The combustion of sucrose (C12H22O11) can be described by the following reaction:
C12H22O11 + 12 O2 → 12 CO2 + 11 H2O
When 10.0 g of sucrose is burnt in a bomb calorimeter with a heat capacity of 7.50 kJ/°C, we can determine the amount of heat released by using the calorimeter’s heat capacity. The heat released during the combustion reaction is equal to the change in temperature multiplied by the heat capacity of the calorimeter.
First, we need to calculate the moles of sucrose burned:
Molar mass of sucrose = 12(12.01) + 22(1.008) + 11(16.00) = 342.30 g/mol
Moles of sucrose = A0 \frac{10.0 g}{342.30 g/mol} A0 \approx 0.0292 mol
If we assume that the complete combustion of 1 mole of sucrose releases a specific amount of heat, we can find the total heat released.
Now, let’s say the combustion of sucrose releases around -5600 kJ/mol (this value can vary based on specific conditions, but we’ll use this common approximation). Therefore, for 0.0292 moles of sucrose:
Heat released = 0.0292 mol × -5600 kJ/mol = -163.52 kJ
This means that when 10.0 g of sucrose is burned in the bomb calorimeter, approximately 163.5 kJ of heat is released.
Now, because the calorimeter measures how the temperature changes when combustion occurs, we can also relate this heat to the increase in the temperature of the calorimeter using the heat capacity:
\Delta T = \frac{q}{C}\text{(where } \Delta T \text{ is the change in temperature, } q \text{ is heat, and } C \text{ is the heat capacity)}
If we want to calculate the change in temperature using the heat capacity of the calorimeter:
\Delta T = \frac{-163.52 kJ}{7.50 kJ/°C} = -21.8 °C
This significant drop in temperature reflects the considerable amount of heat released by the combustion of sucrose. Thus, the process of combustion involves both the breakdown of sucrose into byproducts and the release of energy, which can significantly affect the temperature of the surrounding environment in a calorimetric setup.