Equilibrium Constant and Free Energy Change
for an Electrochemical Cell

Two important important parameters that can be determined from a cell potential are the equilibrium constant for the cell reaction and the free energy change for the cell reaction.

• Determining the Equilibrium Constant from E^o_cell
• Determining the Standard State Free Energy Change from E^o_cell
• Determining the Non-Standard Free Energy Change

To calculate the equilibrium constant for an electrochemical cell we need to know:

• the standard state potential for a cell
• the half-reactions involved

At equilibrium Q = K. Substituting in K for Q, and the values for R, T, and F, we get:

Example:  Find the value of the equilibrium constant at 25^oC for the cell reaction for the following electrochemical cell:

• Write the equations for the cell half-reactions, calculate the standard cell potential, and determine the number of electrons transferred.

2 Ag+(aq) + 2 e-  2 Ag(s)	Eoreduction = + 0.799 V
Cu(s)  Cu2+(aq) + 2 e-	Eooxidation = - 0.518 V
2 Ag+(aq) + Al(s)  2 Ag(s) + Cu2+(aq)	Eocell = + 0.281 V

• Substitute into the above equation and solve for K.

Note:  values for the equilibrium constant for electrochemical cell reactions are sometimes very large.

Determining the Standard State Free Energy Change from E^o_cell

To determine the standard state free energy change for a cell reaction

• determine the E^o_cell
• determine the number of moles of electrons transfered in the reaction.
• solve for DG^o using the equation

        DG^o = standard state free energy change (joules)
        n = number of moles of electrons transferred
        F = Faraday's constant (96,485 C/mol e^-)
        E^o_cell = standard state cell potential (volts or joules/C)

Example:  Find the value of the equilibrium constant at 25^oC for the cell reaction for the following electrochemical cell:

(The solution for the determination of the E^o_cell and the number of moles of electrons, n, are shown in the example in the previous section. Click HERE to see the solution.)

• Determine the E^o_cell.
E^o_cell = + 0.281 volts
• Determine the number of moles of electrons transfered.
n = 2 moles of e^-
• Substitute into the equation and solve.

Determining the Non-Standard State Free Energy Change

To determine the non-standard state free energy change:

• calculate the standard cell potential, E^o_cell
• determine the number of moles of electrons transferred, n
• calculate the reaction quotient, Q
• calculate the non-standard cell potential, E_cell, using the Nernst equation
• Calculate the non-standard free energy change using the equation:

Example: Calculate the free energy change for the following electrochemical cell.

• Calculate E^o_cell.

Zn(s)  Zn2+(aq) + 2 e-	Eooxidiation = + 0.762 volts
Cu2+(aq) + 2 e-  Cu(s)	Eoreduction = + 0.339 volts
Zn(s) + Cu2+(aq)  Zn2+(aq) + Cu(s)	Eocell =  + 1.101 volts

• Determine "n".
n = 2 moles of electrons
• Calculate Q

• Calculate E_cell

• Calculate DG.