. Thermodynamics of cell reactions We have just learnt that in a galvanic cell, the chemical energy is converted into electrical energy. The electrical energy produced by the cell is equal to the product of the total charge of electrons and the emf of the cell which drives these electrons between the electrodes. If ‘n’ is the number of moles of electrons exchanged between the oxidising and reducing agent in the overall cell reaction, then the electrical energy produced by the cell is given as below.
Electrical energy = Charge of ’n’ mole of electrons E cel l ......( . ) Charge of mole of electrons = one Faraday (1F) Charge of ’n’ mole ∴ of electrons = nF Equation ( . ) Electrical energy = nF ⇒ E cell ......( . Charge of one elctron = .
Charge - ∴ one mole of elctron = . = 96488 C i.e., 1F 96500 C This energy is used to do the electric work. Therefore the maximum work that can be obtained from a galvanic cell is (W = - nFE max cell cell .....( . ) Here the (-) sign is introduced to indicate that the work is done by the system on the surroundings.
We know from the Second Law of thermodynamics that the maximum work done by the system is equal to the change in the Gibbs free energy of the system. max i.e., W = G ∆ .....( . ) From ( . ) and ( .
), D G = - nFE cell .....( . ) For a spontaneous cell reaction, the D G should be negative. The above expression ( . ) indicates that E cell should be positive to get a negative D G value.
When all the cell components are in their standard state, the equation ( . ) becomes D G = - nFE o cell o .....( . ) We know that the standard free energy change is related to the equilibrium constant as per the following expression. XII U9 Electro XII U9 Electro - - - - D G = - RT lnK o eq .....( .
) Comparing ( . ) and ( . ), nFE = RT lnK cell eq ⇒ E = . RT nF log K cell eq .....( .
) . . Nernst equation Nernst equation is the one which relates the cell potential and the concentration of the species involved in an electrochemical reaction. Let us consider an electrochemical cell for which the overall redox reaction is, x y l A B mD The reaction quotient Q for the above reaction is given below Q = [C] [D] [A] [B] m x y l .....( .
) We have already learnt that, D D G = G + RT lnQ .....( . ) The Gibbs free energy can be related to the cell emf as follows ∴