Answer:
350 kJ/mol
Explanation:
1. Calculate the energy absorbed by the water:
- The specific heat capacity of water is 4.18 J/g°C.
- The mass of water is 100.0 g.
- The change in temperature is 75.8°C.
\( q = mcΔT \)
\( q = (100.0 g)(4.18 J/g°C)(75.8°C) \)
The energy absorbed by the water (q) is calculated to be 31453.24 J.
2. Calculate the energy released by the burning cyclopentane:
- The mass of cyclopentane burned is 0.730 g.
- The energy density of cotton is 5000 J/g.
\( q = mc \)
\( q = (0.730 g)(5000 J/g) \)
The energy released by the burning cyclopentane (q) is calculated to be 3650 J.
3. Calculate the molar enthalpy of combustion:
- Convert the energy values to kilojoules:
- Energy absorbed by water: \(31453.24 J = 31.45324 kJ\)
- Energy released by cyclopentane: \(3650 J = 3.65 kJ\)
\( ΔH = \frac{Energy \, released \, by \, cyclopentane}{n} \)
\( n = \frac{0.730 g}{Cyclopentane \, molar \, mass} \)
The molar mass of cyclopentane is 70.13 g/mol.
\( n = \frac{0.730 g}{70.13 g/mol} = 0.0104 mol \)
\( ΔH = \frac{3.65 kJ}{0.0104 mol} = 350 kJ/mol \)
Therefore, the molar enthalpy of combustion of cyclopentane, using the given calorimetry data and the average cotton energy density of 5000 J/g, is approximately **350 kJ/mol**.
