Question

Consider the combustion of propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\), the fuel that is commonly used in portable gas barbeque grills. The products of combustion are carbon dioxide and liquid water. (a) Write a thermochemical equation for the combustion of one mole of propane. (b) Calculate \(\Delta E\) for the combustion of propane at \(25^{\circ} \mathrm{C}\).

Short answer

Question: Calculate the energy change for the combustion of one mole of propane at 25°C. Answer: The energy change for the combustion of one mole of propane at 25°C is -2220 kJ/mol.

Step-by-step solution

Write the unbalanced thermochemical equation

Write down the basic reaction for the combustion of propane, which involves propane reacting with oxygen to produce carbon dioxide and liquid water. \(C_3H_8 + O_2 \rightarrow CO_2 + H_2O\)

Balance the equation

In order to balance the equation, we need to ensure that there are the same number of each element on both sides of the equation. Balancing the carbon and hydrogen atoms: \(C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O\) The balanced thermochemical equation is: \(C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O\)

(a) Write the thermochemical equation for the combustion of one mole of propane

We can write down the balanced thermochemical equation for the combustion of one mole of propane: \(\mathrm{C}_{3} \mathrm{H}_{8(g)} + 5\mathrm{O}_{2(g)} \rightarrow 3\mathrm{CO}_{2(g)} + 4\mathrm{H}_{2}\mathrm{O}_{(l)}\)

(b) Step 1: Find heats of formation for reactants and products

We need to know the heats of formation (\(\Delta H^\circ_\mathrm{f}\)) for propane, oxygen, carbon dioxide, and liquid water. These can be found in standard thermodynamic tables: \(\Delta H^\circ_\mathrm{f}(\mathrm{C}_{3} \mathrm{H}_{8})=-103.8 \,\mathrm{kJ/mol}\) \(\Delta H^\circ_\mathrm{f}(\mathrm{O}_{2})=0\) (since it´s an element at standard state) \(\Delta H^\circ_\mathrm{f}(\mathrm{CO}_{2})=-393.5\, \mathrm{kJ/mol}\) \(\Delta H^\circ_\mathrm{f}(\mathrm{H}_{2}\mathrm{O}_{(l)})=-285.8 \,\mathrm{kJ/mol}\)

(b) Step 2: Calculate the change in energy for the combustion of propane

We can calculate the change in energy (\(\Delta E\)) for the combustion of propane at \(25^{\circ}\mathrm{C}\) using the balanced thermochemical equation and the heats of formation (\(\Delta H^\circ_\mathrm{f}\)): \(\Delta E=-\Delta H^\circ_\mathrm{f}(\mathrm{C}_{3} \mathrm{H}_{8}) + 3\Delta H^\circ_\mathrm{f}(\mathrm{CO}_{2}) + 4\Delta H^\circ_\mathrm{f}(\mathrm{H}_{2}\mathrm{O}_{(l)})\) \(\Delta E=-(-103.8) + 3(-393.5) + 4(-285.8) \,\mathrm{kJ/mol}\) \(\Delta E=103.8 - 1180.5 - 1143.2 \,\mathrm{kJ/mol}\) \(\Delta E=-2220\, \mathrm{kJ/mol}\) The change in energy for the combustion of propane at \(25^{\circ}\mathrm{C}\) is -2220 kJ/mol.