Thermodynamics of Electrochemical Cells

Thermodynamics of Electrochemical Cells

If in a cell n equivalents of reactants are converted into products, then the quantity of electricity that flows through the cell is nF, where F is the Faraday constant. If this amount of charge is transported through the cell of Emf E volts, the amount of electrical work done by the cell is nEF.

Gibbs free energy decrease in a cell reaction is therefore given by;

-G=nEF

or G=-nEF                                                                                                                   (18)

If at constant temperature and pressure (G)_P,T< 0 or E_cell> 0, the cell reaction can proceed spontaneously. However, if(G)_P,T =0 E_cell= 0, the cell is in a state of equilibrium..

or

Eqn (18) provides a method for determining free energy changes of electrochemical cell reactions.

The enthalpy change for a cell reaction may also be deduced from Emf measurements. From Gibbs-Helmoholtz equation we have;

H =-G –T []_P                                                                                                   (19)

Differentiating G with respect to temperature at constant pressure in eqn (18) yields;

[(G/T]_P = -nF _P                                                                                                                                                    (20)

The quantity _P  is the temperature coefficient of the cell. Substituting the value of [(G/T]_P in eqn (2) we get;

H= G + nFT _P

And substituting for ΔG from eqn (1) gives;

H=nFE + nFT _P

Thus from a measurement of the cell Emf and the rate of change of Emf with temperature, the enthalpy change, H, may be calculated.

Entropy changes for cell reactions are determined from temperature coefficient of the cell Emf.

From the third law of thermodynamics we have

G =H –TS                                                                                                       (21)

Differentiating G with respect to temperature at constant pressure we get

[(G/T]_P = -S                                                                                            (22)

                                                                                                                         Substituting the value of [(G/T]_P from equation (20) gives

-nF_{P =} S

or

S = nF_P                                                                                                                  (23)

Eqn (23) above can be used for calculating entropy changes from the temperature coefficient of the cell.

Although electrochemical methods of determining the thermodynamics quantities G, H and S are most attractive in theory, in practice it is difficult to obtain accurate results unless immense precautions are taken during the experiment. The values obtained can only be regarded as approximate.

Exercise 5

Given the following electrochemical cell

Pb/PbCl₂/HCl (1M)/AgCI/Ag

The Emf of the cell at 298K is 0.490V. If the rate of change of the Emf with temperature is 1.86 x 10^-4 volt/degree, calculate G, H and S for the cell reaction.