To determine the amount of heat produced during the combustion of the hexane sample, follow these steps:
1. Understanding the variables in the problem:
- Mass of the calorimeter, \( m \): 1.900 kg (which is equivalent to 1900 g)
- Specific heat capacity of the calorimeter, \( C_p \): 3.21 J/gK
- Temperature change, \( \Delta T \): 4.542 K
2. Applying the formula for heat:
The formula to calculate the amount of heat (\( q \)) absorbed or released is:
[tex]\[
q = m \cdot C_p \cdot \Delta T
\][/tex]
3. Substituting the given values into the formula:
[tex]\[
q = 1900 \, \text{g} \cdot 3.21 \, \text{J/gK} \cdot 4.542 \, \text{K}
\][/tex]
4. Calculating the heat produced:
[tex]\[
q = 1900 \times 3.21 \times 4.542
\][/tex]
[tex]\[
q = 27701.658 \, \text{J}
\][/tex]
5. Converting the heat produced from Joules to kilojoules:
Since \(1 \, \text{kJ} = 1000 \, \text{J}\),
[tex]\[
q = \frac{27701.658 \, \text{J}}{1000}
\][/tex]
[tex]\[
q = 27.701658 \, \text{kJ}
\][/tex]
Therefore, the amount of heat produced during the combustion of hexane is approximately \(27.7 \, \text{kJ}\).
So, the correct answer is:
[tex]\[
27.7 \, \text{kJ}
\][/tex]
This matches the third option from the provided choices:
- \( 8.46 \, \text{kJ} \)
- \( 16.1 \, \text{kJ} \)
- \( 27.7 \, \text{kJ} \)
- \( 47.8 \, \text{kJ} \)
Thus, the correct answer is [tex]\(27.7 \, \text{kJ}\)[/tex].
