Final answer:
The standard heat of formation of methane (ΔHf° CH₄(g)) is calculated using the provided reaction data and standard heats of formation for CO₂(g) and H₂O(l), yielding a value of -74.8 kJ/mol.
Step-by-step explanation:
The student is asking about the standard heat of formation (ΔHf°) of methane (CH₄(g)), which can be calculated using the given thermochemical equation and the standard heats of formation for CO₂(g) and H₂O(l). The equation provided is:
CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l); ΔH = - 889.1 kJ
According to Hess's Law, the heat of reaction (ΔH) for the overall process is equal to the sum of the heats of formation of the products minus the sum of the heats of formation of the reactants. As we are provided with ΔHf° values for H₂O(l) and CO₂(g), we can calculate ΔHf° for CH₄(g) using the following formula:
ΔH = [∑ΔHf°(products)] - [∑ΔHf°(reactants)]
Let ΔHf°(CH₄(g)) = x, then:
-889.1 kJ = (1 mol CO₂(g) x -393.3 kJ/mol + 2 mol H₂O(l) x -285.8 kJ/mol) - (1 mol CH₄(g) x x)
Solving for x, we have:
x = [(-393.3 kJ) + 2(-285.8 kJ) + 889.1 kJ]
x = -74.8 kJ/mol
Therefore, the standard heat of formation of methane, ΔHf° CH₄(g), is -74.8 kJ/mol.