The combustion of exactly 1.000 g of benzoic acid in a bomb calorimeter releases 26.38 kj of heat. if the combustion of 0.550 g of benzoic acid causes the temperature of the calorimeter to increase from 22.01∘c to 24.27∘c, calculate the heat capacity of the calorimeter.

A bomb calorimeter whose temperature increases from 22.01 °C to 24.27 °C  due to the combustion of 0.550 g of benzoic acid, has a heat capacity of 6.42 kJ/° C.

If the combustion of exactly 1.000 g of benzoic acid in a bomb calorimeter releases 26.38 kJ of heat, the heat released by the combustion of 0.550 g of benzoic acid is:

The negative sign is the convention to indicate that heat is released.

According to the Law of conservation of energy, the sum of the heat released by the combustion (Qc) and the heat absorbed by the bomb calorimeter (Qb) is zero.

When the bomb calorimeter absorbed 14.5 kJ, its temperature increased from 22.01 °C to 24.27 °C. We can calculate the heat capacity of the calorimeter (C) using the following expression.

A bomb calorimeter whose temperature increases from 22.01 °C to 24.27 °C  due to the combustion of 0.550 g of benzoic acid, has a heat capacity of 6.42 kJ/° C.

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Cv=6.41 KJ/°C

Explanation:

Given that

1 g of benzoic acid release 26.38 KJ

So 0.55 g will release 26.38 x 0.55 KJ = 14.509 KJ

We know that

q=  Cv ΔT

Where

q=Heat

Cv= Heat capacity

ΔT=Temperature difference

Now by putting the values

14.509 = Cv ( 24.27 - 22.01)

Cv=6.41 KJ/°C

So the heat capacity of bomb calorimeter is 6.41 KJ/°C.