When 5 litres of a gas mixture of methane and propane is perfectly combusted at 0°C and 1 atmosphere

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When 5 litres of a gas mixture of methane and propane is perfectly combusted at 0°C and 1 atmosphere, 16 litres of oxygen at the same temperature and pressure is consumed. The amount of heat released from this combustion in kJ $(ΔH_{comb.} (CH_4) = 890 kJ mol^{-1}, ΔH_{comb.} (C_3H_8) = 2220 kJ mol^{-1})$ is

(a) 38

(b) 317

(c) 477

(d) 32

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Ans: (b) 317

Sol: $CH_4 + 2O_2 → CO_2 + 2H_2O$

$C_3H_8 + 5O_2 → 3CO_2 + 4H_2O$

$CH_4 + C_3H_8 ={5\over22.4}= 0.22 \text{ moles}$

$O_2 ={16\over22.4}= 0.71 \text{ moles}$

$2x + (0.22 - x)5 = 0.71$

$x = 0.13$

Heat liberated $= 0.13 × 890 + 0.09 × 2220 = 316 kJ$