Thermodynamic quantities of cell reactions

Thermodynamic quantities of cell reactions

The Gibbs free energy change at a given temperature for the overall cell reaction for an electrochemical cell can be obtained from the reversible e.m.f. (E) of the cell determined by Poggendorf’s compensation method.

ΔG= –nF E

where n is the number of faradays of electricity delivered by the cell. E is positive by convention and being an intensive quantity, does not depend on how the stoichiometric equation for the spontaneous overall cell reaction is written. But ΔG being an extensive quantity does depend on how the overall cell reaction is written. The same is true about the corresponding enthalpy and the entropy changes (ΔH and ΔS). These thermodynamic quantities are usually expressed in kJ mol–1 (ΔS in J K–1 mol–1) when these become intensive quantities.

From thermo dynamics we have,

Δ = – [ ∂ΔG/∂T]p

or ΔS = nF[∂E/∂T]p

since –ΔG = nF E

The temperature coefficient of the cell e.m.f., (∂E/∂T)p can be obtained by determining the e.m.f at various temperatures.

Again from thermodynamics we have,

          ΔG = ΔH – TΔS

Or     –n F E = ΔH – TΔS

or     ΔH = – n F E + TΔS

or     ΔH = – nF E + TnF [ ∂E/∂T]p

Thus the enthalpy change associated with the overall cell reaction for a reversible cell can be determined from the reversible e.m.f. (E) and the temperature coefficient of the reversible e.m.f. of the cell, .The equilibrium constant is related to standard Gibbs free energy, ΔG^O (or – n F E^O ). Hence we obtain

Since ΔG^O = – RT ln K

Or     – n F E^O = – RT ln K

         ln K = —[ nF E^O/RT]

The above equation enables one to calculate the equilibrium constant of an overall cell reaction at a given temperature from the experimentally determined value of the standard e.m.f. of the cell at the same temperature.

We have seen earlier that the Weston Cadmium Cell has an e.m.f. (E) of 1.01463 V at 298 K and a temperature coefficient of -5.00 × 10^–5 V K^–1. These two data help us to calculate the thermodynamic quantities of the overall cell reaction.

ΔG = – n F E

      = – 2 × 96500 C mol^–1 × 1.01463 V

      = –195824 Jmol^-1

ΔS = nF[ ∂ E/∂T]p

     = 2 (96500 C mol^–1) × (– 5.00 × 10^–5) V K^–1

     = – 9.65 Jmol^-1 K^–1

ΔH = ΔG + T ΔS

      = – 195824 Jmol^-1 + 298 K (– 9.65 Jmol^-1 K^–1)

      = -198700 Jmol^-1

Electrochemistry II: Voltaic or Galvanic cells

Suhaschandra Ghosh and Animesh Kumar Rakshit, 2010, 16