Question

Write the relationship between the standard free energy change and standard cell potential. How much charge is required for the reduction of 1 mole of $C{{u}^{2+}}$ to $Cu$?

Answer 1

By standard free energy, we means the formation of 1 mole of products and by standard cell potential we means difference in potential across the two electrons and both should be in their standard states and we can calculate the charge required for the reduction by simply applying the formula as: $Q = nF$. Now answer the statement.

Complete Solution :
Now, let’s first discuss what is standard Gibbs energy and standard cell potential. By the standard Gibbs free energy, we mean the energy which is required for the formation of 1mole of the substance from its constituents elements or the substances in their standard states i.e. their concentrations should be one mole per litre, pressure should be 1 atmosphere and temperature should be 273K. It is denoted by the symbol as: $\Delta {{G}^{\circ }}$.

- On the other by the standard cell potential we means the cell potential difference between the cathode ( i.e. positively charged) and the anode ( i.e. negatively charged) in their standard states i.e. their concentrations should be one mole per litre, pressure should be 1 atmosphere and temperature should be 273K. It is denoted by the symbol as: $E_{cell}^{\circ }$.

- The relationship between the standard free Gibbs energy and the standard cell potential is as:
$\Delta {{G}^{\circ }}=-nFE_{cell}^{\circ }$ ------------(1)
Here, n is the number of moles of electrons transferred, F is the Faraday’s constant i.e. the charge on one mole of electrons.

- Now, coming to the next part of the question:
Reduction of $C{{u}^{2+}}$ to $Cu$ occurs as:
$C{{u}^{2+}}+2{{e}^{-}}\to Cu$
And we know, that;
$\begin{aligned} & Q=nF \\\ & \text{ = 2}\times \text{96500 (n=2, F=96500C)} \\\ & \text{ =193000C} \\\ \end{aligned}$
Therefore, the charge required for the reduction of 1 mole of $C{{u}^{2+}}$ to $Cu$ is $193000C$.

Note: If we know the value of standard free energy change and the no. of electrons, then we can easily calculate the value of the standard cell potential by using the equation (1) i.e. $\Delta {{G}^{\circ }}=-nFE_{cell}^{\circ }$ and vice-versa.