When 15.68 litres of a gas mixture of methane and propane are fully combusted at `0^@C` and 1 atmosphere, 32 litres of oxygen at the same temperature and pressure are consumed. The amount of heat released from this combustion in kJ is (`DeltaH_C(CH_4)`=-890 kJ `mol^(-1)` and `DeltaH_C(C_3H_8)=-2220 kJ "mol"^(-1)`)

Options

A. `-889 kJ`
B. `-1390` kJ
C. `-3180` kJ
D. `653.66` kJ

Answer

D

Explanation

Given:
`DeltaH_C(CH_4)=-890 "kJ mol"^(-1)`
`DeltaH_C(C_3H_8)=-"-2220 kJ mol"^(-1)`
Let the mixture contain x lit of and lit of propane .
`undersetx(CH_4)+underset(2x)(2O_2) to CO_2 + 2H_2O`
`underset(15.68-x)(C_3H_8+5O_2) to underset"5(15.68-x)"(3CO_2 + 4H_2O)`
Volume of oxygen consumed = 2x+5 (15.68-x)=32 lit
2x + 78.4 -5x =32
78.4 - 3x =32
3x=46.4
x=15.47
Given mixture contains 15.47 liters of methane and 0.213 liters of propane . Hence ,
`DeltaH_C=[((DeltaH_C(CH_4))/"22.4 lit")xx"lit"]+[((DeltaH_C(C_3H_8))/"22.4 lit")(15.68-x)"lit"]`
`DeltaH_C=[((-890 "kJ mol"^(-1))/"22.4 lit")xx"15.47 lit "]+[((-2220)/"22.4 lit")"0.21 lit"]`
`DeltaH_C=[-614.66 "kJ mol"^(-1)]+[-20.81 "kJ mol"^(-1)]`
`DeltaH_C=635.47 "kJ mol"^(-1)`