A sample of octane [tex]$\left( C _8 H _{18}\right)$[/tex] that has a mass of 0.750 g is burned in a bomb calorimeter. As a result, the temperature of the calorimeter increases from [tex]$21.0^{\circ} C$[/tex] to [tex]$41.0^{\circ} C$[/tex]. The specific heat of the calorimeter is [tex]$1.50 J /\left( g \cdot{ }^{\circ} C \right)$[/tex], and its mass is 1.00 kg. How much heat is released during the combustion of this sample?
Use [tex]$q=m C_p \Delta T$[/tex].
A. 22.5 kJ
B. 30.0 kJ
C. 31.5 kJ
D. 61.5 kJ
Answer (1)
Convert the mass of the calorimeter from kg to g: 1.00 kg = 1000 g .
Calculate the change in temperature: Δ T = 41. 0 ∘ C − 21. 0 ∘ C = 20. 0 ∘ C .
Calculate the heat absorbed by the calorimeter: q = (1000 \text{ g}) \times (1.50 \frac{\text{J}}{\text{g} \,^{\circ} C}) \times (20.0^{\circ} C) = 30000 \text{ J} .
Convert the heat to kJ and state the final answer: 30.0 kJ .
Explanation
Problem Analysis We are given the mass of octane burned in a bomb calorimeter, the initial and final temperatures of the calorimeter, the specific heat of the calorimeter, and the mass of the calorimeter. We need to find the amount of heat released during the combustion of the octane sample.
Convert mass of calorimeter First, convert the mass of the calorimeter from kg to g: 1.00 kg = 1000 g .
Calculate change in temperature Next, calculate the change in temperature ( Δ T ): Δ T = T final − T initial = 41. 0 ∘ C − 21. 0 ∘ C = 20. 0 ∘ C .
Calculate heat absorbed by calorimeter Now, calculate the heat absorbed by the calorimeter (q) using the formula q = m C p Δ T : q = (1000 \text{ g}) \times (1.50 \frac{\text{J}}{\text{g} \,^{\circ} C}) \times (20.0^{\circ} C) = 30000 \text{ J} .
Convert Joules to kJ Convert the heat from Joules to kJ: q kJ = 1000 q J = 1000 30000 J = 30.0 kJ .
Final Answer The heat released during the combustion is equal to the heat absorbed by the calorimeter, which is 30.0 kJ.
Examples
Bomb calorimeters are used to measure the heat released or absorbed during a chemical reaction at constant volume. For example, determining the caloric content of food involves combusting a known mass of the food inside a calorimeter and measuring the temperature change. This information is crucial for nutritional labels and dietary planning, helping individuals manage their energy intake effectively.
