Question

a sample of octane (c₈h₁₈) that has a mass of 0.750 g is burned in a bomb calorimeter. as a result, the temperature of the calorimeter increases from 21.0°c to 41.0°c. the specific heat of the calorimeter is 1.50 j/(g·°c), and its mass is 1.00 kg. how much heat is released during the combustion of this sample? use q = mcₚδt. ○ 22.5 kj ○ 30.0 kj ○ 31.5 kj ○ 61.5 kj

Explanation:

Step1: Convert mass to grams

The mass of the calorimeter is 1.00 kg. Since 1 kg = 1000 g, the mass \( m = 1000 \) g.

Step2: Calculate temperature change

The initial temperature \( T_1 = 21.0^\circ\text{C} \) and the final temperature \( T_2 = 41.0^\circ\text{C} \). The temperature change \( \Delta T = T_2 - T_1 = 41.0 - 21.0 = 20.0^\circ\text{C} \).

Step3: Use the formula \( q = mC_p\Delta T \)

The specific heat \( C_p = 1.50 \, \text{J/(g·°C)} \), \( m = 1000 \) g, and \( \Delta T = 20.0^\circ\text{C} \). Plugging in the values: \( q = 1000 \, \text{g} \times 1.50 \, \text{J/(g·°C)} \times 20.0^\circ\text{C} \).
First, calculate \( 1000 \times 1.50 = 1500 \), then \( 1500 \times 20.0 = 30000 \) J. Convert joules to kilojoules: \( 30000 \, \text{J} = 30.0 \, \text{kJ} \) (since 1 kJ = 1000 J).

Answer:

30.0 kJ (corresponding to the option "30.0 kJ")