Combustion calorimetry calculation explanation

A combustion calorimeter was heated up using a spirit burner containing propan-1-ol (DH_C = -2021.0 kJ mol^-1). The burner weighed 12.472 g before combustion and 11.198 g after combustion. The temperature rose from 18.7 ºC to 27.9 ºC. An octan-1-ol burner was now used to raise the temperature of the same calorimeter from 25.2 ºC to 35.0 ºC. The mass of the burner fell from 13.741 g to 12.401 g during combustion. Calculate the enthalpy of combustion of octan-1-ol.

Mass of propan-1-ol burnt = 12.472 - 11.198 = 1.274 g

Just the difference in mass before and after combustion

C₃H₇OH = 60 molar mass of propan-1-ol

\ number of moles of propan-1-ol burnt = 1.274/60 = 0.0212 mol

number of moles = mass divided by the mass of one mole

DH_c = -2021.0 kJ mol^-1

the enthalpy of combustion of propan-1-ol from the data book

\ energy released = 0.0212 × 2021.0 = 42.9 kJ

The enthalpy of combustion value is per mole. Two moles would give out twice as much heat, three moles three times as much, and so on. In other words, multiply the number of moles by the enthalpy change per mole to get the total heat released

Temperature rise = 27.9 - 18.7 = 9.2 K shouldn't need any more explanation!

\ heat capacity of calorimeter = 42.9/9.2 = 4.66 kJ K^-1

We have divided the total energy released by the temperature rise. This gives the heat required to raise the calorimeter by 1 ºC or 1 K. Note that the value is in kilojoules per Kelvin.

Temperature rise in octan-1-ol experiment = 35.0 - 25.2 = 9.8 ºC

\ energy released = 4.66 × 9.8 = 45.7 kJ

This is the heat capacity of the calorimeter (heat required to raise it by 1 ºC) multiplied by the temperature rise. If it takes 4.66 kJ to raise the calorimeter by 1 ºC, then clearly it would take twice that to raise it by 2 ºC, and so on

Mass of octan-1-ol = 13.741 - 12.401 = 1.340 g

As above, the difference in mass before and after combustion

C₈H₁₇OH = 130 molar mass of octan-1-ol

\ number of moles of octan-1-ol burnt = 1.340/130 = 0.0103 mol

number of moles = mass divided by the mass of one mole

\ enthalpy of combustion of octan-1-ol = - 45.7/0.0103 = - 4400 kJ mol^-1

kJ mol^-1 means kilojoules per mole, that is kilojoules divided by moles. As we only had two significant figures to start with (the temperature change measurement), we've rounded off the answer to the nearest hundred.