Question 11

NUMERICALMEDIUM

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is ______.

Use: Universal gas constant (R) = 8.3 J K−1 mol−1J\ K^{-1}\ mol^{-1}; Atomic mass (in amu): H = 1, O = 16

Correct Answer: -29.88

Detailed Solution

Reaction: 2H2O(l)→2H2(g)+O2(g)2H_2O(l) \rightarrow 2H_2(g) + O_2(g). Molar mass of H2O=18 g mol−1H_2O = 18\ g\ mol^{-1}. Moles of H2O=14418=8 molH_2O = \frac{144}{18} = 8\ mol. From stoichiometry, 2 moles of liquid water produce 3 moles of gas. So, 8 moles of liquid water produce Δng=8×32=12 mol\Delta n_g = 8 \times \frac{3}{2} = 12\ mol of gas. Work done W=−PΔV=−ΔngRTW = -P\Delta V = -\Delta n_g RT (for expansion against constant pressure). W=−12×8.3×300=−29880 J=−29.88 kJW = -12 \times 8.3 \times 300 = -29880\ J = -29.88\ kJ.

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