Calculate the entropy change `(J//mol K)` of the given reaction. The molar entropies `(J//K-mol)` are given in brackets after each substance:
`2PbS(s)[19.2]+3O_(2)(g)[205.1]`
` to 2PbO(s)[66.5]+2O_(2)(g)[248.2]`

Options

A. `-113.5`
B. `-168.3`
C. `+72.5`
D. `-149.2`

Explanation

To calculate the entropy change (ΔS) for the given reaction, we will use the formula:

\[ \Delta S = \sum (n_i S_i)_{\text{products}} - \sum (n_i S_i)_{\text{reactants}} \]

where \( n_i \) is the stoichiometric coefficient and \( S_i \) is the molar entropy of each substance.

### Step 1: Identify the products and reactants
The reaction is:

\[ 2 \text{PbS}(s) + 3 \text{O}_2(g) \rightarrow 2 \text{PbO}(s) + 2 \text{O}_2(g) \]

**Products:**
- 2 PbO(s) with molar entropy = 66.5 J/(K·mol)
- 2 O2(g) with molar entropy = 248.2 J/(K·mol)

**Reactants:**
- 2 PbS(s) with molar entropy = 19.2 J/(K·mol)
- 3 O2(g) with molar entropy = 205.1 J/(K·mol)

### Step 2: Calculate the total entropy for products
For the products:

\[ \text{Total entropy of products} = (2 \times 66.5) + (2 \times 248.2) \]

Calculating this:

\[ = 133.0 + 496.4 = 629.4 \text{ J/(K·mol)} \]

### Step 3: Calculate the total entropy for reactants
For the reactants:

\[ \text{Total entropy of reactants} = (2 \times 19.2) + (3 \times 205.1) \]

Calculating this:

\[ = 38.4 + 615.3 = 653.7 \text{ J/(K·mol)} \]

### Step 4: Calculate the change in entropy
Now, we can find the change in entropy (ΔS):

\[ \Delta S = \text{Total entropy of products} - \text{Total entropy of reactants} \]

Substituting the values we calculated:

\[ \Delta S = 629.4 - 653.7 = -24.3 \text{ J/(K·mol)} \]

### Final Answer
The entropy change (ΔS) for the reaction is:

\[ \Delta S = -24.3 \text{ J/(K·mol)} \]

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