A gas mixture of 3.67 litres of ethylene and methane on complete combustion at 25^(@)C produces 6.11 litres of CO_(2). Find out the amount of heat evolved on burning one litre of the gas mixture. The heats of combustion of ethylene and methane are -1423 and -891 "kJ mol"^(-1) at 25^(@)C.

A gas mixture of 3.67 litres of ethylene and methane on complete combu

1.	A gas mixture of 3.67 litres of ethylene and methane on complete combustion at 25^(@)C produces 6.11 litres of CO_(2). Find out the amount of heat evolved on burning one litre of the gas mixture. The heats of combustion of ethylene and methane are -1423 and -891 "kJ mol"^(-1) at 25^(@)C.
Answer» Solution : `or x "moles (3.67-x)moles6.11moles"` Applying POAC for C atoms, `2xxx+1xx(3.67-x)=1xx6.11,x=2.44 "lit"` Thus, the volume of `C_(2)H_(4)=2.44` lit, and volume of `CH_(4)=1.23` lit. `:.` volume of `C_(2)H_(4)` in a 1-LITRE mixture `=(2.44)/(3.67)=0.665` lit and volume of `CH_(4)` in a 1-litre mixture `=1-0.665=0.335` lit. Now, thermochemical reactions for `C_(2)H_(4)` and `CH_(4)` are `C_(2)H_(4)+3O_(2) to 2CO_(2)+2H_(2)O,DeltaH=-1423 "kJ"` `CH_(4)+2O_(2) to CO_(2)+2H_(2)O, DeltaH=-891 "kJ"` As DeltaH values given are at `25^(@)C` (supposing pressure as 1 atm) Volume per mole at `25^(@)C=(298)/(273)xx22.4=24.45 "lit"` Thus, heat evolved in the combustion of 0.665 lit. of `C_(2)H_(4)` `=-(1423)/(24.45)xx0.665=-38.70"kJ"` and heat evolved in the combustion of 0.335 "lit". of `CH_(4)` `=-(891)/(24.45)xx0.335=-12.20"kJ"` `:.` TOTAL heat evolved in the combustion of 1 litre of the mixture `=-38.70+(-12.20)` `=-50.90 kJ`