The enthalpy of combustion of benzoic acid(C6H5COOH) which is often used to calibratecalorimeters, is −3227 kJ/mol. When 1.316 gof benzoic acid was burned in a calorimeter, the temperature increased by 2.226◦C. What is the overall heat capacity of the calorimeter? The overall heat capacity includes the calorimeter hardware and the water that is in it.
Answer in units of kJ/◦C
mols benzoic acid = grams/molar mass = 1.316/122.123 = ?
delta H combustion = 3227 x mols benzoic acid.
Then Ccal = delta H/delta T.
To find the overall heat capacity of the calorimeter, we can use the equation:
q = C × ΔT
Where:
q is the heat transferred
C is the overall heat capacity of the calorimeter
ΔT is the change in temperature
Given:
Enthalpy of combustion of benzoic acid = -3227 kJ/mol
Mass of benzoic acid = 1.316 g
Change in temperature = 2.226°C
First, let's calculate the amount of heat transferred:
q = (Enthalpy of combustion × Mass of benzoic acid) / Molar mass of benzoic acid
Molar mass of benzoic acid (C6H5COOH):
(C: 12.011 g/mol) + (H: 1.008 g/mol × 7) + (O: 15.999 g/mol × 2) = 122.123 g/mol
q = (-3227 kJ/mol × 1.316 g) / 122.123 g/mol
q ≈ -34.808 kJ
Next, we can calculate the overall heat capacity:
C = q / ΔT
C = -34.808 kJ / 2.226°C
C ≈ -15.650 kJ/°C
Therefore, the overall heat capacity of the calorimeter is approximately -15.650 kJ/°C.
To find the overall heat capacity of the calorimeter, we can use the equation:
q = mCΔT
Where:
- q is the heat transfer (in this case, it would be the heat absorbed by the calorimeter and water)
- m is the mass of the benzoic acid (given as 1.316 g)
- C is the overall heat capacity of the calorimeter
- ΔT is the temperature change (given as 2.226°C)
We're told that the enthalpy of combustion of benzoic acid is -3227 kJ/mol. Therefore, when 1 mole of benzoic acid is burned, it releases 3227 kJ of heat energy.
To find the heat transfer when 1.316 g of benzoic acid is burned, we need to convert grams to moles. The molar mass of benzoic acid (C6H5COOH) is:
(6*12) + (5*1) + 12 + 16 + 16 + 1 = 122 g/mol
Converting 1.316 g to moles:
1.316 g * (1 mol / 122 g) = 0.0108 mol
Now, using the heat of combustion, we can find the heat transfer when 0.0108 mol of benzoic acid is burned:
q = 0.0108 mol * -3227 kJ/mol = -34.86 kJ
Now we can rearrange the equation to solve for the overall heat capacity (C):
C = q / (m * ΔT)
C = -34.86 kJ / (1.316 g * 2.226°C)
C ≈ -11.975 kJ/°C
So, the overall heat capacity of the calorimeter is approximately -11.975 kJ/°C.