A constant volume (bomb) calorimeter was calibrated in an analytical laboratory by

burning 1.057g of benzoic acid (C7H6O2) which has an enthalpy of combustion of -3228 kJ/mol. The temperature of the calorimeter rose from 22.75°C to 29.00°C. What is the heat capacity of the calorimeter?

3228 x (1.057 g/molar mass benzoic acid)= q in kJ

q = Ccal*(Tfinal-Tinitial)

To find the heat capacity of the calorimeter, we need to use the equation:

q = mcΔT

where:
q = heat absorbed or released by the system (calorimeter)
m = mass of the substance being heated (benzoic acid)
c = specific heat capacity of the substance being heated (benzoic acid)
ΔT = change in temperature (final temperature - initial temperature)

First, let's calculate the heat absorbed by the calorimeter using the given data.

1. Calculate the moles of benzoic acid burned:
To find the moles, we need to divide the given mass of benzoic acid by its molar mass.

Molar mass of benzoic acid (C7H6O2):
7(12.01 g/mol) + 6(1.01 g/mol) + 2(16.00 g/mol)
= 122.13 g/mol

moles of benzoic acid = mass / molar mass
= 1.057 g / 122.13 g/mol

2. Calculate the heat absorbed or released by the benzoic acid using its enthalpy of combustion:

Heat absorbed by benzoic acid = moles of benzoic acid * enthalpy of combustion
= (1.057 g / 122.13 g/mol) * -3228 kJ/mol

3. Calculate the change in temperature:

ΔT = final temperature - initial temperature
= (29.00°C - 22.75°C)

Now, we can substitute the values into the equation q = mcΔT:

q = (m + mc)ΔT

where m is the mass of water and c is the specific heat capacity of water.

4. Calculate the heat capacity of the calorimeter:

heat absorbed by calorimeter = (m + mc)ΔT
heat absorbed by calorimeter = q - heat absorbed by benzoic acid

Finally, we can solve for the heat capacity of the calorimeter.

Note: To find the specific heat capacity of water (c), you can use the value of 4.18 J/g°C.