The normal boiling point of a liquid X is 400 K. Which of the following statement is true about the process `X(l) to X(g)` ?

Options

A. at 400 K and 1 atm pressure `DeltaG = 0`
B. at 400 K and 2 atm pressure `DeltaG = + ve`
C. at 400 K and 0.1 atm pressure `DeltaG = - ve`
D. at 410 K and 1 atm pressure `DeltaG = + ve`

Explanation

To determine which statements are true about the process of converting liquid X to gas X at its normal boiling point of 400 K, we can analyze the thermodynamic principles involved.

### Step-by-Step Solution:

1. **Understanding Normal Boiling Point**:
- The normal boiling point of a substance is the temperature at which its vapor pressure equals the external pressure (1 atm). At this point, the liquid and gas phases are in equilibrium.

2. **Analyzing the First Statement**:
- At 400 K and 1 atm, the process \( X(l) \rightarrow X(g) \) is at equilibrium. Therefore, the change in Gibbs free energy (\( \Delta G \)) for this process is zero.
- **Conclusion**: The first statement is true: \( \Delta G = 0 \).

3. **Analyzing the Second Statement**:
- If the pressure is increased to 2 atm at 400 K, the equilibrium will shift towards the liquid phase (as per Le Chatelier's principle). This means that the conversion of liquid to gas is less favorable.
- Therefore, \( \Delta G \) will be positive, indicating a non-spontaneous reaction.
- **Conclusion**: The second statement is true: \( \Delta G > 0 \).

4. **Analyzing the Third Statement**:
- If the pressure is decreased to 0.1 atm at 400 K, the equilibrium will shift towards the gaseous phase. This means that the conversion of liquid to gas becomes more favorable.
- Therefore, \( \Delta G \) will be negative, indicating a spontaneous reaction.
- **Conclusion**: The third statement is true: \( \Delta G < 0 \).

5. **Analyzing the Fourth Statement**:
- At 410 K and 1 atm, the temperature is above the normal boiling point. The reaction will favor the gaseous phase, making the conversion spontaneous.
- Therefore, \( \Delta G \) should be negative, but the statement claims \( \Delta G > 0 \).
- **Conclusion**: The fourth statement is false: \( \Delta G \) should be negative.

### Final Answer:
The true statements are the first, second, and third statements.