Which reaction among the following will have the maximum value of `Delta S` ?

Options

A. `Ca(s)+(1)/(2)O_(2)(g)to CaO(s)`
B. `CaCO_(3)(s)to CaO(s)+CO_(2)(g)`
C. `C(s)+O_(2)(g)to CO_(2)(g)`
D. `N_(2)(g)+O_(2)(g)to 2NO(g)`

Answer

To determine which reaction among the given options will have the maximum value of ΔS (entropy change), we can follow these steps:

### Step 1: Understand the concept of entropy (ΔS)
Entropy is a measure of the randomness or disorder of a system. A higher entropy indicates a greater degree of disorder.

### Step 2: Calculate Δng for each reaction
Δng is defined as the change in the number of moles of gaseous products minus the number of moles of gaseous reactants. The formula is:
\[ \Delta n_g = n_{\text{products}} - n_{\text{reactants}} \]

### Step 3: Analyze each option
We will analyze each reaction provided in the options to calculate Δng.

1. **Option 1**:
- Reactants: 1 mole of O2 (g)
- Products: 0 moles (solid)
- Calculation:
\[ \Delta n_g = 0 - 1 = -1 \]

2. **Option 2**:
- Reactants: 0 moles (solid)
- Products: 1 mole (g)
- Calculation:
\[ \Delta n_g = 1 - 0 = 1 \]

3. **Option 3**:
- Reactants: 1 mole (g)
- Products: 0 moles (g)
- Calculation:
\[ \Delta n_g = 0 - 1 = -1 \]

4. **Option 4**:
- Reactants: 1 mole of NO (g)
- Products: 2 moles of NO (g)
- Calculation:
\[ \Delta n_g = 2 - 1 = 1 \]

### Step 4: Compare the Δng values
Now we compare the Δng values calculated for each option:
- Option 1: Δng = -1
- Option 2: Δng = 1
- Option 3: Δng = -1
- Option 4: Δng = 1

### Step 5: Determine which reaction has the maximum ΔS
The maximum value of Δng is 1, which occurs in Options 2 and 4. Since both options have the same Δng, they both indicate an increase in entropy. However, typically, the option with more gaseous products compared to reactants is preferred.

### Conclusion
The reaction in **Option 2** has the maximum value of ΔS, as it shows a clear increase in gaseous products from a solid reactant.

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