Sure, let's analyze the given problem step by step:
1. Determine the Mass of the Calorimeter in Grams:
The mass of the calorimeter is given as [tex]\(1.900 \, \text{kg}\)[/tex]. We need to convert this mass into grams for consistency in the units.
[tex]\[
1.900 \, \text{kg} = 1.900 \times 1000 \, \text{g} = 1900 \, \text{g}
\][/tex]
2. Identify the Specific Heat of the Calorimeter:
The specific heat capacity ([tex]\(C_p\)[/tex]) of the calorimeter is given as [tex]\(3.21 \, \text{J/g/K}\)[/tex].
3. Determine the Temperature Increase:
The temperature increase [tex]\(\Delta T\)[/tex] during the combustion is given as [tex]\(4.542 \, \text{K}\)[/tex].
4. Use the Formula to Calculate the Heat Produced ([tex]\(q\)[/tex]):
Using the formula provided [tex]\( q = m C_p \Delta T \)[/tex]:
- [tex]\(m\)[/tex] is the mass of the calorimeter. We already converted this to grams:
[tex]\[
m = 1900 \, \text{g}
\][/tex]
- [tex]\(C_p\)[/tex] is the specific heat capacity:
[tex]\[
C_p = 3.21 \, \text{J/g/K}
\][/tex]
- [tex]\(\Delta T\)[/tex] is the change in temperature:
[tex]\[
\Delta T = 4.542 \, \text{K}
\][/tex]
Plugging these values into the formula:
[tex]\[
q = 1900 \, \text{g} \times 3.21 \, \text{J/g/K} \times 4.542 \, \text{K}
\][/tex]
5. Calculate [tex]\(q\)[/tex] (the Heat Produced in Joules):
Performing the multiplication gives:
[tex]\[
q = 1900 \times 3.21 \times 4.542 \approx 27701.658 \, \text{J}
\][/tex]
6. Convert the Heat from Joules to Kilojoules:
Since there are [tex]\(1000 \, \text{J}\)[/tex] in [tex]\(1 \, \text{kJ}\)[/tex]:
[tex]\[
q = \frac{27701.658 \, \text{J}}{1000} = 27.701658 \, \text{kJ}
\][/tex]
7. Select the Closest Numerical Option:
Among the given options, the closest value to our calculated result [tex]\(27.701658 \, \text{kJ}\)[/tex] is:
[tex]\[
27.7 \, \text{kJ}
\][/tex]
Therefore, the amount of heat produced during the combustion of hexane is 27.7 kJ.
