The standard entroples of `N_(2)(g), H_(2) (g) and NH_(3) (g)` are `191.5, 130.5, 192.6 Jk^(-1) mol ^(-1)`. The value of `DeltaS^(@)` of formation of ammonia is

Options

A. `-98.9 JK^(-1) mol^(-1)`
B. `Zero`
C. `+129.4 JK^(-1) mol^(-1)`
D. `-29.4 JK^(-1) mol^(-1)`

Answer

To find the standard entropy change of formation (\( \Delta S^\circ_f \)) of ammonia (\( NH_3(g) \)), we will use the standard entropies of the reactants and products involved in the formation reaction. The balanced chemical equation for the formation of ammonia from nitrogen and hydrogen is:

\[ \frac{1}{2} N_2(g) + \frac{3}{2} H_2(g) \rightarrow NH_3(g) \]

### Step-by-Step Solution:

1. **Identify the standard entropies**:
- Standard entropy of \( N_2(g) = 191.5 \, J \, K^{-1} \, mol^{-1} \)
- Standard entropy of \( H_2(g) = 130.5 \, J \, K^{-1} \, mol^{-1} \)
- Standard entropy of \( NH_3(g) = 192.6 \, J \, K^{-1} \, mol^{-1} \)

2. **Write the formula for the change in standard entropy**:
The change in standard entropy (\( \Delta S^\circ \)) for the reaction can be calculated using the following formula:
\[ \Delta S^\circ = S^\circ_{\text{products}} - S^\circ_{\text{reactants}} \]

3. **Calculate the standard entropy of the products**:
For the product \( NH_3(g) \):
\[ S^\circ_{\text{products}} = S^\circ_{NH_3} = 192.6 \, J \, K^{-1} \, mol^{-1} \]

4. **Calculate the standard entropy of the reactants**:
For the reactants \( \frac{1}{2} N_2(g) \) and \( \frac{3}{2} H_2(g) \):
\[ S^\circ_{\text{reactants}} = \left(\frac{1}{2} S^\circ_{N_2}\right) + \left(\frac{3}{2} S^\circ_{H_2}\right) \]
Substituting the values:
\[ S^\circ_{\text{reactants}} = \left(\frac{1}{2} \times 191.5\right) + \left(\frac{3}{2} \times 130.5\right) \]
\[ = 95.75 + 195.75 = 291.5 \, J \, K^{-1} \, mol^{-1} \]

5. **Calculate \( \Delta S^\circ \)**:
Now substituting the values into the entropy change formula:
\[ \Delta S^\circ = 192.6 - 291.5 \]
\[ = -98.9 \, J \, K^{-1} \, mol^{-1} \]

### Final Answer:
The value of \( \Delta S^\circ_f \) of formation of ammonia is:
\[ \Delta S^\circ_f = -98.9 \, J \, K^{-1} \, mol^{-1} \]