Answer :
To determine the heat capacity of the calorimeter, let's go step-by-step through the problem:
1. Understand the Given Information:
- We have a 6.55 g sample of aniline ([tex]\(C_6H_5NH_2\)[/tex]).
- The molar mass of aniline is 93.13 g/mol.
- The temperature rise during the reaction is [tex]\(32.9^\circ C\)[/tex].
- The enthalpy change for the reaction involving 4 moles of aniline is [tex]\(-1.28 \times 10^4 \, \text{kJ}\)[/tex].
2. Calculate the Number of Moles of Aniline:
[tex]\[
\text{moles of aniline} = \frac{\text{mass of sample}}{\text{molar mass}} = \frac{6.55 \, \text{g}}{93.13 \, \text{g/mol}} \approx 0.07033 \, \text{moles}
\][/tex]
3. Calculate the Heat Released:
Since the reaction involves 4 moles of aniline releasing [tex]\(-1.28 \times 10^4 \, \text{kJ}\)[/tex], the heat released for the combusted amount is:
[tex]\[
\text{heat released} = \text{moles of aniline} \times \Delta H_r = 0.07033 \, \text{moles} \times (-1.28 \times 10^4 \, \text{kJ/mol})
\][/tex]
[tex]\[
\approx -900.25 \, \text{kJ}
\][/tex]
Note: The negative sign indicates that heat is released.
4. Calculate the Heat Capacity of the Calorimeter:
Heat capacity is defined as the amount of heat required to change the temperature of the system by one degree Celsius. Therefore:
[tex]\[
\text{Heat Capacity} = \frac{\text{heat released}}{\Delta T} = \frac{-900.25 \, \text{kJ}}{32.9^\circ C}
\][/tex]
[tex]\[
\approx 27.36 \, \text{kJ/}^\circ C
\][/tex]
Based on these calculations, the heat capacity of the calorimeter is approximately [tex]\(27.36 \, \text{kJ/}^\circ C\)[/tex].
1. Understand the Given Information:
- We have a 6.55 g sample of aniline ([tex]\(C_6H_5NH_2\)[/tex]).
- The molar mass of aniline is 93.13 g/mol.
- The temperature rise during the reaction is [tex]\(32.9^\circ C\)[/tex].
- The enthalpy change for the reaction involving 4 moles of aniline is [tex]\(-1.28 \times 10^4 \, \text{kJ}\)[/tex].
2. Calculate the Number of Moles of Aniline:
[tex]\[
\text{moles of aniline} = \frac{\text{mass of sample}}{\text{molar mass}} = \frac{6.55 \, \text{g}}{93.13 \, \text{g/mol}} \approx 0.07033 \, \text{moles}
\][/tex]
3. Calculate the Heat Released:
Since the reaction involves 4 moles of aniline releasing [tex]\(-1.28 \times 10^4 \, \text{kJ}\)[/tex], the heat released for the combusted amount is:
[tex]\[
\text{heat released} = \text{moles of aniline} \times \Delta H_r = 0.07033 \, \text{moles} \times (-1.28 \times 10^4 \, \text{kJ/mol})
\][/tex]
[tex]\[
\approx -900.25 \, \text{kJ}
\][/tex]
Note: The negative sign indicates that heat is released.
4. Calculate the Heat Capacity of the Calorimeter:
Heat capacity is defined as the amount of heat required to change the temperature of the system by one degree Celsius. Therefore:
[tex]\[
\text{Heat Capacity} = \frac{\text{heat released}}{\Delta T} = \frac{-900.25 \, \text{kJ}}{32.9^\circ C}
\][/tex]
[tex]\[
\approx 27.36 \, \text{kJ/}^\circ C
\][/tex]
Based on these calculations, the heat capacity of the calorimeter is approximately [tex]\(27.36 \, \text{kJ/}^\circ C\)[/tex].
