Hess's Law & ΔHf°

the idea

ΔH is a state function, like altitude.

Drive from the plant to the top of a mountain and your change in altitude is the same whether you took the highway or the switchbacks. Enthalpy works the same way: ΔH depends only on the starting and ending substances, not the path. So if you can't measure a reaction directly, you can add up reactions you can measure that get you to the same place.

Flip a reaction

Change the sign of ΔH

Multiply by n

Multiply ΔH by n

Add reactions

Add their ΔH values. Species on both sides cancel.

Plant version: it's like reconciling inventory through a transfer. Moving 500 lb from silo A to tank B and then 500 lb from B to the filler gives the same net result as A straight to the filler. Tank B shows up on both sides of the ledger and cancels out. Hess's law is that same cancellation, done with energy.

puzzle

Build the target reaction

Flip and scale each given step until everything that isn't in the target cancels. The running sum updates as you go.

Target

standard enthalpy of formation

ΔH°rxn = Σ n ΔH_f°(products) − Σ m ΔH_f°(reactants)

ΔH_f° is the enthalpy change to make 1 mol of a compound from its elements in their standard states. Elements in their standard state (O₂(g), C(graphite), H₂(g)) are zero by definition. That one table lets you compute ΔH for almost any reaction. Think of it as tearing everything down to elements and rebuilding.

reference

ΔH_f° values used here (kJ/mol, 25 °C)

engineering version

The 4-4-9 on a nutrition label is thermochemistry.

Food energy values come from burning food in a bomb calorimeter and correcting for what the body can't use: about 17 kJ/g (4 kcal) for carbohydrate and protein, and 38 kJ/g (9 kcal) for fat. Fat is so energy-dense because it's mostly C–H bonds with very little oxygen. It's "less burned" to begin with, so more energy is released getting it to CO₂ and H₂O. One food Calorie is 1 kcal = 4.184 kJ.

Fat (g) Carbohydrate (g) Protein (g)

practice

ΔH from formation enthalpies

practice

Hess's law moves

exam traps

Common mistakes

Doing reactants − products. It's products − reactants.
Forgetting to multiply ΔHf° by the coefficient.
Giving O₂(g) a nonzero ΔHf°. Elements in their standard state are 0. O₃ and C(diamond) are not.
Using H₂O(g) when the equation says H₂O(l). They differ by 44 kJ/mol, which is the heat of vaporization.
Flipping a reaction in a Hess's law problem but forgetting to flip the sign of ΔH.