MCQ
When  $5\, liter$  of a gas mixture of methane and propane is perfectly combusted at  $0\,^oC$  and  $1$  atmosphere,  $16\, liter$  of oxygen at the same temperature and pressure is consumed. The amount of heat released from this combustion in $kJ$$(\Delta H_{comb.} \, (CH_4) = 890\, kJ\, mol^{-1},$ $\Delta H_{comb.} (C_3H_8) = kJ \,mol^{-1})$ is
  • A
    $38$
  • $317$
  • C
    $477$
  • D
    $32$

Answer

Correct option: B.
$317$
b
$\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$

$\mathrm{C}_{3} \mathrm{H}_{8}+5 \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2}+4 \mathrm{H}_{2} \mathrm{O}$

$\mathrm{CH}_{4}+\mathrm{C}_{3} \mathrm{H}_{8}=\frac{5}{22.4}=0.22 \,\mathrm{moles}$

$\mathrm{O}_{2}=\frac{16}{22.4}=0.71\, \mathrm{moles}$

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

$x=0.13$

Heat liberated $=0.13 \times 890+0.09 \times 2220=316\;kJ$

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