AP Chemistry Hess's Law

Two ways to calculate reaction enthalpy, three full worked examples.

Reaction enthalpy can be calculated two ways: directly from a table of standard formation enthalpies, or by combining a set of given equations using Hess's Law. Both methods rest on the same fact, enthalpy is a state function, and for the same reaction, they always agree.

The Two Enthalpy Calculation Methods

Enthalpy of formation method: ΔH°_rxn = ΣΔH°_f(products) − ΣΔH°_f(reactants), using each substance's tabulated standard enthalpy of formation. An element in its standard state always has ΔH°_f = 0.

Hess's Law equation-combination method: reverse, scale, and add a set of given thermochemical equations so everything cancels except the target reaction, applying the same reversal/scaling to each equation's ΔH.

Worked Example 1: Enthalpy of Formation Method

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l). Using ΔH°_f: CO₂(g) = −393.5 kJ/mol, H₂O(l) = −285.8 kJ/mol, CH₄(g) = −74.8 kJ/mol, O₂(g) = 0 kJ/mol (element), find ΔH°_rxn.

ΔH°_rxn = [(−393.5) + 2(−285.8)] − [(−74.8) + 2(0)]
= (−393.5 − 571.6) − (−74.8)
= −965.1 + 74.8 = −890.3 kJ

Worked Example 2: Hess's Law Equation Combination

Given:
(1) C(s) + O₂(g) → CO₂(g), ΔH₁ = −393.5 kJ
(2) H₂(g) + ½O₂(g) → H₂O(l), ΔH₂ = −285.8 kJ
(3) CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH₃ = −890.3 kJ
Find ΔH for: C(s) + 2H₂(g) → CH₄(g)

Keep equation (1) as written, double equation (2), and reverse equation (3) so CH₄ ends up as a product:
(1) C + O₂ → CO₂, ΔH = −393.5 kJ
2×(2) 2H₂ + O₂ → 2H₂O, ΔH = 2(−285.8) = −571.6 kJ
reverse (3) CO₂ + 2H₂O → CH₄ + 2O₂, ΔH = +890.3 kJ

Adding all three and cancelling CO₂, 2H₂O, and 2O₂ from both sides leaves exactly the target: C + 2H₂ → CH₄.
ΔH = −393.5 + (−571.6) + 890.3 = −74.8 kJ

Worked Example 3: Confirming Both Methods Agree

The result of Example 2, −74.8 kJ for C(s) + 2H₂(g) → CH₄(g), is exactly ΔH°_f of CH₄, because that reaction is methane's formation reaction from its elements in their standard states. Hess's Law equation combination and the enthalpy-of-formation method aren't two different facts to memorize, they're the same underlying idea, applied two different ways.

Common Hess's Law Mistakes

Forgetting to flip ΔH's sign when reversing an equation. This is the single most common error in these problems.
Scaling an equation's coefficients without scaling its ΔH by the same factor. Doubling a reaction doubles its enthalpy change too.
Forgetting that an element in its standard state has ΔH°_f = 0. Leaving it out of the sum is correct, treating it as a nonzero value is not.
Not fully cancelling intermediate substances. If anything other than the target reaction's own reactants and products remains after adding the equations, a reversal or scaling factor was set up incorrectly somewhere.

Frequently Asked Questions

What is Hess's Law?

Because enthalpy is a state function, the total enthalpy change for a reaction only depends on the initial and final states, not the path taken. That means thermochemical equations can be added like algebra: reverse a reaction and you reverse the sign of its ΔH, multiply a reaction by a coefficient and you multiply its ΔH by that same coefficient, and adding a set of equations together adds their ΔH values.

What is the enthalpy-of-formation method, and how is it different from Hess's Law?

ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants) uses tabulated standard formation enthalpies directly, rather than combining given equations. It's really the same underlying idea as Hess's Law, just applied through one formula instead of an equation-combination exercise, and the two methods always agree for the same reaction.

What is the standard enthalpy of formation of an element in its standard state?

Zero, always. Since ΔH°f measures the enthalpy change to form a compound from its elements in their standard states, an element forming from itself has no enthalpy change to measure.

What's the most common mistake in a Hess's Law problem?

Forgetting to flip the sign of ΔH when reversing a given reaction, or forgetting to multiply ΔH by the same factor used to scale an equation's coefficients. Both errors are easy to make when juggling several equations at once.

Do the equations have to be combined in the order they were given?

No. Work backward from the target reaction: identify which given equation contains each substance in the target, decide whether it needs to be reversed or scaled so that substance ends up on the correct side in the correct amount, then check that everything except the target's own reactants and products cancels out.

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