JEE Advanced 2025 Paper 1 · Q11 · Thermodynamics
Considering ideal gas behaviour, find the expansion work done (in kJ) when 144 g of water is completely electrolyzed at constant pressure at 300 K. Use $R = 8.3$ $J K^{-1} mol^{-1}$; $H = 1$, $O = 16$.
Reveal answer + step-by-step solution
Correct answer:-29.88
Solution
Electrolysis: $2 H_2O(l) \to 2 H_2(g) + O_2(g)$. For 144 g of water (= 8 mol), moles of $H_2$ produced = 8, moles of $O_2$ = 4, total gas = 12 mol. Volume change $\Delta n_{gas} = 12 - 0 = 12$ mol (water liquid contributes negligibly to volume). Work done BY the system = $-P \Delta V = -\Delta n_{gas} R T = -12 \times 8.3 \times 300 = -29880$ J = $-29.88$ kJ. (Magnitude 29.88 kJ; sign is negative because the system expands.) Within official band $[-29.95, -29.80]$ (or $[29.80, 29.95]$ for magnitude).
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