Calculate Δ G° and K at 25°C for the reactions in Exercises 37 and 41.

Interpretation:

The equations for different chemical reactions are given. The value of ΔG° and K for different reactions is to be calculated.

Concept introduction:

The relationship between reduction potential and standard reduction potential value and activities of species present in an electrochemical cell at a given temperature is given by the Nernst equation.

The value of Ecell is calculated using Nernst formula,

E=E°−(RTnF)ln(Q)

At room temperature the above equation is specifies as,

E=E°−(0.0591n)log(Q)

This relation is further used to determine the relation between ΔG° and K , ΔG° and E°cell .

To determine: The value of ΔG° and K for different reactions.

The given cell reaction is,

Cr3+(aq)+Cl2(g)⇌Cr2O72−(aq)+Cl−(aq)

The reaction taking place on cathode,

Cl2(g)+2e−→2Cl−(aq)   E°red=1.36 V

The reaction taking place at anode,

2Cr3+(aq)+7H2O(l)→Cr2O72−(aq)+14H+(aq)+6e−   E°ox=−1.33 V

Multiply reduction half-reaction with a coefficient of 3 and then add both the reduction half and oxidation half-reaction.

Cl2(g)+2e−→2Cl−(aq)   2Cr3+(aq)+7H2O(l)→Cr2O72−(aq)+14H+(aq)+6e−   

The overall cell reaction is,

2Cr3+(aq)+7H2O(l)+3Cl2(g)→Cr2O72−(aq)+14H+(aq)+6Cl−(aq)

The overall cell potential is calculated as,

E°cell=E°ox+E°red=−1.33 V+(1.36 V)=0.03 V_

The relationship between cell potential and Gibbs free energy change is given by the formula,

ΔG°=−nFE°cell

Where,

• ΔG° is the Gibbs free energy change at the standard conditions.
• n is the number of electrons involved in the reaction.
• F is the Faraday’s constant.
• E°cell is the cell potential at the standard condition.

The number of moles of electrons involved in the reaction is 6 .

Substitute the values in above equation,

ΔG°=−(6 mol e−)(96,485Cmol e-)(0.03JC)=−17,367.3 J=-17.36 kJ_

The value of ΔG° is calculated as -17.36 kJ_

The relationship between Gibbs free energy change and equilibrium constant is given by the formula,

ΔG°=−RTlnK=−nFE°cell

Where,

• ΔG° is the Gibbs free energy change at the standard conditions.
• R  is the universal gas constant.
• T is the temperature in Kelvin.
• K is the equilibrium constant.

Rearranged equation at 25 °C is obtained as,

log K=(−(n)(E°)0.0591)

Substitute the obtained values in above equation,

log K=(−(6)(0

Interpretation:

The equations for different chemical reactions are given. The value of ΔG° and K for different reactions is to be calculated.

Concept introduction:

The relationship between reduction potential and standard reduction potential value and activities of species present in an electrochemical cell at a given temperature is given by the Nernst equation.

The value of Ecell is calculated using Nernst formula,

E=E°−(RTnF) ln(Q)

At room temperature the above equation is specifies as,

E=E°−(0.0591n) log(Q)

This relation is further used to determine the relation between ΔG° and K , ΔG° and E°cell .

To determine: The standard line notation for the given cell reaction.