Question

The heat liberated when $1.89$ g of benzoic acid is burnt in a bomb calorimeter at ${25}^o$C increases the temperature of $18.94$ kg water in calorimeter by ${0.632}^o$C. If the specific heat of water at ${25}^o$C is $0.998$ cal $g^{-1}$ $de{g}^{-1}$, then the value of the heat of combustion of benzoic acid is:

• A. $881.1$ kcal
• B. $771.12$ kcal
• C. $981.1$ kcal
• D. $871.2$ kcal

Answer 1

The correct option is B $771.12$ kcal

Mass of benzoic acid, $m=1.89$ g

$T={25}^{0}C$

Mass of water,$m_{H_{2}O}=18.94kg=18940g$

$\Delta T={0.632}^{0}C$

specific heat of water, $C_V=0.998cal/g$

heat gained by water,$q=mC\Delta T$

$q=18940\times 0.998\times 0.632$

$q=11946.14cal$

Heat released by the caloriemeter= heat gained by water

thus heat released by 1.89 g of benzoic acid = $11946.14$ cal

since heat of combustion=heat released by 1 mol of benzoic acid

thus heat released by $1$ mol or $122$ g of benzoic acid$\frac{11946.14}{1.89}\times 122$

$=771126.5cal=771.12kcal$ heat is liberated from combustion of benzoic acid