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Answer :
To find the heat capacity of the calorimeter, we'll follow a step-by-step approach:
1. Determine the Moles of Aniline Combusted:
- Mass of Aniline: 6.55 g
- Molar Mass of Aniline (C₆H₅NH₂): 93.13 g/mol
Calculate the moles of aniline using the formula:
[tex]\[
\text{Moles of aniline} = \frac{\text{Mass of aniline}}{\text{Molar mass of aniline}} = \frac{6.55 \, \text{g}}{93.13 \, \text{g/mol}} \approx 0.0703 \, \text{mol}
\][/tex]
2. Calculate the Enthalpy Change (Heat Released):
- We know the combustion reaction for aniline involves 4 moles of aniline, and for simplicity, assume that this hypothetical enthalpy change for the reaction is given as -66.4 kJ (just to follow through with information).
For the combustion of aniline:
[tex]\[
\text{Enthalpy change per mole of aniline} = \frac{-66.4 \, \text{kJ}}{4}
\][/tex]
[tex]\[
\text{Total enthalpy change} = \text{Moles of aniline} \times \left(\text{Enthalpy change per mole}\right)
\][/tex]
[tex]\[
\text{Total enthalpy change} \approx 0.0703 \, \text{mol} \times -16.6 \, \text{kJ/mol} \approx -1.1675 \, \text{kJ}
\][/tex]
3. Calculate the Heat Capacity of the Calorimeter:
- The heat absorbed by the calorimeter can be equated to the absolute value of the enthalpy change:
[tex]\[
q = C \times \Delta T
\][/tex]
- Where [tex]\( q \)[/tex] is the heat absorbed, [tex]\( C \)[/tex] is the heat capacity of the calorimeter, and [tex]\(\Delta T\)[/tex] is the temperature rise.
Solving for [tex]\( C \)[/tex]:
[tex]\[
C = \frac{| q |}{\Delta T} = \frac{1.1675 \, \text{kJ}}{32.9 \, ^\circ\text{C}} \approx 0.0355 \, \text{kJ}/^\circ\text{C}
\][/tex]
4. Select the Correct Answer Choice:
- The calculated heat capacity of the calorimeter is approximately [tex]\(0.0355 \, \text{kJ}/^\circ\text{C}\)[/tex], which is not one of the options provided. This means there might be an issue based on the hypothetical value chosen or options provided do not match the calculation result.
Given the results:
- The closest choice based on the expected calculations would be identified if there’s a discrepancy with information provided (hypothetical values or option choices you've seen). Given the options provided in your context, typically find the closest match or identify discrepancy in actual option calculations if different.
Unfortunately, the calculations show a result here that doesn't align neatly with your provided options without changing reaction hypothetical values or roles of combustion reactions potentially misunderstood in the initial interpretation.
1. Determine the Moles of Aniline Combusted:
- Mass of Aniline: 6.55 g
- Molar Mass of Aniline (C₆H₅NH₂): 93.13 g/mol
Calculate the moles of aniline using the formula:
[tex]\[
\text{Moles of aniline} = \frac{\text{Mass of aniline}}{\text{Molar mass of aniline}} = \frac{6.55 \, \text{g}}{93.13 \, \text{g/mol}} \approx 0.0703 \, \text{mol}
\][/tex]
2. Calculate the Enthalpy Change (Heat Released):
- We know the combustion reaction for aniline involves 4 moles of aniline, and for simplicity, assume that this hypothetical enthalpy change for the reaction is given as -66.4 kJ (just to follow through with information).
For the combustion of aniline:
[tex]\[
\text{Enthalpy change per mole of aniline} = \frac{-66.4 \, \text{kJ}}{4}
\][/tex]
[tex]\[
\text{Total enthalpy change} = \text{Moles of aniline} \times \left(\text{Enthalpy change per mole}\right)
\][/tex]
[tex]\[
\text{Total enthalpy change} \approx 0.0703 \, \text{mol} \times -16.6 \, \text{kJ/mol} \approx -1.1675 \, \text{kJ}
\][/tex]
3. Calculate the Heat Capacity of the Calorimeter:
- The heat absorbed by the calorimeter can be equated to the absolute value of the enthalpy change:
[tex]\[
q = C \times \Delta T
\][/tex]
- Where [tex]\( q \)[/tex] is the heat absorbed, [tex]\( C \)[/tex] is the heat capacity of the calorimeter, and [tex]\(\Delta T\)[/tex] is the temperature rise.
Solving for [tex]\( C \)[/tex]:
[tex]\[
C = \frac{| q |}{\Delta T} = \frac{1.1675 \, \text{kJ}}{32.9 \, ^\circ\text{C}} \approx 0.0355 \, \text{kJ}/^\circ\text{C}
\][/tex]
4. Select the Correct Answer Choice:
- The calculated heat capacity of the calorimeter is approximately [tex]\(0.0355 \, \text{kJ}/^\circ\text{C}\)[/tex], which is not one of the options provided. This means there might be an issue based on the hypothetical value chosen or options provided do not match the calculation result.
Given the results:
- The closest choice based on the expected calculations would be identified if there’s a discrepancy with information provided (hypothetical values or option choices you've seen). Given the options provided in your context, typically find the closest match or identify discrepancy in actual option calculations if different.
Unfortunately, the calculations show a result here that doesn't align neatly with your provided options without changing reaction hypothetical values or roles of combustion reactions potentially misunderstood in the initial interpretation.
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