Bomb Calorimeter

Question

A bomb calorimeter is filled with 7.2 atm of an unknown gaseous hydrocarbon fuel and an excess of oxygen gas at a temperature of 24.2 °C. The bomb calorimeter has a volume of 2.8 L and a heat capacity of 9.06 kJ/K. After the combustion reaction is complete the final temperature of the calorimeter is found to be 105.4 °C. Answer the following questions based on this information.

(a) What amount of heat in kJ was released from the combustion reaction of the unknown fuel?

(b) What is the molar heat of combustion for the reaction in kJ/mol?

Answer 1

The combustion reaction releases 736kJ and the molar heat of combustion is 890kJ/mole.

Detailed Solution:

To find the amount of heat released, you need to work backwards from the temperature change. If the temperature rose, you know that heat was released into the calorimeter from the reaction. The temperature rose from 24.2 to 105.4 degrees Celsius; the difference is 81.2 degrees. If the heat capacity is 9.06 kJ/K, it means there needs to be 9.06 kJ of energy to increase the temperature by 1 Kelvin. A temperature increase of 1 degree Celsius is the same as an increase of 1 degree in Kelvin. Therefore, the heat released into the calorimeter that caused the temperature to increase by 81.2 degrees is 81.2 degrees multiplied by the heat capacity, which equals 736 kJ when rounded to 3 significant figures.

The molar heat of combustion is this number divided by the number of moles of gas. We use the ideal gas law to calculate the number of moles using the parameters given. n=(PV)/(RT)=[(7.2atm*2.8L)]/[(.0820Latm/Kmol)(24.2+273.15K)] =.83 moles. Note the units and that the Celsius temperature needs to be converted into Kelvin by adding 273.15K, which is the same as 0 degrees Celsius.

The molar heat of combustion = 736kJ/.83 moles=890 kJ/mole when rounded to two significant figures.

I hope this answers your question!