Diesel engines convert the chemical energy in fuel to mechanical energy. Energy is released in a series of combustions as fuel reacts with oxygen from the air. The chemical equation of diesel fuel combustion is 4 C12H23 +71 O2 –> 48 CO2 + 46 H2O. Combustion reactions are spontaneous yielding a -∆G. The reaction goes from 71 moles of O2 gas to 48 moles of CO2 yielding a -∆S. Combustion reactions break bonds between the molecules signaling an exothermic reaction or -∆H.
To find the value of ∆G, we will use the values 50.1 kJ/mol for C12H23, 0 kJ/mol for O2, -393.5 kJ/mol for CO2, and -229 kJ/mol for H2O. To solve for ∆G, we calculate 46(-229) + 48(-394) – 4(50.1) which equates to -29622 kJ, a -∆G for a spontaneous reaction. To find the value of ∆S, we can use the equation ∆G = ∆H – T∆S. Using the -56,000 kJ for ∆H from our prior blog post,-29622 kJ for ∆G, and the 483 K ignition temperature of diesel fuel we can calculate the ∆S. This equates to -54 kJ, a -∆S.
The ultimate goal of the diesel engine is to convert the potential energy of the diesel fuel into mechanical energy that moves the car forward. It has already been explained that the combustion reaction of the diesel fuel is responsible for this. The reaction is 4 C12H23 +71 O2 –> 48 CO2 + 46H2O. Of course there is more going on. This is for the complete combustion of diesel, which does not actually happen. There are other products that can include CO and unburned fuel. When the reaction is not the complete combustion this results in the reaction yielding less energy. This happens when there is a lack of oxygen so not all of the fuel can combust and can also be seen in a Bunsen burner. For simplicities sake, we will assume the diesel fuel completely combusts.
The combustion of diesel fuel is clearly exothermic, which can be seen from the energy that is released as light and heat. This means the change in enthalpy of the reaction has to be negative. The change in enthalpy of a reaction is equal to the change in enthalpy of the products minus the change in enthalpy of the reactants. With numbers that can easily be found on the internet or in the appendix of a chemistry book you can find the exact change in enthalpy for one mole of diesel fuel. The heat of formation of diesel, oxygen, carbon dioxide, and water respectively are 6,700 kJ/mole (converted from kJ/kg and assuming the a molecular formula of C12H23), 0kJ/mole, -393.5 kJ/mole, and -242 kJ/mole. If you multiply all of those numbers by the moles present and subtract reactants from products you get the change in enthalpy for the combustion of diesel. It is 46 *(-242) + 48 * (-393.5) – 4 * (6,700) you get -56,000 kJ as the heat of formation for the combustion reaction for diesel.