Among the following, the reaction that is accompanied by a decrease in the entropy is

Options

A. `N_(2)(g)+3H_(2)(g)rarr 2NH_(3)(g)`
B. `C_(6)H_(12)O_(6)(s)+6O_(2)(g)rarr6CO_(2)(g)+6H_(2)O(l)`
C. `PCl_(5)(s)rarr PCl_(3)(l)+Cl_(2)(g)`
D. `2H_(2)O(l)rarr2H_(2)+O_(2)(g)`

Answer

To determine which reaction is accompanied by a decrease in entropy, we can follow these steps:

### Step 1: Understand Entropy
Entropy (S) is a measure of the randomness or disorder of a system. A decrease in entropy indicates that the products of the reaction are more ordered than the reactants.

### Step 2: Use ΔNG
To analyze the changes in entropy, we can use the concept of ΔNG, which is the difference in the number of moles of gaseous products and gaseous reactants:
\[ \Delta NG = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]

### Step 3: Analyze Each Option
Now, we will analyze each option given in the question:

1. **Option 1:** \( N_2 + 3H_2 \rightarrow 2NH_3 \)
- Moles of gaseous products = 2 (NH3)
- Moles of gaseous reactants = 4 (1 N2 + 3 H2)
- \( \Delta NG = 2 - 4 = -2 \)

2. **Option 2:** \( 6 \text{ moles of gaseous products} \)
- Moles of gaseous products = 6
- Moles of gaseous reactants = 6
- \( \Delta NG = 6 - 6 = 0 \)

3. **Option 3:** \( 1 \text{ mole of gaseous product} \)
- Moles of gaseous products = 1
- Moles of gaseous reactants = 0
- \( \Delta NG = 1 - 0 = 1 \)

4. **Option 4:** \( O_2 + H_2 \rightarrow \text{products} \)
- Assuming H2 is gaseous, we have:
- Moles of gaseous products = 1 (O2) + 1 (H2) = 2
- Moles of gaseous reactants = 0
- \( \Delta NG = 2 - 0 = 2 \)

### Step 4: Determine the Reaction with Decrease in Entropy
From the calculations:
- Option 1: \( \Delta NG = -2 \) (decrease in entropy)
- Option 2: \( \Delta NG = 0 \) (no change in entropy)
- Option 3: \( \Delta NG = 1 \) (increase in entropy)
- Option 4: \( \Delta NG = 2 \) (increase in entropy)

The only reaction that shows a decrease in entropy is **Option 1**.

### Final Answer
The reaction that is accompanied by a decrease in entropy is **Option 1: \( N_2 + 3H_2 \rightarrow 2NH_3 \)**.

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