.0.50 g of benzoic acid was subjected to combustion in a calorimeter when the temperature of the calorimeter system was found to rise by `0.55^(@)C.` Calculate the enthalpy of combustion of benzoic acid (i) at constant volume (ii) at constant pressure. The thermal capacity of the calorimeter including water was found to be `23.85 kJ K^(-1).`

Explanation

(i) Here, `z =22.85 kJ K ^(-1) , Delta T =0.55 ^(@)C, M = 122 g mol ^(-1) , m = 0.5 g.`
Heat of combustion at constant volume, `q _(v)= z xx Delta T xx M // m`
`=23.85 kJ K ^(-1) xx 0.55 K xx 122 g mol ^(-1) // 0.5g = 3200.7 kJ mol ^(-1) =- 3200.7 kJ mol ^(-1)`
(ii) Enthalpy of conbustio at constant pressure, `q _(p) = q _(v) + Delta n _(g) RT`
Combustion of benzoic acid at `25 ^(@)C` involves of following reaction:
`C _(6) H _(5) COOH (s) + 15 //2 O _(2) (g) to 7 CO _(2) (g) + 3 H _(2)O (l)`
Change in the number of moles, `Delta n =7-7.5=-0.5`
`q _(p) =- 3200 .7 kJ mol ^(-1) + (-0.5) ( 8.314 xx 10 ^(-3) kJ K ^(-1) mol ^(-1)) (298K) =- 3201.9 kJ mol ^(-1)`