A 0.84 g sample of caffeine, C8H10N4O2, burns in a constant-volume calorimeter that has a heat capacity of 7.85 kJ/K. The temperature increases from 298.30 K to 303.35 K. What is the molar heat of combustion of caffeine (in kJ).
q = 7.85 kJ/K x (303.35-298.30) = 39.01 kJ
So 39.01 x (molar mass caffeine/0.84) = ? kJ/mol caffeine.
To calculate the molar heat of combustion of caffeine, we need to use the heat capacity of the calorimeter and the change in temperature.
The heat transferred during the combustion can be calculated using the equation:
q = CΔT
Where:
q = heat transferred
C = heat capacity of the calorimeter
ΔT = change in temperature
In this case, the heat capacity of the calorimeter (C) is given as 7.85 kJ/K, and the change in temperature (ΔT) is the difference between the final temperature (303.35 K) and the initial temperature (298.30 K):
ΔT = 303.35 K - 298.30 K = 5.05 K
Substituting these values into the equation, we get:
q = 7.85 kJ/K × 5.05 K = 39.67 kJ
Since the given mass of caffeine is 0.84 g, we need to convert this to moles of caffeine. The molar mass of caffeine (C8H10N4O2) can be calculated by summing up the atomic masses of its constituent elements:
Molar Mass of Caffeine = 12.01 g/mol × 8 + 1.01 g/mol × 10 + 14.01 g/mol × 4 + 16.00 g/mol × 2 = 194.19 g/mol
Now, we can convert the mass of caffeine to moles:
Moles of Caffeine = 0.84 g / 194.19 g/mol ≈ 0.00433 mol
Finally, we can calculate the molar heat of combustion of caffeine using the equation:
Molar Heat of Combustion = q / Moles of Caffeine
Plugging in the known values, we have:
Molar Heat of Combustion = 39.67 kJ / 0.00433 mol ≈ 9175.48 kJ/mol
Therefore, the molar heat of combustion of caffeine is approximately 9175.48 kJ/mol.