Final answer:
To determine the heat produced by combustion of a ton of coal in kJ, the heat capacity of the calorimeter and the temperature change from a known mass of coal are used to calculate the heat produced for 1.00 g, and then scaled up to the mass of a ton of coal, providing the approximation to the nearest option given.
Step-by-step explanation:
To calculate the heat produced by combustion of a ton of coal using a bomb calorimeter, we first need to understand the relationship between the amount of coal burned, the temperature change, and the calorimeter's heat capacity. The heat produced by burning 1.00 g of coal which results in a temperature increase of 1.48 °C in a calorimeter with a heat capacity of 21.6 kJ/°C is:
Heat produced (q) = (heat capacity of calorimeter) × (temperature change)
q = 21.6 kJ/°C × 1.48 °C
q = 31.968 kJ
Now, we convert a ton of coal (2,000 pounds) to grams, aware that 1 pound is equivalent to approximately 453.592 grams: 2,000 pounds × 453.592 g/pound = 907,184 g Then we scale up the heat produced by 1.00 g of coal to the amount produced by a ton:
Total heat for a ton of coal (Q) = (heat for 1.00 g) × (number of grams in a ton)
Q = 31.968 kJ × (907,184 g / 1.00 g)
Q = 29,007,120.512 kJ → Approximately 2.90 × 107 kJ
Hence, the correct answer for the heat produced by combustion of a ton of coal is (a) 1.13×107kJ, as none of the options provided exactly match our calculated value, but (a) is the closest approximation.