Question

You have a concentration cell in which the cathode has a silver electrode with 0.10 M Ag+. The anode also has a silver electrode with Ag+ (aq), 0.050 M S2O3^2-, and 1.0 x 10^-3 M Ag (S2O3)2^3-. You read the voltage to be 0.76 V

a. Calculate the concentration of Ag+ at the anode.
b. Determine the value of the equilibrium constant for the formation of Ag(S2O3)2 ^3-.

Ag+ (aq) + 2S2O3 ^2- (aq) --> Ag(S2O3)2 ^3- (aq) K=?

Answer 1

You have a concentration cell in which the cathode has a silver electrode with 0.10 M Ag+. The anode also has a silver electrode with Ag+ (aq), 0.050 M S2O3^2-, and 1.0 x 10^-3 M Ag (S2O3)2^3-. You read the voltage to be 0.76 V

a. Calculate the concentration of Ag+ at the anode.
We use the Nernst equation in terms of concentration of Ag+ in anode compartment and in cathode compartment.

The equation is

Ecell = E⁰_cell – (0.0591 / n ) * log ( [Ag+]_anode / [Ag+]_cathode )

We know E⁰ = 0 for this cell.

Ecell is given = 0.76 V

Concentration of Ag+ in cathode compartment = 0.10 M

Lets plug all the value in Nernst equation to get concentration of Ag+ in anode compartment

0.76 V = 0 - (0.0591 /1 ) * log ( [Ag+]_anode / [0.10 M ]_cathode )

0.76 = - 0.0591 * log ( [Ag+]_anode / [0.10 M ]_cathode )

- 12.859 = log ( [Ag+]_anode / [0.10 M ]_cathode )

Lets take antilog of both side

Antilog (-12.859 )   = ( [Ag+]_anode / [0.10 M ]_cathode )

( [Ag+]_anode / [0.10 M ]_cathode ) = 1.38 E -13

[Ag+]_anode= 1.38E-14 M

b. Determine the value of the equilibrium constant for the formation of Ag(S2O3)2 ^3-.

Ag+ (aq) + 2S2O3 ^2- (aq) --> Ag(S2O3)2 ^3- (aq) K=?

we got Ag+ concentration we set up equilibrium expression for above reaction

K = [Ag(S2O3)2 ^3- (aq)] /[ Ag+ (aq)][S2O3 ^2- (aq) ]²

Lets plug the corresponding values

K = (1.0 x 10^-3 M ) / ( 1.38E -14) ( 0.05)²

K = 2.89 E+13