molar enthalpy of formation of octane

Question

Octane, C8H18(l), one of the major components in gasoline, burns completely with oxygen, producing carbon dioxide and water vapour. The molar enthalpy of combustion of octane in these conditions is -5074.1 kJ/mol. Determine the molar enthalpy of formation of octane.

Answer 1

First we must write an equation for the chemical reaction:

C₈H_18(g) + O_2(g) --> CO_2(g) + H₂O_(g)

Next balance the chemical equation. We can do this by first balancing carbon and hydrogen atoms:

C₈H_18(g) + O_2(g) --> 8CO_2(g) + 9H₂O_(g)

We see that there are 2 oxygens on the left and 25 oxygens on the right. Create a common factor.

C₈H_18(g) + (25/2)O_2(g) --> 8CO_2(g) + 9H₂O_(g)

Multiply the entire equation by 2 to get rid of the fraction

2C₈H_18(g) + 25O_2(g) --> 16CO_2(g) + 18H₂O_(g)

In order to find the enthalpy of formation of a reactant we must use the equation

dH⁰rxn = dH_f⁰_products - dH_f⁰_reactants

In this case dH⁰_rxn = dH⁰_combustion = -5074.1 kJ/mol. However, the enthalpy of combustion is defined per mole of hydrocarbon. Using the balanced chemical equation, we see that dH⁰_combustion = -5074.1 kJ/mol octane x 2 = -10148.2 kJ/mol octane

You did not provide the standard enthalpies of formation for the other reactants and products so I found these online. Double check with your textbook to make sure these are consistent

O_2(g) = 0 kJ/mol

CO_2(g) = -393.5 kJ/mol

H₂O_(g) = -241.8 kJ/mol

Use the stoichiometric coefficients from the balanced equation when calculating dH⁰_rxn. In this problem we are given dH⁰_rxn and are trying to solve for the H_f of octane (one of the reactants). Plug all of your known variables into the following equation (X represents the unknown H_f for octane):

dH⁰rxn = dH_f⁰_products - dH_f⁰_reactants

-10148.2 kJ/mol = [16(-393.5 kJ/mol) + 18(-241.8 kJ/mol)] - [2X + 25(0 kJ/mol)]

-10148.2 kJmol = (-6296 kJ/mol - 4352.4 kJ/mol) - 2X

-10148.2 kJ/mol = -10648.4 kJ/mol - 2X

500.2 kJ/mol = -2X

-250.1 kJ/mol = X

The heat of formation for octane is equal to -250.1 kJ/mol