(NO3)2(0.1M)| Pb(s)

Given: Ecell
at 298K = 0.236V.

At the anode :
Pb⟶Pb2++2e−
Pb2++SO42−⟶PbSO4

Overall: Pb+SO42−⟶PbSO4+2e−

So, Eanode = E0anode - 0.0592 log1[SO42−]

At the cathode : Pb2++2e−⟶Pb

Pb(NO3)2⟶Pb2++2NO3−

Overall: Pb(NO3)2+2e−⟶Pb+2NO3−

and, Ecathode = E0cathode - 0.0592 log[NO3−]2

Ecell = Ecathode - Eanode

Ecell = E0cell - 0.0592 log[NO3−]2[SO42−]

Thus, E0cell = 0.236 + 0.0592 log(0.1)2(0.01) = 0.118 V

At equilibrium, Ecell = 0, so logKsp = (2)E0cell0.059

So, logKsp = 4

Ksp = 104

However, the answer comes out to be 10−11 when I consider it to be a concentration cell of Pb2+. Where am I going wrong or why does this method not work?

Answer 1

The mistake in calculating the Ksp of PbSO4 arises from not applying the Nernst equation correctly for a concentration cell. The Ksp is calculated by relating the measured cell potential to the potential obtained from the Nernst equation and using the equilibrium concentrations of the ions.

Step-by-step explanation:

The discrepancy in the calculation of the solubility product (Ksp) for PbSO4 arises from not using the appropriate expression for a concentration cell.

The Nernst equation should be used to calculate the cell potential, Ecell, considering the concentration gradient of Pb2+ ions across the two compartments.

For a concentration cell, the Nernst equation is given by:

Ecell = E0cell - (0.0592/n) log(Q)

where n is the number of electrons transferred, E0cell is the standard cell potential, and Q is the reaction quotient. At equilibrium, Ecell is zero, which allows us to find Ksp by relating the concentrations of the ions involved in the dissolution of PbSO4.

To find Ksp correctly, use the following relationship which links the equilibrium of PbSO4 dissolution and Ksp:

[Pb2+][SO42-] = Ksp

Apply the above concepts by setting the measured cell potential equal to the potential calculated from the Nernst equation at equilibrium, and solve for Ksp using the known concentrations of ions and the cell potential provided.