Question

\(\Delta G^\circ\) value for the following oxidation process is:
\[ A \rightarrow A^{3+} + 3e^- \] Given: \[ A \rightarrow A^+ + e^- \quad \Delta G^\circ = 1J \] \[ A^+ \rightarrow A^{3+} + 2e^- \quad \Delta G^\circ = 3J \]

• A. 1 J
• B. 2 J
• C. 3 J
• D. 4 J

Hint:

\(\Delta G^\circ\) is a state function, so for multi-step reactions always add the Gibbs energies of individual steps.

Answer 1

The Correct Option is D

Step 1: State function property.
ΔG° depends solely on initial and final states, so overall ΔG° for a multistep process is the sum of stepwise ΔG° values.

Step 2: Target half-reaction.
The desired overall oxidation is A → A³⁺ + 3e⁻.

Step 3: Given sequential steps.
Step 1: A → A⁺ + e⁻ (ΔG° = 1 J). Step 2: A⁺ → A³⁺ + 2e⁻ (ΔG° = 3 J). Summation yields the complete three-electron oxidation.

Step 4: Summing the free energies.
ΔG°_total = 1 J + 3 J = 4 J.

Step 5: Conceptual note.
The total free energy change for successive electron removals equals the arithmetic sum of individual step energies.

Step 6: Conclusion.
Thus, the Gibbs free energy change for A → A³⁺ + 3e⁻ is 4 J.