Question

A 5.19 g sample of anthracite coal is burned in a bomb calorimeter, which causes the - temperature of the calorimeter to increase by 9.37 °C. The calorimeter contains 3.45 kg of water (heat capacity of H₂O = 4.184 J/g· °C) and the heat capacity of the empty calorimeter is 2.23 kJ/°C. How much thermal energy, in kJ, is released per gram of anthracite coal when it is burned?

Answer 1

To calculate the heat released per gram of anthracite coal when burned, first find the heat absorbed by the water, then add the heat absorbed by the calorimeter, and finally divide the total heat by the mass of coal burned. The total heat released is 30.20242 kJ per gram of anthracite coal.

Step-by-step explanation:

To find the total amount of thermal energy released when the anthracite coal is burned, we would add the heat absorbed by the water and the calorimeter together. The heat absorbed by water can be found using the formula q = m × c × ΔT, where m is the mass of the water in grams, c is the specific heat capacity of water, and ΔT is the change in temperature. To obtain the energy in kJ, it's necessary to convert the mass of water from kg to g.

Calculating for water: (3450 g) × (4.184 J/g°C) × (9.37 °C) = 135872.46 J or 135.87246 kJ

For the calorimeter: (2.23 kJ/°C) × (9.37 °C) = 20.8881 kJ

Now, to get the total heat released, we sum the heat absorbed by water and calorimeter: 135.87246 kJ + 20.8881 kJ = 156.76056 kJ

To find the heat released per gram of anthracite coal, divide the total heat by the mass of coal burned: 156.76056 kJ / 5.19 g = 30.20242 kJ/g