Question

Which from the following is the correct relationship between standard Gibbs energy change and standard cell potential?

• A. $-\Delta G^\circ = -nFE_{\mathrm{cell}}^\circ$
• B. $\Delta G^\circ = \frac{E_{\mathrm{cell}}^\circ}{nF}$
• C. $E_{\mathrm{cell}}^\circ = \Delta G^\circ \times nF$
• D. $\Delta G^\circ = -nFE_{\mathrm{cell}}^\circ$

Hint:

Spontaneous reactions always have a negative Gibbs free energy change ($\Delta G^\circ < 0$) and a positive cell potential ($E_{\mathrm{cell}}^\circ > 0$). The minus sign in $\Delta G^\circ = -nFE_{\mathrm{cell}}^\circ$ ensures that these two conditions physically align!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem asks for the standard thermodynamic equation that relates the standard Gibbs free energy change ($\Delta G^\circ$) of an electrochemical reaction to its standard cell potential ($E_{\mathrm{cell}}^\circ$).

Step 2: Key Formula or Approach:
The maximum electrical work ($W_{\mathrm{max}}$) done by an electrochemical cell is equal to the decrease in Gibbs free energy ($\Delta G$) of the system: $$W_{\mathrm{max}} = -\Delta G$$ Electrical work is also defined as the total charge passed multiplied by the cell potential: $$W_{\mathrm{electrical}} = \text{Charge} \times E_{\mathrm{cell}} = nFE_{\mathrm{cell}}$$ Under standard state conditions, these values are directly converted to their standard forms.

Step 3: Detailed Explanation:
Equating the maximum electrical work done by the system to the standard Gibbs free energy change gives: $$-\Delta G^\circ = nFE_{\mathrm{cell}}^\circ$$ Multiplying both sides by $-1$ yields the standard form of the relationship: $$\Delta G^\circ = -nFE_{\mathrm{cell}}^\circ$$ Where:

• $\Delta G^\circ$ is the standard Gibbs free energy change.

• $n$ is the number of moles of electrons exchanged in the balanced redox reaction.

• $F$ is the Faraday constant ($\approx 96485\ \mathrm{C\ mol^{-1}}$).

• $E_{\mathrm{cell}}^\circ$ is the standard electromotive force (EMF) or standard potential of the cell.
Evaluating the choices, option (D) perfectly matches this mathematical expression.

Step 4: Final Answer:
The correct relationship is $\Delta G^\circ = -nFE_{\mathrm{cell}}^\circ$, corresponding to option (D).