Question

Standard entropies of \( \mathrm{N_2(g)}, \mathrm{H_2(g)} \) and \( \mathrm{NH_3(g)} \) are \( a_1 \), \( a_2 \) and \( a_3 \) J K\(^{-1}\) mol\(^{-1}\) respectively. What is the value of \( \Delta S^\circ \) for the formation of \( \mathrm{NH_3(g)} \)? 

• A. \( a_3 - \dfrac{1}{2}a_1 + \dfrac{3}{2}a_2 \)
• B. \( a_1 - \left(\dfrac{1}{2}a_3 + \dfrac{3}{2}a_2\right) \)
• C. \( a_2 - \left(\dfrac{1}{2}a_1 + \dfrac{3}{2}a_2\right) \)
• D. \( a_3 - \left(\dfrac{1}{2}a_1 + \dfrac{3}{2}a_2\right) \)

Hint:

Always multiply entropy values by stoichiometric coefficients before calculating \(\Delta S^\circ\).

Answer 1

The Correct Option is D

Step 1: Write the balanced chemical equation.
\[ \dfrac{1}{2}\mathrm{N_2(g)} + \dfrac{3}{2}\mathrm{H_2(g)} \rightarrow \mathrm{NH_3(g)} \]
Step 2: Write the entropy change expression.
\[ \Delta S^\circ = \sum S^\circ(\text{products}) - \sum S^\circ(\text{reactants}) \]
Step 3: Substitute the given values.
\[ \Delta S^\circ = a_3 - \left(\dfrac{1}{2}a_1 + \dfrac{3}{2}a_2\right) \]
Step 4: Conclusion.
The correct expression for entropy change is option (D).