14.E: Thermochemistry (Exercises)
13.5: Calorimetry
Q13.5.1
After going through combustion in a bomb calorimeter a sample gives off 5,435 cal. The calorimeter experiences an increase of 4.27°C in its temperature. Using this information, determine the heat capacity of the calorimeter in kJ/°C.
Q13.5.2
Referring to the example given above about the heat of combustion, calculate the temperature change that would occur in the combustion of 1.732 g \(C_{12}H_{22}O_{12}\) in a bomb calorimeter that had the heat capacity of 3.87 kJ/°C.
Q13.5.3
Given the following data calculate the heat of combustion in kJ/mol of xylose,\(C_{5}H_{10}O_{5}\)(s), used in a bomb calorimetry experiment: mass of \(C_{5}H_{10}O_{5}\)(s) = 1.250 g, heat capacity of calorimeter = 4.728 kJ/°C, Initial Temperature of the calorimeter = 24.37°C, Final Temperature of calorimeter = 28.29°C.
Q13.5.4
Determine the heat capacity of the bomb calorimeter if 1.714 g of naphthalene, \(C_{10}H_{8}\)(s), experiences an 8.44°C increase in temperature after going through combustion. The heat of combustion of naphthalene is -5156 kJ/mol \(C_{10}H_{8}\).
Q13.5.5
What is the heat capacity of the bomb calorimeter if a 1.232 g sample of benzoic acid causes the temperature to increase by 5.14°C? The heat of combustion of benzoic acid is -26.42 kJ/g.
S13.5.1
Use equation 4 to calculate the heat of capacity:
\(q_{calorimeter} = \; heat \; capicity \; of \; calorimeter \; x \; \Delta{T}\)
5435 cal = heat capacity of calorimeter x 4.27°C
Heat capacity of calorimeter = (5435 cal/ 4.27°C) x (4.184 J/1 cal) x (1kJ/1000J) = 5.32 kJ/°C
S13.5.2
The temperature should increase since bomb calorimetry releases heat in an exothermic combustion reaction.
Change in Temp = (1.732 g \(C_{12}H_{22}O_{11}\)) x (1 mol \(C_{12}H_{22}O_{11}\)/342.3 g \(C_{12}H_{22}O_{11}\)) x (6.61 x 10³ kJ/ 1 mol \(C_{12}H_{22}O_{11}\)) x (1°C/3.87kJ) = 8.64°C
S13.5.3
[(Heat Capacity x Change in Temperature)/mass] =[ ((4.728 kJ/°C) x(28.29 °C – 24.37 °C))/1.250 g] = 14.8 kJ/g xylose
\(q_{rxn}\) = (-14.8 kJ/g xylose) x (150.13 g xylose/ 1 mol xylose) = -2.22x10³ kJ/mol xylose
S13.5.4
Heat Capacity = [(1.714 g \(C_{10}H_{8}\)) x (1 mol \(C_{10}H_{8}\)/128.2 g \(C_{10}H_{8}\)) x (5.156x10³ kJ/1 mol \(C_{10}H_{8}\))]/8.44°C = 8.17 kJ/ °C
S13.5.5
Heat Capacity = [(1.232 g benzoic acid) x (26.42 kJ/1 g benzoic acid)]/5.14°C = 6.31 kJ/ °C