In a bomb calorimeter, a 6.50 g sample of octane (C8H18) is combusted. The combustion enthalpy for octane is -5.45 MJ per mol C8H18. The temperature change of the calorimeter is 16.5 oC. What is the heat capacity of the calorimeter?
To find the heat capacity of the calorimeter, we can use the equation:
q = C * ΔT
Where:
q = heat absorbed or released by the system (in this case, the calorimeter)
C = heat capacity of the calorimeter
ΔT = temperature change
We can calculate q using the enthalpy change (ΔH) of the reaction:
ΔH = ΔE + PΔV
Since the reaction is performed in a bomb calorimeter, there is no change in volume (ΔV = 0), so we can simplify the equation to:
ΔH = ΔE
Now, we can calculate the energy change (ΔE) using the given values. The sample of octane has a mass of 6.50 g, and the molar mass of octane (C8H18) is 114 g/mol. Therefore, the number of moles of octane is:
moles = mass / molar mass = 6.50 g / 114 g/mol
Next, we can calculate the energy change (ΔE) using the combustion enthalpy (ΔH) and the number of moles:
ΔE = ΔH * moles
ΔE = -5.45 MJ/mol * (6.50 g / 114 g/mol)
Note that we convert the units of the given enthalpy to match the units of the sample mass.
Now, we can use the equation q = C * ΔT to solve for the heat capacity (C). Given that the temperature change (ΔT) is 16.5°C, we can substitute the values into the equation:
q = C * ΔT
ΔE = C * ΔT
Therefore:
C = ΔE / ΔT = -5.45 MJ/mol * (6.50 g / 114 g/mol) / 16.5°C
Now, we can calculate the heat capacity of the calorimeter by plugging in the values and performing the calculations.