Question

Under constant-volume conditions the heat of combustion of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) is \(15.57 \mathrm{~kJ} / \mathrm{g}\). A \(2.500-\mathrm{g}\) sample of glucose is burned in a bomb calorimeter. The temperature of the calorimeter increased from \(20.55^{\circ} \mathrm{C}\) to \(23.25^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) If the size of the glucose sample had been exactly twice as large, what would the temperature change of the calorimeter have been?

Short answer

The total heat capacity of the calorimeter (C) is approximately \(14.40 \, \text{kJ/°C}\). If the glucose sample size was exactly twice as large, the temperature change of the calorimeter (ΔT') would be approximately \(5.40 \, \text{°C}\).

Step-by-step solution

Calculate the heat released by the combustion of glucose.

To find the total heat released by glucose, we can use the heat of combustion of glucose given and the mass of the glucose sample: Heat released per gram of glucose = 15.57 kJ/g Glucose sample mass = 2.500 g Total heat released (q) = Heat released per gram × mass = 15.57 kJ/g × 2.500 g

Calculate the temperature change of the calorimeter

The temperature change of the calorimeter can be found by subtracting the initial temperature from the final temperature: ΔT = T_final - T_initial ΔT = 23.25°C - 20.55°C ΔT = 2.70 °C

Calculate the total heat capacity of the calorimeter

To determine the heat capacity of the calorimeter, we need to divide the total heat released (q) by the temperature change (ΔT): Heat capacity (C) = Total heat released (q) / ΔT Plug in the values from Step 1 and Step 2: C = (15.57 kJ/g × 2.500 g) / 2.70°C

Calculate the temperature change for a doubled glucose sample

If the sample size of glucose was exactly twice as large, the heat released would also be twice as much: Total heat released (q') = 2 × (15.57 kJ/g × 2.500 g) We can use the heat capacity calculated in Step 3 (C) and the new heat released (q') to find the new temperature change (ΔT'): ΔT' = q' / C Plug in the values: ΔT' = (2 × 15.57 kJ/g × 2.500 g) / [(15.57 kJ/g × 2.500 g) / 2.70°C]