28.0 L of $\mathrm{CO}_{2}$ is produced on complete combustion of 16.8 L gaseous mixture of ethene and methane at $25^{\circ}\mathrm{C}$ and 1 atm. Heat evolved during the combustion process is \_\_\_\_ kJ. Given: $\Delta\mathrm{H}_{\mathrm{C}}\left(\mathrm{CH}_{4}\right)=-900\mathrm{~kJ}\mathrm{~mol}^{-1}$ $\Delta\mathrm{H}_{\mathrm{C}}\left(\mathrm{C}_{2}\mathrm{H}_{4}\right)=-1400\mathrm{~kJ}\mathrm{~mol}^{-1}$

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Chemical Thermodynamics

28.0 L of

CO_{2}

is produced on complete combustion of 16.8 L gaseous mixture of ethene and methane at

2 5^{\circ} C

and 1 atm. Heat evolved during the combustion process is ____ kJ.

Given:

Δ H_{C} (CH_{4}) = - 900 kJ mol^{- 1}

Δ H_{C} (C_{2} H_{4}) = - 1400 kJ mol^{- 1}

Answer: 847

Letting the volume of ethene be

x

litres and that of methane

(16.8 - x)

litres, and noting that ethene yields two volumes of carbon dioxide while methane yields one, the carbon dioxide formed is

2 x + (16.8 - x) = x + 16.8

. Setting this equal to

28.0

gives

x = 11.2 L

of ethene and

5.6 L

of methane. At

298 K

and

1 atm

the molar volume is about

24.45 L

, so these amount to

0.458 mol

of ethene and

0.229 mol

of methane. The heat released is

0.458 \times 1400 + 0.229 \times 900

, which comes to about

847 kJ

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer