Question

Consider the electrochemical reactions shown below. Mercury(I) chloride, also known as calomel, is a solid used in reference electrodes. The two reactions are

Zn = Zn²⁺ + 2e^-

Hg₂Cl₂ + 2e^- = 2Cl^- + 2Hg

1. What is the overall chemical reaction?
2. Develop an expression for U, the equilibrium potential of the cell.
3. Write down an expression for the standard potential of the cell in terms of the standard Gibbs energies of formation.
4. Use standard half-cell potentials from the table to determine the standard Gibbs energy of formation for aqueous ZnCl₂. Why is this value different than the value for solid ZnCl₂?
5. What is the standard Gibbs energy of formation for Hg₂Cl₂?

Answer 1

The two reactions are:

Zn = Zn2+ + 2e-

Hg2Cl2 +2e- = 2Cl- + 2Hg

Adding the two reactions we get the overall reactions:

Zn + Hg2Cl2 = Zn2+ + 2Cl- + 2Hg

which is the required overall reaction.

The potential for this cell is given by:

At equilibrium; Ecell = 0

Here; n = 2 (as 2 electrons are exchanged)

Therefore;

or;

which is the equation of the required equilibrium potential.

In a galvanic cell, the Gibbs free energy is related to the equilibrium potential by:

ΔG° = −nFU

where ΔG° is the gibbs free energy change of the above overall chemical reaction.

Here; n = 2

Therefore;

ΔG° = −2FU

Rearranging; we get:

U = - ΔG° / 2F

The  ΔG° for the overall reaction is:

Substituting this expression of ΔG° in the above expression of U we get:

which is the required expression.

The standard gibbs energy of formation of ZnCl2 is given by:

ΔGo(ZnCl2 (aq)) = [1 X ΔGo(Zn+2 (aq)) + 2 XΔGo(Cl-1 (aq))] - [1 X ΔGo(ZnCl2 (s))]

From ΔG° values:
ΔGo(ZnCl2 (aq)) = [1 X ΔGo(Zn+2 (aq)) + 2 XΔGo(Cl-1 (aq))] - [1 X ΔGo(ZnCl2 (s))]

ΔGo(ZnCl2 (aq)) = [1(-147.1) + 2(-131.25)] - [1(-369.43)] = - 40.17 kJ

The standard Gibbs energy of formation for aqueous ZnCl2 is different than the value for solid ZnCl2 because it also includes the solvation energy required for solvating the ions.

The standard gibbs energy of formation of Hg2Cl2 is given by:

ΔGo(Hg2Cl2 (aq)) = [1 X ΔGo(Hg2+2 (aq)) + 2 XΔGo(Cl-1 (aq))] - [1 X ΔGo(Hg2Cl2 (s))]

From ΔGf° values:

ΔGo(Hg2Cl2 (aq)) = [1 X ΔGo(Hg2+2 (aq)) + 2 XΔGo(Cl-1 (aq))] - [1 X ΔGo(Hg2Cl2 (s))]

ΔGo(Hg2Cl2 (aq)) = [1(153.5) + 2(-131.25)] - [1(-210.78)] = 101.78 kJ