Calculate the entropy change for the following reaction
`H_(2)(g) +CI_(2)(g) rarr 2HCI (g) at 298 K`
Given `S^(Theta)H_(2) = 131 J K^(-1) mol^(-1), S^(Theta)CI_(2) = 233 J K^(-1) mol^(-1)`, and `S^(Theta) HCI = 187 J K^(-1) mol^(-1)`

Options

A. `10 JK^(-1)mol^(-1)`
B. `-20 JK^(-1) mol^(-1)`
C. `167 JK^(-1) mol^(-1)`
D. `-167 JK^(-1) mol^(-1)`

Explanation

To calculate the entropy change for the reaction:

\[ \text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2 \text{HCl}(g) \]

at 298 K, we can follow these steps:

### Step 1: Write the formula for entropy change
The entropy change (\(\Delta S\)) for a reaction can be calculated using the formula:

\[ \Delta S = S_{\text{products}} - S_{\text{reactants}} \]

### Step 2: Identify the entropies of the reactants and products
From the problem, we have the following standard molar entropies:

- \( S^{\Theta}_{\text{H}_2} = 131 \, \text{J K}^{-1} \text{mol}^{-1} \)
- \( S^{\Theta}_{\text{Cl}_2} = 233 \, \text{J K}^{-1} \text{mol}^{-1} \)
- \( S^{\Theta}_{\text{HCl}} = 187 \, \text{J K}^{-1} \text{mol}^{-1} \)

### Step 3: Calculate the total entropy of products
Since there are 2 moles of HCl produced, we calculate the total entropy for the products:

\[ S_{\text{products}} = 2 \times S^{\Theta}_{\text{HCl}} = 2 \times 187 \, \text{J K}^{-1} \text{mol}^{-1} = 374 \, \text{J K}^{-1} \text{mol}^{-1} \]

### Step 4: Calculate the total entropy of reactants
Now, we calculate the total entropy for the reactants:

\[ S_{\text{reactants}} = S^{\Theta}_{\text{H}_2} + S^{\Theta}_{\text{Cl}_2} = 131 \, \text{J K}^{-1} \text{mol}^{-1} + 233 \, \text{J K}^{-1} \text{mol}^{-1} = 364 \, \text{J K}^{-1} \text{mol}^{-1} \]

### Step 5: Calculate the entropy change
Now, we can substitute the values into the entropy change formula:

\[ \Delta S = S_{\text{products}} - S_{\text{reactants}} = 374 \, \text{J K}^{-1} \text{mol}^{-1} - 364 \, \text{J K}^{-1} \text{mol}^{-1} = 10 \, \text{J K}^{-1} \text{mol}^{-1} \]

### Step 6: Conclusion
The entropy change for the reaction at 298 K is:

\[ \Delta S = 10 \, \text{J K}^{-1} \text{mol}^{-1} \]