Question

Identify from following reactions that exhibits negative work done.

• A. 2H\(_2\)O\(_2(\ell) \rightarrow\) 2H\(_2\)O\((\ell) +\) O\(_2(g)\)
• B. NH\(_{3(g)} +\) HCl\(_{(g)} \rightarrow\) NH\(_4\)Cl\(_{(s)}\)
• C. H\(_{2(g)} +\) Cl\(_{2(g)} \rightarrow\) HCl\(_{(g)}\)
• D. N\(_{2(g)} + 3\)H\(_{2(g)} \rightarrow\) 2NH\(_{3(g)}\)

Hint:

$W<0$ for expansion (increase in gas moles); $W>0$ for compression (decrease in gas moles).

Answer 1

The Correct Option is A

Step 1: Formula
Work done $W = -P_{ext}\Delta V = -\Delta n_g RT$.
Negative work ($W<0$) implies expansion, meaning $\Delta n_g>0$.
Step 2: Check $\Delta n_g$
- (A) $\Delta n_g = 1 - 0 = +1$ (Expansion, $W$ is negative). - (B) $\Delta n_g = 0 - 2 = -2$ (Compression, $W$ is positive). - (C) $\Delta n_g = 2 - 2 = 0$ ($W = 0$). - (D) $\Delta n_g = 2 - 4 = -2$ (Compression, $W$ is positive).
Final Answer: (A)