Which of the following statement(s) is/are false?

Options

A. All adiabatic process are isoentropic (or isentropic) processes
B. When `(DeltaG_("system"))_(T,P)lt0,` the reaction must be exothermic
C. dG=VdP-SdT is applicable for closed system, both PV and non-PV work
D. The heat of vaporisation of water at `100^(@)C` is 40.6 kJ/mol. When 9 gm of water vapour condenses to liquid at `100^(@)C` and 1 atm, then `DeltaS_("system")` = 54.42 J/K

Explanation

To determine which of the statements are false, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement A**: "All adiabatic processes are isoentropic processes."
- **Analysis**: This statement is false. Only reversible adiabatic processes are isoentropic. In an isoentropic process, the entropy remains constant (ΔS = 0), which is only true for reversible processes. Therefore, this statement is false.

2. **Statement B**: "When ΔG of the system at constant temperature and pressure is less than zero, then the reaction must be exothermic."
- **Analysis**: This statement is also false. The Gibbs free energy change (ΔG) indicates the spontaneity of a reaction, not whether it is exothermic or endothermic. A reaction can have a negative ΔG and still be endothermic, depending on the enthalpy change (ΔH) and entropy change (ΔS). Thus, this statement is false.

3. **Statement C**: "dG = VdP - SdT is applicable for closed systems for both PV and non-PV work."
- **Analysis**: This statement is false. The equation dG = VdP - SdT is valid only for systems where the work done is pressure-volume (PV) work. It does not apply to non-PV work, such as electrical work. Therefore, this statement is false.

4. **Statement D**: "The heat of vaporization of water at 100 degrees Celsius is 40.6 kilojoules per mole. When 9 grams of water vapor condenses to liquid at 100 degrees Celsius and 1 atmosphere, the ΔS system is 54.42 joules per Kelvin."
- **Analysis**: To check this statement, we can calculate ΔS using the formula:
\[ \Delta S = \frac{\Delta H_{vaporization}}{T} \times n \]
Where:
- ΔH_vaporization = 40.6 kJ/mol = 40600 J/mol (conversion from kJ to J)
- T = 100°C = 373 K
- n = moles of water = \(\frac{9 \text{ g}}{18 \text{ g/mol}} = 0.5 \text{ mol}\)

Now substituting the values:
\[ \Delta S = \frac{40600 \text{ J/mol}}{373 \text{ K}} \times 0.5 \text{ mol} = \frac{40600}{373} \times 0.5 \approx 54.42 \text{ J/K} \]
This calculation confirms that the ΔS value is correct. Therefore, this statement is true.

### Conclusion:
The false statements are:
- Statement A
- Statement B
- Statement C