Question:
\(\Delta G^\circ\) value for the following oxidation process is:
\[
A \rightarrow A^{3+} + 3e^-
\]
Given:
\[
A \rightarrow A^+ + e^- \quad \Delta G^\circ = 1J
\]
\[
A^+ \rightarrow A^{3+} + 2e^- \quad \Delta G^\circ = 3J
\]
\(\Delta G^\circ\) value for the following oxidation process is:
\[ A \rightarrow A^{3+} + 3e^- \] Given: \[ A \rightarrow A^+ + e^- \quad \Delta G^\circ = 1J \] \[ A^+ \rightarrow A^{3+} + 2e^- \quad \Delta G^\circ = 3J \]
\[ A \rightarrow A^{3+} + 3e^- \] Given: \[ A \rightarrow A^+ + e^- \quad \Delta G^\circ = 1J \] \[ A^+ \rightarrow A^{3+} + 2e^- \quad \Delta G^\circ = 3J \]
Show Hint
\(\Delta G^\circ\) is a state function, so for multi-step reactions always add the Gibbs energies of individual steps.
Updated On: Jun 19, 2026
- 1 J
- 2 J
- 3 J
- 4 J
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the concept of Gibbs free energy additivity.
Gibbs free energy change (\(\Delta G^\circ\)) is a state function, which means it depends only on initial and final states. Therefore, when a reaction occurs in multiple steps, the total \(\Delta G^\circ\) is the algebraic sum of individual steps.
Step 2: Identifying the target reaction.
We are required to find: \[ A \rightarrow A^{3+} + 3e^- \] This is a three-electron oxidation process, and it can be constructed using the given stepwise reactions.
Step 3: Writing the given steps clearly.
First step: \[ A \rightarrow A^+ + e^- \quad (\Delta G^\circ = 1J) \] Second step: \[ A^+ \rightarrow A^{3+} + 2e^- \quad (\Delta G^\circ = 3J) \]
These two steps together exactly produce the required overall reaction.
Step 4: Adding Gibbs free energy changes.
Since \(\Delta G^\circ\) is additive: \[ \Delta G^\circ_{total} = 1J + 3J \] \[ \Delta G^\circ_{total} = 4J \]
Step 5: Physical interpretation.
The total free energy change for multi-step electron removal equals the sum of free energies of each electron removal step, irrespective of the number of electrons involved in each intermediate step.
Step 6: Final verification.
Thus, the oxidation of \(A\) to \(A^{3+}\) with removal of 3 electrons has total Gibbs free energy change equal to 4 J.
Final Answer: \[ \boxed{4J} \]
Gibbs free energy change (\(\Delta G^\circ\)) is a state function, which means it depends only on initial and final states. Therefore, when a reaction occurs in multiple steps, the total \(\Delta G^\circ\) is the algebraic sum of individual steps.
Step 2: Identifying the target reaction.
We are required to find: \[ A \rightarrow A^{3+} + 3e^- \] This is a three-electron oxidation process, and it can be constructed using the given stepwise reactions.
Step 3: Writing the given steps clearly.
First step: \[ A \rightarrow A^+ + e^- \quad (\Delta G^\circ = 1J) \] Second step: \[ A^+ \rightarrow A^{3+} + 2e^- \quad (\Delta G^\circ = 3J) \]
These two steps together exactly produce the required overall reaction.
Step 4: Adding Gibbs free energy changes.
Since \(\Delta G^\circ\) is additive: \[ \Delta G^\circ_{total} = 1J + 3J \] \[ \Delta G^\circ_{total} = 4J \]
Step 5: Physical interpretation.
The total free energy change for multi-step electron removal equals the sum of free energies of each electron removal step, irrespective of the number of electrons involved in each intermediate step.
Step 6: Final verification.
Thus, the oxidation of \(A\) to \(A^{3+}\) with removal of 3 electrons has total Gibbs free energy change equal to 4 J.
Final Answer: \[ \boxed{4J} \]
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