Respuesta :
Explanation:
1). The given data is as follows.
[tex]T_{i} = 25.87^{o}C[/tex], [tex]T_{f} = 38.13^{o}C[/tex]
C = 5.73 [tex]kJ/^{o}C[/tex]
Hence, calculate the change in enthalpy of the reaction as follows.
[tex]\Delta E_{rxn} = -C \times \Delta T[/tex]
= [tex]-5.73 \times (38.13 - 25.87)^{o}C[/tex]
= -70.25 KJ
As, number of moles = [tex]\frac{mass}{\text{molar mass}}[/tex]
= [tex]\frac{1.55}{(6 \times 12 + 14 \times 1)}[/tex]
= 0.018 mol
Therefore, enthalpy of reaction in kJ/mol hexane is as follows.
[tex]\Delta E_{rxn} = \frac{-70.25 KJ}{0.018 mol}[/tex]
= [tex]-3.90 \times 10^{3}[/tex] kJ/mol
Thus, we can conclude that [tex]\Delta E_{rxn}[/tex] for the reaction in kJ/mol hexane is [tex]-3.90 \times 10^{3}[/tex] kJ/mol .
2). As we know that,
Number of moles = [tex]\frac{mass}{\text{molar mass}}[/tex]
= [tex]\frac{1.55}{(7 \times 12 + 8 \times 1)}[/tex]
= 0.017 mol
[tex]\Delta E_{rxn} = \E_{rxn} per mol \times \text{number of moles}[/tex]
= [tex]-3.91 \times 10^{3} \times 0.017[/tex]
= -65.875 kJ
As, [tex]\Delta E_{rxn} = C \times \Delta T [/tex]
-65.875 kJ = [tex]-C \times (37.57 - 23.12)^{o}C[/tex]
C = 4.56 [tex]kJ/^{o}C[/tex]
Hence, heat capacity of the bomb calorimeter is 4.56 [tex]kJ/^{o}C[/tex].
When 1.550 g of liquid hexane (C₆H₁₄) undergoes combustion in a bomb calorimeter, the temperature rises from 25.87 °C to 38.13 °C. The change in the internal energy of the reaction is -3.90 × 10³ kJ/mol.
When 1.55 g of toluene (C₇H₈) undergoes combustion in a bomb calorimeter, the temperature rises from 23.12 °C to 37.57 °C. The heat capacity of the bomb calorimeter is 4.55 kJ/°C.
- 1. When 1.550 g of liquid hexane (C₆H₁₄) undergoes combustion in a bomb calorimeter, the temperature rises from 25.87 °C to 38.13 °C. Find ΔErxn for the reaction in kJ/mol hexane. The heat capacity of the bomb calorimeter, determined in a separate experiment, is 5.73 kJ/∘C. Express your answer in kilojoules per mole to three significant figures.
First, we will calculate the moles corresponding to 1.550 g of hexane using its molar mass (86.18 g/mol).
[tex]n = 1.550 g \times \frac{1mol}{86.18 g} = 0.01799mol[/tex]
Then, we will calculate the heat (Q) absorbed by the bomb calorimeter using the following expression.
[tex]Q = C \times \Delta T = \frac{5.73kJ}{\° C} \times (38.13\° C - 25.87\° C) = 70.2 kJ[/tex]
According to the law of conservation of energy, the sum of the heat absorbed by the bomb calorimeter (Qb) and the heat released by the combustion (Qc) is zero.
[tex]Qb + Qc = 0\\\\Qc = -Qb = -70.2 kJ[/tex]
Finally, we will calculate the change in the internal energy of the reaction (ΔErxn) using the following expression.
[tex]\Delta Erxn = \frac{Qc}{n} = \frac{-70.2kJ}{0.01799mol} = -3.90 \times 10^{3} kJ/mol[/tex]
- 2. The combustion of toluene has a ΔErxn of –3.91 × 10³ kJ/mol. When 1.55 g of toluene (C₇H₈) undergoes combustion in a bomb calorimeter, the temperature rises from 23.12 °C to 37.57 °C. Find the heat capacity of the bomb calorimeter. Express the heat capacity in kilojoules per degree Celsius to three significant.
First, we will calculate the moles corresponding to 1.55 g of toluene using its molar mass (92.14 g/mol).
[tex]1.55 g \times \frac{1mol}{92.14g} = 0.0168 mol[/tex]
The combustion of toluene has a ΔErxn of –3.91 × 10³ kJ/mol. The heat released by the combustion of 0.0168 moles of toluene is:
[tex]0.0168 mol \times \frac{-3.91\times 10^{3}kJ }{mol} = -65.7 kJ[/tex]
According to the law of conservation of energy, the sum of the heat absorbed by the bomb calorimeter (Qb) and the heat released by the combustion (Qc) is zero.
[tex]Qb + Qc = 0\\\\Qb = -Qc = 65.7 kJ[/tex]
We can calculate the heat capacity of the bomb calorimeter (C) using the following expression.
[tex]C = \frac{Qb}{\Delta T } = \frac{65.7 kJ}{37.57 \° C - 23.12 \° C } = 4.55 kJ/ \° C[/tex]
- When 1.550 g of liquid hexane (C₆H₁₄) undergoes combustion in a bomb calorimeter, the temperature rises from 25.87 °C to 38.13 °C. The change in the internal energy of the reaction is -3.90 × 10³ kJ/mol.
- When 1.55 g of toluene (C₇H₈) undergoes combustion in a bomb calorimeter, the temperature rises from 23.12 °C to 37.57 °C. The heat capacity of the bomb calorimeter is 4.55 kJ/°C.
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