The enthalpy of combustion of benzoic acid
(C6H5COOH) which is often used to calibrate
calorimeters, is −3227 kJ/mol. When 1.402 g
of benzoic acid was burned in a calorimeter,
the temperature increased by 3.401
◦
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
How much heat did you put into the system. That will be (1.402g/molar mass benzoic acid) x 3227 kJ/mol = Ccal*delta T.
Solve for Ccal.
To find the overall heat capacity of the calorimeter, we need to use the equation:
q = mcΔT
Where:
q is the heat transferred
m is the mass of the substance (benzoic acid)
c is the specific heat capacity
ΔT is the change in temperature
First, we need to find the heat transferred (q). We can use the enthalpy of combustion of benzoic acid to calculate this. The enthalpy change (ΔH) can be calculated using the equation:
ΔH = q/n
Where:
ΔH is the enthalpy change
q is the heat transferred
n is the number of moles of benzoic acid
From the given information, the enthalpy of combustion of benzoic acid is -3227 kJ/mol. To calculate the enthalpy change (ΔH), we need to convert the mass of benzoic acid to moles using its molar mass.
The molar mass of benzoic acid (C6H5COOH) can be calculated as follows:
(6 x 12.01 g/mol) + (5 x 1.01 g/mol) + 12.01 g/mol + 16.00 g/mol + 16.00 g/mol + 1.01 g/mol = 122.12 g/mol
Given that the mass of benzoic acid is 1.402 g, we can calculate the number of moles (n) using the equation:
n = mass / molar mass
n = 1.402 g / 122.12 g/mol
Next, we can calculate the heat transferred (q) using the equation:
q = ΔH x n
q = -3227 kJ/mol x n
Now we need to find the specific heat capacity (c) of the calorimeter. The specific heat capacity of water is approximately 4.18 J/g°C.
To convert the specific heat capacity from J/g°C to kJ/°C, divide it by 1000:
c = 4.18 J/g°C / 1000 = 0.00418 kJ/g°C
Now we can substitute the values into the equation:
q = mcΔT
-q = mcΔT (because q represents the heat transferred to the surroundings)
-q = (m + m_water) x c x ΔT
Where:
m is the mass of benzoic acid
m_water is the mass of water in the calorimeter
c is the specific heat capacity of water
ΔT is the change in temperature
From the given information, the change in temperature (ΔT) is 3.401°C.
Let's assume the mass of water (m_water) in the calorimeter is x grams. The total mass in the calorimeter (m + m_water) will be the sum of the mass of benzoic acid (1.402 g) and the mass of water (x g).
Now we can calculate the overall heat capacity (C) using the equation:
C = -q / ΔT
C = -(-q) / ΔT (we remove the negative sign)
C = q / ΔT
C = (m + m_water) x c
C = (1.402 g + x g) x 0.00418 kJ/g°C
We know that the change in temperature (ΔT) is given as 3.401°C.
Now you can substitute the values into the equation and solve for x to find the mass of water in the calorimeter. Once you have the mass of water, you can calculate the overall heat capacity (C).