Question

A sample of hexane (C6H14) has a mass of 0.580 g. The sample is burned in a bomb calorimeter that has a mass of 1.900 kg and a specific heat of 3.21 J/giK. What amount of heat is produced during the combustion of hexane if the temperature of the calorimeter increases by 4.542 K?
Use q equals m C subscript p Delta T..
8.46 kJ
16.1 kJ
27.7 kJ
47.8 kJ

Answer 1

To calculate the amount of heat produced during the combustion of hexane, we can use the formula:

\[ q = m \cdot C_p \cdot \Delta T \]

where:
- \( q \) is the heat produced (in joules)
- \( m \) is the mass of the calorimeter (in grams)
- \( C_p \) is the specific heat capacity of the calorimeter (in J/g·K)
- \( \Delta T \) is the change in temperature (in K)

Given the following values from the problem:
- Mass of the calorimeter, \( m = 1.900 \, \text{kg} = 1900 \, \text{g} \) (since \( 1 \, \text{kg} = 1000 \, \text{g} \))
- Specific heat capacity, \( C_p = 3.21 \, \text{J/g·K} \)
- Change in temperature, \( \Delta T = 4.542 \, K \)

Now we can substitute these values into the equation:

\[
q = (1900 \, \text{g}) \cdot (3.21 \, \text{J/g·K}) \cdot (4.542 \, K)
\]

Calculating it step-by-step:

1. Calculate \( 1900 \cdot 3.21 \):

\[
1900 \cdot 3.21 = 6099 \, \text{J/K}
\]

2. Now multiply by \( \Delta T \):

\[
q = 6099 \, \text{J/K} \cdot 4.542 \, K \approx 27768.438 \, \text{J}
\]

3. Convert joules to kilojoules (since \( 1 \, \text{kJ} = 1000 \, \text{J} \)):

\[
q \approx 27.77 \, \text{kJ}
\]

Rounding to two decimal places, the result is approximately:

\[
q \approx 27.7 \, \text{kJ}
\]

Thus, the amount of heat produced during the combustion of hexane is **27.7 kJ**.