Standard Cell Potentials and Thermodynamics of Galvanic Cells

Galvanic cells are electrochemical cells that convert chemical energy into electrical energy. The standard potential of a galvanic cell is a measure of the cell's ability to produce electrical energy from the redox reactions occurring in the cell. The standard potential is denoted by E°cell and is a measure of the difference in the standard reduction potentials of the two half-reactions that occur in the cell. The standard potential of a galvanic cell can be calculated using the Nernst equation:

E°cell = E°cathode - E°anode

where E°cathode is the standard reduction potential of the cathode and E°anode is the standard reduction potential of the anode.

(i) Calculation of Standard Cell Potential and Thermodynamics for the Reaction: 2Cr(s) 3Cd2+(aq) → 2Cr3+(aq) 3Cd(s)

The half-reactions for the given cell reaction are:

Cr3+(aq) + 3e- → Cr(s) E° = -0.744 V
Cd2+(aq) + 2e- → Cd(s) E° = -0.403 V

Using the Nernst equation, we can calculate the standard cell potential as:

E°cell = E°cathode - E°anode
E°cell = 0.00 - (-0.744) = 0.744 V

The standard cell potential is positive, indicating that the reaction is spontaneous and can produce electrical energy.

The Gibbs free energy change (∆rG°) of the reaction can be calculated using the equation:

∆rG° = -nFE°cell

where n is the number of electrons transferred in the reaction and F is the Faraday constant (96,485 C/mol).

For the given reaction, n = 6 (3 electrons transferred in each half-reaction), and therefore:

∆rG° = -6 x 96,485 x 0.744 = -42,172 J/mol

The negative value of ∆rG° indicates that the reaction is spontaneous and can proceed to completion.

The equilibrium constant (K) of the reaction can be calculated using the equation:

∆rG° = -RT lnK

where R is the gas constant (8.314 J/mol K) and T is the temperature in Kelvin.

Assuming a temperature of 298 K, we can calculate the equilibrium constant as:

K = e^(-∆rG°/RT) = e^(-(-42,172)/ (8.314 x 298)) = 1.1 x 10^13

The high value of the equilibrium constant indicates that the reaction strongly favors the products and can proceed almost to completion.

(ii) Calculation of Standard Cell Potential and Thermodynamics for the Reaction: Fe2+(aq) Ag+(aq) → Fe3+(aq) Ag(s)

The half-reactions for the given cell reaction are:

Fe3+(aq) + e- → Fe2+(aq) E° = 0.771 V
Ag+(aq) + e- → Ag(s) E° = 0.799 V

Using the Nernst equation, we can calculate the standard cell potential as:

E°cell = E°cathode - E°an