At constant volume, the heat of combustion of a particular compound is –3334.0 kJ/mol. When 1.569 g of this compound (molar mass = 125.76 g/mol) was burned in a bomb calorimeter, the temperature of the calorimeter (including its contents) rose by 5.173 °C. What is the heat capacity (calorimeter constant) of the calorimeter?
How many mols did you start with? That's 1.569g x (1 mol/125.76 g) = ? mol.
How much heat was generated. That's
3334.0 kJ/mol x ? mol = ? joules.
?joules = Ccal x delta T.
Solve for Ccal
To find the heat capacity of the calorimeter, we can use the formula:
q = C * ΔT
Where:
q is the heat absorbed or released by the calorimeter and its contents
C is the heat capacity of the calorimeter
ΔT is the change in temperature of the calorimeter and its contents
First, let's convert the mass of the compound burned into moles:
moles = mass / molar mass
moles = 1.569 g / 125.76 g/mol
moles = 0.01248 mol
Now, we can calculate the heat absorbed or released by the calorimeter and its contents, using the heat of combustion:
q = moles * ΔH
q = 0.01248 mol * (-3334.0 kJ/mol)
q = -41.60 kJ
Next, let's convert the temperature change from Celsius to Kelvin:
ΔT = 5.173 °C + 273.15
ΔT = 278.323 K
Now, we can rearrange the formula to solve for the heat capacity:
C = q / ΔT
C = -41.60 kJ / 278.323 K
C ≈ -0.1497 kJ/K
Since heat capacity should have a positive value, we take the absolute value:
C ≈ 0.1497 kJ/K
Therefore, the heat capacity (calorimeter constant) of the calorimeter is approximately 0.1497 kJ/K.