A cooking gas cylinder is assumed to contain `11.2kg` isobutane. The combustion of isobutane is given by `:`
`C_(4)H_(10(g))+(13//2)O_(2(g)) rarr 4CO_(2(g))+5H_(2)O_((l)), DeltaH=-2658kJ mol^(-1)` `(a)` If a family needs `15000kJ` of energy per day for cooking, how long would the cylinder last ?
`(b)` Assuming that `30%` of the gas is wasted due to incomplete combustion, how long would the cylinder last ?

Explanation

`(a) :' 58g` isobutane provides energy `=2658kJ`
`11.2xx10^(3)g` isobutane provides energy
`=(3658xx11.2xx10^(3))/(58)kJ=513268.9kJ`
The daily requirement of energy `=15000kJ`
`:. ` Cylinder wil last `=(513268.9)/(15000)~=34 days`
`(b)` Total loss of energy due to wastage `=(513268.9xx70)/(100)`
`kJ` is `30%` and thus energy used for work
`:. ` Cylinder will last `=(513268.9xx70)/(100xx15000)=24days`