Answer:
C = -0.624 kJ/K
To calculate the heat capacity of the calorimeter, we need to use the following formula:
q = CΔT
where q is the heat released by the benzoic acid, C is the heat capacity of the calorimeter, and ΔT is the temperature rise observed.
First, we need to calculate the heat released by the benzoic acid:
q = m × ΔH
where m is the mass of the benzoic acid and ΔH is its heat of combustion.
The heat of combustion of benzoic acid is -3226 kJ/mol.
The molar mass of benzoic acid is 122.12 g/mol.
So, the number of moles of benzoic acid used in the experiment is:
n = m / M = 6.54 g / 122.12 g/mol = 0.0535 mol
The heat released by the combustion of the benzoic acid is:
q = n × ΔH = 0.0535 mol × (-3226 kJ/mol) = -172.6 kJ
The negative sign indicates that the reaction is exothermic (i.e., it releases heat).
Next, we need to calculate the heat absorbed by the calorimeter, which can be determined using the heat capacity equation:
q = C × ΔT
We know the value of q from the combustion of benzoic acid and the value of ΔT from the temperature rise observed, which is 3.6°C.
The mass of the fuse wire is not relevant to the calculation, so we can ignore it.
Substituting the values, we get:
-172.6 kJ = C × (3.6°C)
We need to convert the temperature rise to kelvin:
ΔT (K) = ΔT (°C) + 273.15 = 3.6°C + 273.15 = 276.75 K
Substituting this value, we get:
-172.6 kJ = C × (276.75 K)
Solving for C, we get:
C = -172.6 kJ / 276.75 K = -0.624 kJ/K
The heat capacity of the calorimeter is -0.624 kJ/K. The negative sign indicates that the calorimeter loses heat as the temperature rises, which is a common feature of bomb calorimeters.