Question

The heat is liberated when 1.8g benzoic acid is burnt in a bomb calorimeter at \[{25^0}C\] and it increases the temperature of \[18.94{\text{ kg}}\] water by \[{0.632^0}C\]. If the specific heat of water at \[{25^0}C\] is \[0.998{\text{cal/g}}{\text{.deg}}\], then the value of the heat of combustion of benzoic acid is:
A.$881.1{\text{kcal}}$
B.$981.1{\text{kcal}}$
C.$771.1{\text{kcal}}$
D.$871.2{\text{kcal}}$

Answer 1

Hint: In this question, we have 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.

Formula used: \[{\Delta \text{Q = ms t}}\] where ${\text{m}}$=Mass of water, \[{\Delta \text{t}}\]=Increase in temperature and ${\text{s}}$=Specific heat of the water.

Complete step by step answer:
The molar mass of benzoic acid =\[122{\text{ g}}\]. Given the mass of benzoic acid burnt in bomb calorimeter = \[1.89{\text{ g}}\]
The temperature inside the bomb calorimeter = \[{25^0}C\]=\[298{\text{K}}\].
The given values in the question are:
${\text{m}}$= Mass of water = \[18.94{\text{ kg}} = 18940{\text{g}}\]
\[{\Delta \text{t}}\]=Increase in temperature = \[{0.632^0}C = 0.632K\]
${\text{s}}$=Specific heat of water = \[0.998{\text{cal/g}}{\text{.deg}}\].
The heat energy released by benzoic acid = Heat energy absorbed by water = ${\text{Q}}$ .
Substituting these values in the formulas for \[{\text{Q}} = {\Delta \text{ms t}} = 18940 \times 0.998 \times 0.632 = 11946.14{\text{cal}}\].
The heat of combustion of benzoic acid will be the heat energy released by completely burning 1 mole of benzoic acid in the bomb calorimeter. Benzoic acid releases \[11946.14{\text{cal}}\;\]heat energy.
$ \Rightarrow $The heat energy released by 122 g of benzoic acid = \[\dfrac{{11946.14 \times 122}}{{1.89}} = 771126.5{\text{cal}} \approx 771.1{\text{kcal}}\].

Hence, 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. This is why we generally measure the change in enthalpy. The value of this enthalpy change is positive for endothermic reactions while it is negative for exothermic reactions. Coffee-cup calorimeter is used to calculate the enthalpy change. When any chemical reaction occurs in this coffee cup, it is observed that the heat of reaction is absorbed by the water.