The enthalpy of combustion of benzoic acid,C6H5COOH, which is often used to calibrate calorimeters, is
-3227kJ/mol. When 1.236g of benzoic acid was burned in a calorimeter, the tempurature increased by 2.345K. What is the specific heat of the calorimeter?
First, how many moles is 1.236g of benzoic acid? That ought to give you a clue as to how much heat was liberated.
Then.
Heat liberated=specifheatcalorimeter*2.345
and you can solve for the specific heat.
Now a note of error on this method: Enthalpy of combustion is taken as if at constant temperature, so in this method one ignores the heat content of the products when they are not at the original temperature. The products are CO2, H2O vapor. This is valid here because the mass of products will be trivial to the mass of the calorimeter.
Specific Heat of the calorimeter will be calculated here in kJ/Celcius.
To find the specific heat of the calorimeter, we can use the formula:
q = m * c * ΔT
Where:
q = heat absorbed or released by the system (calorimeter)
m = mass of the substance (benzoic acid)
c = specific heat capacity of the substance (calorimeter)
ΔT = change in temperature
First, we need to calculate the heat absorbed by the system (q) using the enthalpy of combustion:
q = n * ΔH
Where:
q = heat absorbed by the system (calorimeter)
n = moles of the substance (benzoic acid)
ΔH = enthalpy change of combustion per mole
To find the moles of benzoic acid, we can use the molecular weight of benzoic acid:
Molecular weight of benzoic acid = 6(12.01) + 5(1.008) + 1(16.00) = 122.12 g/mol
moles = mass / molecular weight
moles = 1.236g / 122.12 g/mol
Now, we have the moles of benzoic acid.
Next, we can calculate the heat absorbed by the system (q):
q = n * ΔH
q = moles * ΔH
q = (1.236g / 122.12 g/mol) * (-3227 kJ/mol)
q = -32.664 kJ
Now, we have the heat absorbed by the system.
Since q = m * c * ΔT, we can rearrange the formula to solve for c:
c = q / (m * ΔT)
c = (-32.664 kJ) / (1.236g * 2.345K)
Using the given values, we can calculate the specific heat capacity of the calorimeter.