Question

To calibrate a bomb calorimeter, the combustion of naphthalene (C10H8),
which releases 5150.1 kJ/mol, is often used. A sample of naphthalene of
mass 1.05-g is burned in a calorimeter, producing a temperature increase of
3.86°C. Combustion of a 1.83-g sample of coal in the same calorimeter
causes a temperature change of 4.90°C. What is the energy density of coal?

Answer 1

The molar mass of naphthalene is 128.17 g/mol. The heat released by burning 1.05 g of naphthalene is:

$Q = 5150.1\cdot\frac{1.05}{128.17} = 42.19$ kJ.

Therefore, the capacity of the calorimeter is:

$C = \frac{Q}{\Delta T} = \frac{42.19}{3.86 K} = 10.93$ kJ/K.

If the combustion of coal causes a temperature change of 4.90 °C, or K (difference temperature value is the same in °C and in K), then the heat released is:

$Q = C\Delta T = 10.93\cdot4.90 = 53.56$ kJ.

Thus, the energy density of coal is:

$d_e = \frac{Q}{m} = \frac{53.56}{1.83} = 29.27$ kJ/g or $29.27\cdot M = 29.27\cdot12.01 = 351.5$ kJ/mol.

Answer: the energy density of coal is 29.27 kJ/g or 351.5 kJ/mol