IB Chemistry SLTopic 4 — Energy CyclesPaper 1 & 2Core idea~11 min read
Hess’s Law
Plenty of enthalpy changes cannot be measured. You cannot make propane by shaking carbon and hydrogen together, and you cannot burn carbon and get it to stop politely at carbon monoxide. Hess’s law gets you the number anyway, by sending the reaction round a route you can measure.
📚 What you need to know
Hess’s law: the enthalpy change of a reaction is the same no matter which route is taken, as long as the starting and finishing conditions are the same.
It follows directly from the conservation of energy.
Draw an enthalpy cycle: the reaction you want along the top, a route you have data for underneath.
Travelling with an arrow you add its ΔH; travelling against an arrow you subtract it.
Reversing a reaction reverses the sign of ΔH. Multiplying a reaction multiplies ΔH.
Used whenever a reaction is impossible, too slow, or too messy to measure directly.
The law itself
Hess’s law
the total enthalpy change of a reaction is independent of the route taken, provided the initial and final conditions are the same
That sounds like a rule someone decided on. It is not — it is forced on us by conservation of energy, and the argument is worth following once.
Suppose two different routes from the same reactants to the same products released different amounts of energy. You could then go forwards along the generous route, come back along the mean one, and finish exactly where you started with energy left over in your hand. Repeat forever and you have made energy out of nothing. Since that is impossible, every route between the same two points must give the same ΔH.
Think of walking up a mountain. Whichever path you take, the altitude gained between the car park and the summit is identical — even though one path is longer, steeper, or more scenic. Enthalpy behaves like altitude: only where you start and where you finish matter.
This is what makes enthalpy so useful. It depends only on the state of the chemicals, not on their history, so we are free to invent whatever imaginary route makes the arithmetic possible. That is exactly what the previous page did: breaking everything into separated atoms and rebuilding is just a Hess’s law route in disguise.
Building an enthalpy cycle
The reaction you want goes along the top. The route you have data for goes underneath. Both must total the same.
🧩 How to draw one
Write the target reaction across the top, reactants on the left, products on the right, with the arrow you are trying to label.
Look at the data given. Find the common substance that both sides can be connected to — usually the elements, or carbon dioxide and water.
Put that substance in a box underneath.
Draw arrows in the direction the given reactions actually go, and write their ΔH values on them.
Trace the long way round from reactants to products, adding or subtracting as you go.
Step 4 is the one to be fussy about. The arrows record the direction of the reactions you were given, not the direction you intend to walk. You are perfectly allowed to walk backwards up an arrow — you just pay for it with a sign change.
The only rule you need for a cycle. With the arrow, add. Against the arrow, subtract.
Keep the operation and the sign apart. Going against an arrow whose value is –283 means subtracting a negative number: – (–283) = +283. Write the brackets in. Almost every lost mark in this topic lives in that one line.
Cycles in action
WORKED EXAMPLE
Given S(s) + O2(g) → SO2(g), ΔH = –297 kJ mol–1 and SO2(g) + ½O2(g) → SO3(g), ΔH = –98 kJ mol–1, find ΔH for S(s) + 1½O2(g) → SO3(g).
Step 1 — check the routeS → SO₂ → SO₃. Both given reactions point the way we want to travel.Step 2 — add them, both with the arrowsΔH = (−297) + (−98)ΔH = −395 kJ mol⁻¹Check the oxygen balances: 1 + ½ = 1½. If the atoms do not add up, the route is wrong.
That one was gentle because both arrows already pointed the right way. The next is the situation examiners actually set: the reaction you want cannot be run at all, and one of your arrows points the wrong way.
Carbon burning in a limited supply of oxygen gives a mixture, never pure CO, so this enthalpy change has to be reached indirectly.
WORKED EXAMPLE
Given C(s) + O2(g) → CO2(g), ΔH = –394 kJ mol–1 and CO(g) + ½O2(g) → CO2(g), ΔH = –283 kJ mol–1, calculate ΔH for C(s) + ½O2(g) → CO(g).
Step 1 — find the routeBoth given reactions end at CO₂, so put CO₂ at the bottom of the cycle.Step 2 — walk itC down to CO₂ is WITH the arrow, so add. CO₂ up to CO is AGAINST the arrow, so subtract.ΔH = (−394) − (−283)= −394 + 283ΔH = −111 kJ mol⁻¹Sensible? Burning carbon only part of the way should release less than burning it fully, and 111 is smaller than 394. It is.
WORKED EXAMPLE
For N2(g) + O2(g) → 2NO(g), ΔH = +180 kJ. What is ΔH for NO(g) → ½N2(g) + ½O2(g)?
Step 1 — reverse it2NO → N₂ + O₂ is the given reaction backwards, so flip the sign.ΔH = −180 kJStep 2 — halve itThe question wants 1 mol of NO, not 2. Halve the equation, halve the enthalpy.−180 ÷ 2 = −90ΔH = −90 kJTwo separate adjustments, done in either order. Reversing changes the sign; scaling changes the size.
💡 Exam tip
You do not need to quote Hess’s law word for word, but you do need to use it confidently. Marks are for the cycle and the arithmetic.
Always draw the cycle, even in a multiple-choice question. A sketch takes fifteen seconds and stops sign errors dead.
Bracket every value before you add or subtract it, so the operation and the sign never blur together.
Check the atoms balance along your route. If they do not, you have connected the wrong boxes.
Sanity check the answer’s sign and size against what the chemistry suggests before moving on.
⚠️ Common mix-up
Adding everything. If one arrow points against your route, that value must be subtracted.
Subtracting a negative and losing the double minus. –(–283) is +283.
Reversing an equation but forgetting the sign. Backwards means the opposite sign, always.
Scaling the equation but not the ΔH. Double the moles, double the energy.
Drawing arrows in the direction you want to walk rather than the direction of the data you were given.
Up next: Applying Hess’s Law — the same idea reduced to three standard set-ups that between them cover almost every question you will be asked.
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