Question

A gas mixture of 3.67 lit of ethylene and methane on complete combustion at 25°C and at 1 atm pressure produce 6.11 lit of carbon dioxide. Find out the amount of heat evolved in kJ, during this combustion. (ΔH_C(CH₄)) = − 890 kJ mol⁻¹ and (ΔH_C(C₂H₄)) = − 1423 kJ mol⁻¹

Answer 1

Given, ΔH_C(CH₄) = − 890 kJ mol⁻¹

ΔH_C(C₂H₄) = − 1423 kJ mol⁻¹

Let the mixture contain x lit of CH₄ and (3.67 − x) lit of ethylene.

\[\ce{\underset{\text{x lit}}{CH4} + 2O2 -> \underset{\text{x lit}}{CO2} + 2H2O}\]

\[\ce{\underset{\text{(3.67 − x) lit}}{C2H4 + 3O2} -> \underset{\text{2 (3.67 − x) lit}}{2CO2 + 2H2O}}\]

Volume of Carbon dioxide formed = x + 2 (3.67 − x) = 6.11 lit

x + 7.34 − 2x = 6.11

7.34 − x = 6.11

x = 1.23 lit

Given mixture contains 1.23 lit of methane and 2.44 lit of ethylene, hence

ΔH_C = `[(Δ"H"_"C" ("CH"_4))/(22.4  "lit") xx ("x")  "lit"] + [(Δ"H"_"C" ("C"_2"H"_4))/(22.4  "lit") xx (3.67 - "x")  "lit"]`

ΔH_C = `[(-890  "kJ mol"^-1)/(22.4  "lit") xx 1.23  "lit"] + [(-1423)/(22.4  "lit") xx (3.67 - 1.23)  "lit"]`

ΔH_C = [−48.87 kJ mol⁻¹] + [−155kJ mol⁻¹]

ΔH_C = −203.87 kJ mol⁻¹