A gaseous mixture of CH4 and H2 totalling 1.00 mol releases 520 kJ of heat on complete combustion to CO2(g) and H2O(l). The enthalpies of combustion are -890 kJ mol^-1 for CH4 and -286 kJ mol^-1 for H2. Find the mole percent of CH4 in the mixture (nearest integer).

JEE Advanced levelNumerical answerDifficulty 3 of 3td088

A gaseous mixture of $CH X_{4}$ and $H X_{2}$ totalling $1.00 mol$ releases $520 kJ$ of heat on complete combustion to $CO X_{2} (g)$ and $H X_{2} O (l)$ . The enthalpies of combustion are $- 890 kJ mo l^{- 1}$ for $CH X_{4}$ and $- 286 kJ mo l^{- 1}$ for $H X_{2}$ . Find the mole percent of $CH X_{4}$ in the mixture (nearest integer).

Numerical answer type, answer in %, tolerance 0.5.

Let the mole fraction of

CH X_{4}

x

. Then

890 x + 286 (1 - x) = 520

, so

604 x = 234

and

x = 0.3874

. Mole percent

= 38.74 %