Consider a galvanic cell based on the following half-reactions:

a. What is the standard potential for this cell?

b. A nonstandard cell is set up at 25°C with [Mg²⁺] = 1.00 × 10⁻⁵ M. The cell potential is observed to be 4.01 V. Calculate [Au³⁺] in this cell.

Interpretation:

The half-reactions taking place in a galvanic cell is given. The value of standard cell potential and the concentration of Au3+ 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 specifies as,

E=E°−(0.0591n)log(Q)

To determine: The value of the standard cell potential for the given cell.

The value of standard cell potential is 3.87 V_ .

The reaction taking place at the cathode is,

Au3++3e−→Au   E°red=1.50 V

The reaction taking place at the anode is,

Mg→Mg2++2e−   E°OX=2.37 V

Multiply reduction half-reaction with a coefficient of 2 and oxidation half-reaction with a coefficient of 3 and then add both the reactions as,

2Au3++6e−→2Au   3Mg→3Mg2++6e−   

The final equation is,

2Au3++3Mg→2Au+3Mg2+     </

Interpretation:

The half-reactions taking place in a galvanic cell is given. The value of standard cell potential and the concentration of Au3+ 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 specifies as,

E=E°−(0.0591n)log(Q)

To determine: The concentration of Au3+ for the given cell.

The concentration of Au3+ in the cell is 6.02×108 M_ .