Which of the following is true fo the reacion `H_(2)O(l)hArr H_(2)O(g)` at `100^(@)C` and 1 atmosphere

Options

A. `Delta S = 0`
B. `Delta H = 0`
C. `Delta H = Delta E`
D. `Delta H = T Delta S`

Answer

To solve the question regarding the reaction \( H_2O(l) \rightleftharpoons H_2O(g) \) at \( 100^\circ C \) and 1 atmosphere, we need to analyze the thermodynamic properties of the reaction.

### Step-by-Step Solution:

1. **Identify the Reaction**: The reaction involves the phase change of water from liquid to gas at a specific temperature and pressure. This is a common equilibrium process.

2. **Understand the Conditions**: The reaction occurs at \( 100^\circ C \) (which is \( 373 \, K \)) and at 1 atmosphere pressure. At this temperature, water is at its boiling point.

3. **Apply the Gibbs Free Energy Equation**: The Gibbs free energy change (\( \Delta G \)) for a reaction at equilibrium is given by:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- \( \Delta G \) is the change in Gibbs free energy,
- \( \Delta H \) is the change in enthalpy,
- \( T \) is the temperature in Kelvin,
- \( \Delta S \) is the change in entropy.

4. **Equilibrium Condition**: At equilibrium, \( \Delta G = 0 \). Therefore, we can set up the equation:
\[ 0 = \Delta H - T \Delta S \]
Rearranging gives:
\[ \Delta H = T \Delta S \]

5. **Interpret the Result**: The equation \( \Delta H = T \Delta S \) indicates that at the boiling point of water (100°C), the enthalpy change of vaporization (\( \Delta H \)) is equal to the product of the temperature and the entropy change (\( \Delta S \)). This is a characteristic of phase transitions.

6. **Conclusion**: Therefore, the correct statement regarding the reaction \( H_2O(l) \rightleftharpoons H_2O(g) \) at \( 100^\circ C \) and 1 atmosphere is that \( \Delta H = T \Delta S \).

### Final Answer:
The correct option is **D: \( \Delta H = T \Delta S \)**.

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