To determine which of the statements are false, let's analyze each option step by step.
### Step-by-Step Solution:
1. **Option 1: All adiabatic processes are isoentropic processes.**
- **Analysis**: An adiabatic process is one where no heat is exchanged with the surroundings. An isoentropic process is both adiabatic and reversible. While all reversible adiabatic processes are isoentropic, not all adiabatic processes are reversible. Therefore, this statement is **false**.
2. **Option 2: If ΔG (Gibbs free energy) of the system at constant temperature and pressure is less than zero, then the reaction must be exothermic.**
- **Analysis**: A negative ΔG indicates that the process is spontaneous, but it does not necessarily mean that the reaction is exothermic. The reaction could also be endothermic under certain conditions. Therefore, this statement is **false**.
3. **Option 3: ΔG = Vdp - SdT is applicable for a closed system where both PV and non-PV work are considered.**
- **Analysis**: The equation ΔG = Vdp - SdT is valid for closed systems but is specifically applicable when only PV work is considered. Non-PV work is not included in this equation. Therefore, this statement is **false**.
4. **Option 4: When 9 g of water vapor is condensed into liquid at 100°C and 1 atm pressure, then ΔS (entropy of the system) is equal to 54.42 J/K.**
- **Analysis**: To calculate ΔS, we can use the formula:
\[
ΔS = -\frac{m}{M} \cdot ΔH_{vap} \cdot \frac{1000}{T}
\]
where:
- \( m = 9 \, \text{g} \)
- \( M = 18 \, \text{g/mol} \)
- \( ΔH_{vap} = 40.6 \, \text{kJ/mol} \)
- \( T = 373 \, \text{K} \)
Substituting the values:
\[
ΔS = -\frac{9}{18} \cdot 40.6 \cdot 1000 / 373
\]
This calculation yields approximately 54.42 J/K, confirming that this statement is **true**.
### Conclusion:
Based on the analysis:
- **False Statements**: Option 1, Option 2, Option 3
- **True Statement**: Option 4
Thus, the false statements are options 1, 2, and 3.
