Which of the following reactions will have the value of `DeltaS` with a negative sign?

Options

A. `H_(2)O_((l))rarrH_(2)O_((g))`
B. `2SO_(2(g))+O_(2(g))rarr2SO_(3(g))`
C. `Cl_(2(g))rarr2Cl_((g))`
D. `CaCO_(3(s))rarr CaO_((s))+CO_(2(g))`

Explanation

To determine which of the following reactions will have a negative value of ΔS (change in entropy), we need to analyze the changes in the number of moles of gas and the states of matter involved in each reaction. A negative ΔS indicates that the final state has less disorder or randomness compared to the initial state.

### Step-by-Step Solution:

1. **Understand the Concept of Entropy (ΔS)**:
- Entropy is a measure of disorder or randomness in a system. A negative ΔS indicates that the disorder has decreased.

2. **Analyze Each Reaction**:
- **Reaction 1**: Liquid to Gas
- When a liquid converts to a gas, the randomness increases (more microstates available), leading to a positive ΔS.
- **Reaction 2**: 2 moles of gas to 3 moles of gas
- More moles of gas means more randomness, thus ΔS is positive.
- **Reaction 3**: Cl2 gas to 2 Cl atoms (gas)
- Breaking a molecule into individual atoms increases randomness, so ΔS is positive.
- **Reaction 4**: CaCO3 (solid) decomposing to CaO (solid) and CO2 (gas)
- Here, a solid produces a gas, which increases randomness, resulting in a positive ΔS.
- **Reaction 5**: 2 moles of gas to 1 mole of gas
- This reaction reduces the number of gas moles, leading to decreased randomness and thus a negative ΔS.

3. **Conclusion**:
- Among the analyzed reactions, the only one that results in a decrease in entropy (negative ΔS) is the reaction where 2 moles of gas produce 1 mole of gas.

### Final Answer:
The reaction that will have a negative value of ΔS is the one where the number of gas moles decreases.

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