Question

The heat is liberated when 1.89 g of benzoic acid is burnt in a bomb calorimeter at $25^{\circ }C$ and it increases the temperature of 18.94 kg of water by  $0.632^{\circ }C$. If the specific heat of water at $25^{\circ }C$ is 0.998cal/g.deg, then the value of the heat of combustion of benzoic acid is :
A. 881.1 kcal
B. 981.1 kcal
C. 771.1 kcal
D. 872.2 kcal

Answer 1

Hint: To solve this question, we need to recall the concept of calorimetry. These techniques are based on thermometric methods carried out in a vessel called calorimeter which is immersed in a known volume of liquid. We shall use the formula given below, substitute appropriate values in it and calculate the heat of combustion.

Complete step by step solution:
The formula which is to be used
$\Delta Q=mS \Delta t$
Where, m = mass of water
T = temperature
S = specific heat of the water
The molar mass of benzoic acid is 122g. given the mass of benzoic acid burnt in the bomb calorimeter is 1.89g.
The temperature inside the bomb calorimeter is 298 K.
The given values in the question are:
M = 18.94 kg = 18940 g
T = 0.632 K
S = 0.998cal/g.deg
The heat energy released by benzoic acid is equal to the heat energy absorbed by water. It is represented as ‘Q’.
Substituting these values in the formula shall give us
$Q=18940\times 0.998\times 0.632=11946.14cal$ .The heat of combustion of benzoic acid will be the heat energy by completely burning 1 mole of benzoic acid in the bomb calorimeter. Benzoic acid releases 11946.14cal heat energy.
The heat energy released by 122g of benzoic acid is
$11946.14\times122\div 1.89=771.1kcal$

Therefore, the correct option is (C).

Note: Enthalpy of a system is a type of variable such that it is impossible to calculate the absolute enthalpy of a system directly. This means that enthalpy for a reaction is calculated around a reference point.