Which of the following statement is correct ?

Options

A. `E_(Cell)` and `Delta_(r)G` of cell reaction both extensive properties.
B. `E_(Cell) and Delta_(r)G` of cell reaction both intensive properties.
C. `E_(Cell)` is an intensive property while `Delta_(r)G` of cell reaction is an extensive property.
D. `E_(Cell)` is an extensive property while `Delta_(r)G` of cell reaction is an intensive property.

Explanation

To determine which statement is correct regarding the properties of E_cell (cell potential) and ΔG (Gibbs free energy) in electrochemistry, we can analyze the definitions and relationships between these two properties.

### Step-by-Step Solution:

1. **Understanding Extensive and Intensive Properties**:
- **Extensive Properties**: These properties depend on the amount of substance present. Examples include mass, volume, and total energy.
- **Intensive Properties**: These properties do not depend on the amount of substance. Examples include temperature, pressure, and density.

2. **Formula for Gibbs Free Energy (ΔG)**:
- The relationship between Gibbs free energy and cell potential is given by the equation:
\[ \Delta G = -nFE_{cell} \]
- Here, \( n \) is the number of moles of electrons transferred, \( F \) is Faraday's constant, and \( E_{cell} \) is the cell potential.

3. **Analyzing ΔG**:
- Since ΔG is directly proportional to \( n \) (the number of moles), if the amount of substance changes, ΔG will also change. Therefore, ΔG is an extensive property.

4. **Analyzing E_cell**:
- Rearranging the equation gives:
\[ E_{cell} = -\frac{\Delta G}{nF} \]
- In this equation, \( E_{cell} \) is expressed per mole of electrons (since it is divided by \( n \)). Thus, it does not change with the amount of substance, making E_cell an intensive property.

5. **Conclusion**:
- From the analysis, we conclude that ΔG is an extensive property, while E_cell is an intensive property. Therefore, the correct statement is:
- E_cell is intensive and ΔG is extensive.

### Final Answer:
The correct statement is: **E_cell is intensive and ΔG is extensive.**