Calculate the entropy of `Br_(2)(g)` in the reaction `H_(2)(g)+Br_(2)(g)rarr2HBr(g), Delta S^(@)=20.1 JK^(-1)` given, entropy of `H_(2)` and HBr is 130.6 and 198.5 J `mol^(-1)K^(-1)` :-

Options

A. `246.3 JK^(-1)`
B. `123.15 JK^(-1)`
C. `24.63 JK^(-1)`
D. `20 KJK^(-1)`

Answer

To calculate the entropy of \( \text{Br}_2(g) \) in the reaction

\[ \text{H}_2(g) + \text{Br}_2(g) \rightarrow 2 \text{HBr}(g) \]

given that the change in entropy \( \Delta S^\circ = 20.1 \, \text{J K}^{-1} \), and the entropies of \( \text{H}_2 \) and \( \text{HBr} \) are \( 130.6 \, \text{J mol}^{-1} K^{-1} \) and \( 198.5 \, \text{J mol}^{-1} K^{-1} \) respectively, we can follow these steps:

### Step 1: Write the expression for the change in entropy
The change in entropy for the reaction can be expressed as:

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

### Step 2: Identify the products and their entropies
In the products, we have 2 moles of \( \text{HBr} \). Therefore, the total entropy for the products is:

\[ S_{\text{products}} = 2 \times S_{\text{HBr}} = 2 \times 198.5 \, \text{J mol}^{-1} K^{-1} = 397 \, \text{J mol}^{-1} K^{-1} \]

### Step 3: Identify the reactants and their entropies
In the reactants, we have \( \text{H}_2 \) and \( \text{Br}_2 \). The total entropy for the reactants is:

\[ S_{\text{reactants}} = S_{\text{H}_2} + S_{\text{Br}_2} = 130.6 \, \text{J mol}^{-1} K^{-1} + S_{\text{Br}_2} \]

Let \( S_{\text{Br}_2} = X \).

### Step 4: Set up the equation
Now we can set up the equation for the change in entropy:

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

Substituting the values we have:

\[ 20.1 = 397 - (130.6 + X) \]

### Step 5: Solve for \( X \)
Rearranging the equation gives:

\[ 20.1 = 397 - 130.6 - X \]

Combine the constants:

\[ 20.1 = 266.4 - X \]

Now, isolate \( X \):

\[ X = 266.4 - 20.1 \]

Calculating this gives:

\[ X = 246.3 \, \text{J mol}^{-1} K^{-1} \]

### Conclusion
Thus, the entropy of \( \text{Br}_2(g) \) is:

\[ S_{\text{Br}_2} = 246.3 \, \text{J mol}^{-1} K^{-1} \]