Determine the standard molar enthalpy of combustion of octane using Hess's law
To determine the standard molar enthalpy of combustion of octane (∆H°comb), we can use Hess's law.
Hess's law states that the total enthalpy change of a reaction is independent of the pathway between the initial and final states. This allows us to calculate the enthalpy change of a reaction by combining other reactions with known enthalpy changes.
The combustion reaction of octane (C8H18) can be represented as follows:
C8H18 + 12.5O2 -> 8CO2 + 9H2O
We need to find other reactions with known enthalpy changes that can be combined to get this reaction. Let's consider the following two reactions:
1) C8H18 + 12.5O2 -> 8CO2 + 9H2O
2) 8C(s) + 8H2(g) + 8O2(g) -> C8H18(l)
The first equation represents the combustion of octane, while the second equation represents the formation of octane from its elements (carbon, hydrogen, and oxygen).
According to Hess's law, we can write:
∆H°comb = ∆H°(8CO2 + 9H2O) - ∆H°(C8H18) - ∆H°(8C + 8H2 + 8O2)
Now, we need to look up the standard enthalpy changes of formation for the involved compounds (∆H°f):
∆H°(8CO2) = 8 * ∆H°f(CO2)
∆H°(9H2O) = 9 * ∆H°f(H2O)
∆H°(C8H18) = ∆H°f(C8H18)
∆H°(8C) = 8 * ∆H°f(C)
∆H°(8H2) = 8 * ∆H°f(H2)
∆H°(8O2) = 8 * ∆H°f(O2)
By subtracting the enthalpy change of the reactants from the enthalpy change of the products, we can then calculate ∆H°comb:
∆H°comb = (8 * ∆H°f(CO2) + 9 * ∆H°f(H2O)) - ∆H°f(C8H18) - (8 * ∆H°f(C) + 8 * ∆H°f(H2) + 8 * ∆H°f(O2))
Using the known values of ∆H°f, we can substitute and calculate ∆H°comb.