A sample of `0.16 g CH_(4)` was subjected to combustion at `27^(@)C` in a bomb calorimeter. The temperature of the calorimeter system (including water) was found to rise by `0.5^(@)C`. Calculate the heat of combustion of methane at (a) constant volume and (b) constant pressure. The thermal capacity of calorimeter system is `17.0 kJ K^(-1)` and `R = 8.314 J K^(-1) mol^(-1)`.

Explanation

(i) Heat of combustion at constant volume, `DeltaU`
`=` Heat capacity of calorimeter system`xx`rise in temperature
`xx("Mol. Mass of compound")/("Mass of compound")`
`=17.7xx0.5xx(16)/(0.16)=885`
i.e., `DeltaU=-885kJ" "mol^(-1)`
(ii) `CH_(4)(g)+2O_(2)(g)toCO_(2)(g)+2H_(2)O(l)`
`Deltan=1-3=-2,T=300K,R=8.314xx10^(-3)kJ" "K^(-1)" "mol^(-1)`
`DeltaH=DeltaU+DeltanRT`
`=-885+(-2)xx8.314xx10^(-3)xx300`
`=-885-4.988=-889.988kJ" "mol^(-1)`