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?
1 mole of C6H5COOH = 122.1234 g
(3227kJ/mol)/(122.1234g/mol) = 26.4241 kJ/g
Multiply that by the mass of the sample given.
Divide the answer by 2.345 C or K to get the number of kJ per degree (the calorimeter constant).
To find the specific heat of the calorimeter, we can use the formula:
q = m * C * ΔT
Where:
q is the heat absorbed by the calorimeter
m is the mass of the substance burned (benzoic acid)
C is the specific heat of the calorimeter
ΔT is the change in temperature of the calorimeter
In this case, we can rearrange the formula to solve for C:
C = q / (m * ΔT)
To calculate q, we can use the enthalpy of combustion of benzoic acid (-3227 kJ/mol) and convert it to kJ/g by dividing by the molar mass of benzoic acid (122.13 g/mol).
First, let's calculate q:
q = (-3227 kJ/mol / 122.13 g/mol) * 1.236 g
q ≈ -32.516 kJ
Next, we can substitute the values into the formula:
C = (-32.516 kJ) / (1.236 g * 2.345 K)
C ≈ -5.29 kJ/(g·K)
The specific heat of the calorimeter is approximately -5.29 kJ/(g·K). Note that the negative sign indicates that the calorimeter releases heat.
To calculate the specific heat of the calorimeter, you can use the equation:
q = mcΔT
Where:
q = heat transfer
m = mass of the substance
c = specific heat capacity
ΔT = change in temperature
In this case, the heat transfer (q) can be calculated using the enthalpy of combustion of benzoic acid:
q = -ΔH
Given:
Enthalpy of combustion of benzoic acid (ΔH) = -3227 kJ/mol
Mass of benzoic acid (m) = 1.236 g
Change in temperature (ΔT) = 2.345 K
First, we need to calculate the number of moles of benzoic acid burned:
Number of moles = mass / molar mass
The molar mass of benzoic acid (C6H5COOH) can be calculated by summing up the molar masses of its individual elements:
C (6 atoms) = 6 * 12.01 g/mol
H (7 atoms) = 7 * 1.008 g/mol
O (2 atoms) = 2 * 16.00 g/mol
Molar Mass of benzoic acid = (6 * 12.01) + (7 * 1.008) + (2 * 16.00) g/mol
Now that we have the molar mass of benzoic acid, we can calculate the number of moles burnt:
Number of moles = 1.236 g / molar mass (g/mol)
Once you have the number of moles, you can calculate the heat transfer:
q = (number of moles) * ΔH
Now, we can calculate the specific heat capacity (c) of the calorimeter using the equation mentioned earlier:
c = q / (m * ΔT)
Substituting the values we have:
c = (q / (m * ΔT))
I hope this helps you in calculating the specific heat of the calorimeter!