What is the free energy change, `'DeltaG'` When 1.0 mole of water at `100^(@)C` and 1 atm pressure is converted into steam at `100^(@)C` and 1 atm pressure

Options

A. 549 cal
B. `-9800 cal`
C. 9800 cal
D. 0 cal

Answer

To calculate the free energy change (ΔG) when 1 mole of water at 100°C and 1 atm pressure is converted into steam at the same temperature and pressure, we can use the following formula:

\[ \Delta G = 2.303 \, n \, R \, T \, \log \left( \frac{P_2}{P_1} \right) \]

### Step-by-Step Solution:

1. **Identify the variables**:
- Number of moles (n) = 1 mole
- Gas constant (R) = 2 cal/(K·mol) (or 8.314 J/(K·mol) if using SI units)
- Temperature (T) = 100°C = 373 K (Convert Celsius to Kelvin by adding 273)
- Initial pressure (P1) = 1 atm
- Final pressure (P2) = 1 atm

2. **Calculate the ratio of pressures**:
\[ \frac{P_2}{P_1} = \frac{1 \, \text{atm}}{1 \, \text{atm}} = 1 \]

3. **Calculate the logarithm**:
\[ \log(1) = 0 \]

4. **Substitute the values into the ΔG equation**:
\[ \Delta G = 2.303 \times 1 \times 2 \times 373 \times 0 \]

5. **Simplify the equation**:
\[ \Delta G = 0 \, \text{calories} \]

### Conclusion:
The free energy change (ΔG) when 1 mole of water is converted into steam at 100°C and 1 atm pressure is **0 calories**.