Question

a sample of hexane (\\(\text{c}_6\text{h}_{14}\\)) has a mass of \\(0.580\text{ g}\\). the sample is burned in a bomb calorimeter that has a mass of \\(1.900\text{ kg}\\) and a specific heat of \\(3.21\text{ j/g}\cdot\text{k}\\). what amount of heat is produced during the combustion of hexane if the temperature of the calorimeter increases by \\(4.542\text{ k}\\)?
use \\(q = mc_p\delta t\\).

• \\(8.46\text{ kj}\\)
• \\(27.7\text{ kj}\\)
• \\(47.8\text{ kj}\\)
• \\(16.1\text{ kj}\\)

Explanation:

Identify given values

We extract the parameters from the problem statement:

• Mass of calorimeter, \(m = 1.900\text{ kg} = 1900\text{ g}\)
• Specific heat capacity of calorimeter, \(C_p = 3.21\text{ J/g}\cdot\text{K}\)
• Temperature change, \(\Delta T = 4.542\text{ K}\)
• Formula: \(q = m C_p \Delta T\)

Calculate heat absorbed

Using the Calorimetry and Specific Heat Capacity concepts:

$$ q = 1900\text{ g} \times 3.21\text{ J/g}\cdot\text{K} \times 4.542\text{ K} $$

$$ q = 27701.658\text{ J} $$

Convert to kilojoules

Convert the energy from Joules to kilojoules:

$$ q = \frac{27701.658\text{ J}}{1000\text{ J/kJ}} \approx 27.7\text{ kJ} $$

Answer:

• 8.46 kJ
• 27.7 kJ (Correct answer)
• 47.8 kJ
• 16.1 kJ