How much of hard coal is required to produce the same amount of heat as is produced by the combustion of 2.0 L of gasoline (mainly isooctance, `C_(8)H_(18)`). Given: `Delta_(c)H^(0)` of `C_(8)H_(18)=-5460kJ*mol^(-1)`, density of isooactane `=0.692g*mL^(-1)` and calorific value of hard coal is `32.75kJ*g^(-1)`.

Explanation

The mass of 2.0 L of gasoline=2000`xx`0.692g=1384g
for 1384g of the gasoline, the number of moles `=(1384)/(114)=12.14` [molar mass of the gasoline=114`g*mol^(-1)`]
For the combustion of 1 mol of the gasoline, the amount of the liberated heat is 5460 kJ
Therefore, the combustion of 12.14 mol of the gasoline will produce `5460xx12.14kJ` of heat.
The calorific value of the hard coal is `32.75kJ*g^(-1)`
so, the amount of the hard coal that will produce
`5760xx12.14kJ` of heat is `(5760xx12.14)/(32.75)g=2135.16g`.