The heat liberated when `1.89 g` of benzoic acid is burnt in a bomb calorimeter at `25^(@)C` increases the temperture of `18.94 kg` of water by `0.632 ^(@)C`. If the specific heat of water at `25^(@)C` is `0.998 cal//g "deg"`, the value of the heat of combustion of benzoic acid is

Options

A. `88.1 kcal`
B. `771.4 kcal`
C. `981.1 kcal`
D. `871.2 kcal`

Answer

B

Explanation

Given :
Weight of benzoic acid `=1.89 g`
Temperature of bomb calorimeter`=25^(@)C`
Mass of water(m)`=18.94kg=18940g`
Increase in temperature `(DeltaT)=0.632^(@)C`
and specific heat of water `(s)=0.998 cal//g//deg`.
We know that heat gained by water or heat liberated by benzoic acid `(Q)=msDeltaT`
`=18940xx0.998xx0.632=11946.14 cal`
Since `1.89g` of acid liberates `11946.14 cal` of heat,
`:. "heat liberated by" 122g "of acid"(1 mol)`
`=(11946.14xx22)/(1.89)`
`=771126.5 cal=771.12 kcal`
(where `122g` is the molecular weight of benzoic acid)