Question

Which from following reactions performs highest + ve work at \(25^{\circ} \mathrm{C}\) ?

• A. \(\mathrm{CH}_{4(\text{ }\mathrm{g})}+\mathrm{Cl}_{2(\text{ }\mathrm{g})}\longrightarrow \mathrm{CH}_{3}\mathrm{Cl}_{(\mathrm{g})}+\mathrm{HCl}_{(\mathrm{g})}\)
• B. \(3\mathrm{H}_{2(\text{ }\mathrm{g})}+\mathrm{N}_{2(\text{ }\mathrm{g})}\longrightarrow 2\mathrm{NH}_{3(\text{ }\mathrm{g})}\)
• C. \(\mathrm{C}_{2}\mathrm{H}_{2(\text{ }\mathrm{g})}+\frac{5}{2}\mathrm{O}_{2(\text{ }\mathrm{g})}\longrightarrow 2\mathrm{CO}_{2(\text{ }\mathrm{g})}+\mathrm{H}_{2}\mathrm{O}_{(l)}\)
• D. \(2\mathrm{C}_{2}\mathrm{H}_{6(\text{ }\mathrm{g})}+7\mathrm{O}_{2(\text{ }\mathrm{g})}\longrightarrow 4\mathrm{CO}_{2(\text{ }\mathrm{g})}+6\mathrm{H}_{2}\mathrm{O}_{(\mathrm{l})}\)

Hint:

Work in chemical reactions depends on the change in moles of gas through the expression involving delta n of gas times RT.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Work done on the system by surroundings is \(w=-\Delta n_gRT\). It is positive and largest when \(\Delta n_g\) is most negative (gas contracts).

Step 2: Find \(\Delta n_g\)
(A) \(2-2=0\)
(B) \(2-4=-2\)
(C) \(2-3.5=-1.5\) (water is liquid)
(D) \(4-9=-5\) (water is liquid)

Step 3: Compare
The most negative value is \(-5\) for reaction (D), which gives the highest positive work.

Final Answer:
Reaction (D) performs the highest positive work. \[ \boxed{\text{(D) }2\mathrm{C}_{2}\mathrm{H}_{6(\mathrm{g})}+7\mathrm{O}_{2(\mathrm{g})}\longrightarrow 4\mathrm{CO}_{2(\mathrm{g})}+6\mathrm{H}_{2}\mathrm{O}_{(\mathrm{l})}} \]