To find the heat of combustion for the ethanol sample, we need to understand the relationship between heat and the specifics of the calorimeter used in the experiment. Follow these steps to derive the solution:
1. Identify the given data:
- Mass of ethanol sample ([tex]\(m_{\text{ethanol}}\)[/tex]): [tex]\(0.2301 \, \text{g}\)[/tex]
- Temperature increase ([tex]\(\Delta T\)[/tex]): [tex]\(1.33 \, ^{\circ} \text{C}\)[/tex]
- Mass of the calorimeter ([tex]\(m_{\text{calorimeter}}\)[/tex]): [tex]\(2000 \, \text{g}\)[/tex] (since [tex]\(2 \, \text{kg} = 2000 \, \text{g}\)[/tex])
- Specific heat capacity of the calorimeter ([tex]\(c_{\text{calorimeter}}\)[/tex]): [tex]\(2.45 \, \text{J} / \text{g} \cdot ^{\circ} \text{C}\)[/tex]
2. Calculate the heat absorbed by the calorimeter:
- The heat absorbed ([tex]\(Q\)[/tex]) can be calculated using the formula for heat transfer:
[tex]\[
Q = m_{\text{calorimeter}} \times c_{\text{calorimeter}} \times \Delta T
\][/tex]
Where:
- [tex]\(m_{\text{calorimeter}}\)[/tex]: mass of the calorimeter
- [tex]\(c_{\text{calorimeter}}\)[/tex]: specific heat capacity
- [tex]\(\Delta T\)[/tex]: change in temperature.
3. Insert the given values into the formula:
[tex]\[
Q = 2000 \, \text{g} \times 2.45 \, \text{J} / (\text{g} \cdot ^{\circ} \text{C}) \times 1.33 \, ^{\circ} \text{C}
\][/tex]
4. Compute the value of [tex]\(Q\)[/tex]:
[tex]\[
Q = 2000 \times 2.45 \times 1.33 = 6517 \, \text{J}
\][/tex]
So the heat absorbed by the calorimeter is [tex]\(6517 \, \text{J}\)[/tex].
5. Convert the heat absorbed (in joules) to kilojoules:
- Since [tex]\(1 \, \text{kJ} = 1000 \, \text{J}\)[/tex], divide the result by [tex]\(1000\)[/tex]:
[tex]\[
Q = \frac{6517 \, \text{J}}{1000} = 6.517 \, \text{kJ}
\][/tex]
Therefore, the heat of combustion for the ethanol sample is approximately 6.517 kJ.
