Question

How does temperature affect the Nernst equation?

Answer 1

Hint:The Nernst equation establishes the relation between cell potential (E), temperature (T) and reaction quotient (Q). It is used to measure cell potential under non-standard conditions using given equation:
\[{{\text{E}}_{\text{cell}}}=\text{E}_{\text{cell}}^{\text{o}}-\dfrac{\text{RT}}{\text{nF}}\ln \text{Q}\]

Complete step-by-step answer:The Nernst equation was established to find out the cell potential of a galvanic cell under non-standard conditions. To understand the effect of temperature in the Nernst equation, let us first derive the actual Nernst equation.
Under standard conditions, the cell potential $\left( \text{E}_{\text{cell}}^{\text{o}} \right)$ and Gibbs free energy $\left( \Delta {{\text{G}}^{\text{o}}} \right)$ are given as follows:
\[\text{E}_{\text{cell}}^{\text{o}}=\text{E}_{\text{reduction half-cell}}^{\text{o}}-\text{E}_{\text{oxidation half-cell}}^{\text{o}} \\
 \Delta {{\text{G}}^{\text{o}}}=-\text{nFE}_{\text{cell}}^{\text{o}}\text{ }................(1) \\
\]
And for non-standard condition: $\Delta \text{G}=-\text{nF}{{\text{E}}_{\text{cell}}}\text{ }.....................\text{ (2)}$
Where ‘n’ is the number of electrons transferred in balanced cell reaction and ‘F’ is Faraday constant.
The thermodynamic relation of Gibbs free energy change under standard and non-standard condition is given as:
\[\Delta \text{G}=\Delta {{\text{G}}^{\text{o}}}+\text{RTlnQ }..............\text{ (3)}\]
 Where ‘R’ is the universal gas constant, ‘T’ is temperature and ‘Q’ is the reaction quotient.
Now, substituting the values from equation (1) and (2) in equation (3):
\[-\text{nF}{{\text{E}}_{\text{cell}}}=-\text{nFE}_{\text{cell}}^{\text{o}}+\text{RTlnQ} \\
 \Rightarrow {{\text{E}}_{\text{cell}}}=\text{E}_{\text{cell}}^{\text{o}}-\dfrac{\text{RT}}{\text{nF}}\ln \text{Q} \\
\]
The above equation is known as the Nernst equation. It indicates that the potential of a cell is dependent on temperature. For any given galvanic cell, as the temperature increases the cell potential decreases as other terms will remain constant for that particular cell.
Hence, the temperature does not affect the Nernst equation but according to the equation, it is inversely proportional to the cell potential when other terms remain constant.

Additional information: There are many applications of the Nernst equation including measurement of the pH of a cell, equilibrium constant and solubility constant.

Note:The cell potential varies inversely with temperature for a cell if $\text{Q}\ne 1$. Also, when ${{\text{E}}_{\text{cell}}}$ is positive, $\Delta \text{G}$will be negative and the cell reaction will occur spontaneously. On the other hand, when ${{\text{E}}_{\text{cell}}}$ is negative, $\Delta \text{G}$ will be positive and thus the cell reaction will not occur spontaneously and such cells are said to be non-feasible.