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If 100 mole of $H_{2} O_{2}$ decomposes at 1 bar and 300K, the work done (kJ) by one mole of $O_{2} (g)$ as it expands against 1 bar pressure is:
$2 H_{2} O_{2} (l) ⇌ 2 H_{2} O (l) + O_{2} (g) (R = 8.3 {JK}^{- 1} {mol}^{- 1})$

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Detailed Solution

$2 H_{2} O_{2} (l) ⇌ 2 H_{2} O (l) + O_{2} (g) w = - P_{ext} (ΔV) = - n_{O_{2}} RT$

$∵$ 100 mole $H_{2} O_{2}$ on decomposition give 50 mole $O_{2}$

$∴ w = - (50) (8.3) (300) = - 124500 J = - 124.5 k J$

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