Short on time? This page is the recap. For explanations, diagrams and worked examples, use the full study guide.
Recap
- Any chemical or physical process can be written as a series of steps. Each step has its own ΔH.
- The steps can be imaginary. They only need to start and end with the same substances as the process.
- Why the ΔH values add: each step transfers thermal energy to or from the surroundings, and energy is conserved (first law of thermodynamics). So the net energy transferred, ΔH at constant pressure, is the sum of the steps.
- If two routes gave different totals, you could go out by one and back by the other and create energy. That is impossible.
- The formation-enthalpy equation from Topic 6.8 is Hess’s law with a route through the elements.
Key relationships
| Operation on the equation | Effect on ΔH | Example |
|---|---|---|
| Reverse it | same size, opposite sign | ΔH = −96 becomes +96 |
| Multiply by c (whole number or fraction) | multiply by c | ½ × (−312) = −156 |
| Add two or more equations | add the ΔH values | +57 + (−120) = −63 |
| Reverse and multiply | do both | reverse of −96, doubled: +192 |
Method for a target equation
- Write the target.
- For each target substance, find the given equation that contains it (start with substances that appear only once).
- Reverse that equation if the substance is on the wrong side.
- Multiply it so the coefficient matches the target.
- Add the changed equations; cancel what appears on both sides.
- Check the sum is exactly the target, then add the changed ΔH values.
Assumptions behind the numbers
- All ΔH values refer to the same conditions (usually standard conditions and 25 °C).
- “kJ mol⁻¹” means per mole of reaction as written; that is why multiplying the equation multiplies ΔH.
- State symbols match the target: H₂O(l) and H₂O(g) are different substances for Hess’s law.
Mistakes to avoid
- Reversing without flipping the sign.
- Multiplying the equation but not ΔH (or ΔH but not the equation).
- Cancelling the whole of a substance when the amounts on each side differ. Cancel only the smaller amount.
- Ignoring states. A liquid and a gas of the same compound do not cancel; the phase change is a step with its own ΔH.
- Adding ΔH values before checking that the equations add to the target.
- Dropping signs when you halve or double a negative value.
Quick self-check
- ΔH for J → L is −96 kJ mol⁻¹. What is ΔH for 2L → 2J? (+192 kJ mol⁻¹)
- ΔH for an equation is −312 kJ mol⁻¹. What is ΔH if every coefficient is divided by 3? (−104 kJ mol⁻¹)
- Step 1 has ΔH = +57 kJ mol⁻¹ and step 2 has ΔH = −120 kJ mol⁻¹. What is ΔH for the overall change? (−63 kJ mol⁻¹)
- Why must two routes between the same start and end give the same ΔH? (Energy is conserved; a difference would let you create energy by going one way and returning the other.)
Next: practice questions.