Statement : If two half reaction with electrode potential `E_(1)^(@)` and `E_(2)^(@)` gives a third reaction then,
`DeltaG_(3)^(@) = DeltaG_(1)^(@) + DeltaG_(2)^(@)`
Explanation : `E_(3)^(@) = E_(1)^(@) + E_(2)^(@)`

Options

A. STATEMENT-1 is True, STATEMENT-2 is True, STATEMENT -2 is correct explanation for STATEMENT-1
B. STATEMENT 1 is True, STATEMENT-2 Is True, STATEMENT -2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT - 1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True

Answer

To solve the question, we need to analyze the statements regarding the relationship between the Gibbs free energy change (ΔG) and the standard electrode potentials (E) of half-reactions.

### Step-by-Step Solution:

1. **Understanding the Gibbs Free Energy Change (ΔG)**:
- The Gibbs free energy change (ΔG) is a thermodynamic potential that can predict the direction of chemical reactions. It is an extensive property, meaning it depends on the amount of substance present.
- For a reaction, the relationship between ΔG and the standard electrode potential (E) is given by the equation:
\[ \Delta G = -nFE \]
where:
- \( n \) = number of moles of electrons transferred,
- \( F \) = Faraday's constant (approximately 96485 C/mol),
- \( E \) = standard electrode potential.

2. **Applying the Relationship to Half-Reactions**:
- For two half-reactions with standard electrode potentials \( E_1^{\circ} \) and \( E_2^{\circ} \):
- The Gibbs free energy changes for these half-reactions can be expressed as:
\[ \Delta G_1^{\circ} = -n_1FE_1^{\circ} \]
\[ \Delta G_2^{\circ} = -n_2FE_2^{\circ} \]

3. **Combining the Half-Reactions**:
- When these two half-reactions are combined to form a third reaction, the Gibbs free energy change for the overall reaction (ΔG3) can be expressed as:
\[ \Delta G_3^{\circ} = \Delta G_1^{\circ} + \Delta G_2^{\circ} \]
- This is valid because ΔG is an extensive property and can be added for the overall reaction.

4. **Analyzing the Electrode Potentials**:
- The standard electrode potential for the overall reaction (E3) is related to the individual potentials:
\[ E_3^{\circ} \neq E_1^{\circ} + E_2^{\circ} \]
- This is because electrode potential is an intensive property, which means it does not depend on the amount of material and cannot be simply added.

5. **Conclusion**:
- The first statement regarding ΔG is correct:
\[ \Delta G_3^{\circ} = \Delta G_1^{\circ} + \Delta G_2^{\circ} \]
- The second statement regarding the electrode potentials is incorrect:
\[ E_3^{\circ} \neq E_1^{\circ} + E_2^{\circ} \]

### Final Answer:
- The correct option is that the first statement is true, and the second statement is false.