For which reaction change of entropy be positive ?

Options

A. `H_2(g)+I(g)hArr2HI(g)`
B. `MgO(s)+H_2(g)hArrMg(g)+H_2O(l)`
C. `NH_4NO_3(s)hArrN_2O(g)+2H_2O(g)`
D. `HCl(g)+NH_3(g)hArrNH_4Cl(s)`

Answer

To determine for which reaction the change of entropy (ΔS) will be positive, we need to analyze the reactions based on the states of the reactants and products involved. Here's a step-by-step solution:

### Step 1: Understand Entropy
Entropy (S) is a measure of the disorder or randomness of a system. Generally, the order of entropy in different states of matter is:
- Gas > Liquid > Solid

This means that gases have the highest entropy, followed by liquids, and solids have the lowest.

### Step 2: Identify the Formula for Change in Entropy
The change in entropy for a reaction can be calculated using the formula:
\[ \Delta S = S_{\text{products}} - S_{\text{reactants}} \]
Where \( S_{\text{products}} \) is the total entropy of the products and \( S_{\text{reactants}} \) is the total entropy of the reactants.

### Step 3: Analyze the Given Reactions
We need to analyze the reactions based on the number of gaseous products and reactants:

1. **Reaction 1**: Produces 2 moles of gas.
2. **Reaction 2**: Produces 1 mole of gas.
3. **Reaction 3**: Produces 3 moles of gas.
4. **Reaction 4**: Produces no gas (0 moles of gas).

### Step 4: Determine the Change in Entropy
- For reactions that produce more moles of gas, the entropy will increase, leading to a positive ΔS.
- Conversely, reactions that produce fewer moles of gas or convert gas to solid or liquid will have a negative ΔS.

### Step 5: Conclusion
Among the reactions analyzed:
- **Reaction 3** produces the most gas (3 moles), which will result in the highest increase in entropy.
- Therefore, the reaction with the maximum change in entropy (ΔS positive) is the one that produces the highest number of gas moles.

### Final Answer
The reaction with the maximum positive change in entropy is **option C** (NH4NO3 ⇌ N2O + 2H2O).

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