Which of the following statements is correct?

Options

A. `E_(cell)^(@) and Delta_(r) G` of cell reaction both are extensive properties
B. `E_(cell)^(@) and Delta_(r)G` of cell reaction both are intensive properties
C. `E_(cell)^(@)` is an intensive properrty 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.

Answer

To solve the question, we need to analyze the properties of standard cell potential and free energy change of a cell reaction. Let's break down the steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Intensive Properties**: These are properties that do not depend on the amount of substance present. Examples include boiling point, density, and standard cell potential.
- **Extensive Properties**: These are properties that depend on the quantity of substance present. Examples include mass, volume, and Gibbs free energy change.

2. **Identify the Properties of Standard Cell Potential**:
- The standard cell potential (E°cell) is a measure of the voltage of a cell reaction under standard conditions. It is an intensive property because it does not change with the amount of reactants or products present.

3. **Identify the Properties of Free Energy Change of Reaction**:
- The free energy change (ΔG) of a reaction is calculated using the Gibbs Helmholtz equation: ΔG = ΔH - TΔS. This value is dependent on the amount of substance involved in the reaction, making it an extensive property.

4. **Analyze the Options**:
- **Option A**: "Standard cell potential and free energy change of reaction of cell reaction both are extensive." - This is incorrect because standard cell potential is intensive.
- **Option B**: "Standard cell potential and standard reaction free energy of cell reaction both are intensive." - This is incorrect because free energy change is extensive.
- **Option C**: "Standard cell potential is an intensive property while free energy change of reaction of cell reaction is extensive." - This is correct.
- **Option D**: "Standard cell potential is an extensive property while free energy change of reaction of cell reaction is an intensive property." - This is incorrect because standard cell potential is intensive.

5. **Conclusion**:
- The correct statement is **Option C**: "Standard cell potential is an intensive property while free energy change of reaction of cell reaction is extensive."