Why is the enthalpy of formation of an element zero?

The standard enthalpy of formation is the energy change to form one mole of a substance from its elements in their standard states. To 'form' an element like O₂(g) from its standard state (which is O₂(g)), there is no change, so the enthalpy change is zero by definition.

What's the difference between the cycles for formation and combustion data?

For formation data, the cycle's intermediate step is the constituent elements, and the arrows point 'up' from the elements to the reactants and products. For combustion data, the intermediate step is the combustion products (CO₂ and H₂O), and the arrows point 'down' from the reactants and products to these products.

Can I use a mix of formation and combustion data in one calculation?

While theoretically possible if you construct a very complex cycle, it is not a standard method and is highly prone to error. For A-Level Chemistry, you will always be given a consistent set of data – either all formation or all combustion values needed for the calculation.

What if a substance in the equation is an element, like in the hydrogenation of ethene?

When using formation data ($\Delta H_f^\ominus$), the value for the element (e.g., H₂(g)) is zero. When using combustion data ($\Delta H_c^\ominus$), the element will have a non-zero value (e.g., the enthalpy of combustion of hydrogen is -286 kJ mol⁻¹), which you must include in your calculation.

Where can I learn Hess's law for Cambridge 9701?

This free lesson on MarkScheme covers syllabus point 5.2 (Hess's law) for Cambridge A-Level Chemistry. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9701/5-2-hesss-law.

Is Hess's law (5.2) on 9701 free to study?

Yes. The Chemistry 9701 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Hess's law.

Hess's law 9701 — Free A-Level Chemistry

Hess's law

Welcome to the world of indirect energy calculations. Some chemical reactions are just not cooperative enough to let us measure their enthalpy change in a simple lab experiment. They might be explosive, incredibly slow, or form a messy mixture of products. Hess's Law provides an elegant solution, allowing us to calculate these elusive enthalpy changes by taking a clever 'detour' using data from other, more measurable reactions.

BY THE END, YOU CAN…

1State Hess's Law and explain its basis in the conservation of energy.
2Construct and interpret enthalpy cycles to calculate unknown enthalpy changes.
3Calculate enthalpy changes of reaction from standard enthalpy changes of formation ( $\Delta H_f^\ominus$ ).
4Calculate enthalpy changes of reaction from standard enthalpy changes of combustion ( $\Delta H_c^\ominus$ ).

In simple terms

A friendly intro before the formal notes — no formulas yet.

The Chemical Detour

Hess's Law states that the total energy change for a chemical reaction is the same, no matter which route you take. This allows us to calculate tricky enthalpy changes by using a series of easier, indirect steps.

THINK OF IT LIKE…

Imagine you want to travel from home (reactants) to school (products). The change in your straight-line distance is fixed. You could walk directly, or you could take a detour via a friend's house. Hess's Law is like saying that if you add up the distances of your detour (home to friend's, then friend's to school), and account for the directions, you can still figure out the direct distance from home to school.

1
Hess’s law: total ΔH is independent of the route taken.
2
Enthalpy cycles: reverse a step → sign of ΔH reverses.
3
Use formation/combustion data tables with careful sign and stoichiometry.
4
State the cycle clearly in exams — examiners award diagram marks.

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Key formulas

Tap any symbol to reveal exactly what it means and its units.

$\Delta H_{reaction}^\ominus = \sum n\Delta H_f^\ominus(\text{products}) - \sum m\Delta H_f^\ominus(\text{reactants})$

$\Delta H_{reaction}^\ominus = \sum m\Delta H_c^\ominus(\text{reactants}) - \sum n\Delta H_c^\ominus(\text{products})$

Full topic notes

Formal explanation with the rigour you need for the exam.

Hess's Law: The First Law of Thermodynamics in Disguise

Hess's Law is a direct consequence of the principle of conservation of energy. It states that the total enthalpy change for a reaction depends only on the initial state (reactants) and the final state (products), not on the specific pathway or intermediate steps between them. This means that whether a reaction occurs in a single step or through a series of steps, the overall enthalpy change will be the same.

Core Principle: Total enthalpy change is route-independent.
Foundation: Based on the First Law of Thermodynamics (conservation of energy).
Application: Allows calculation of $\Delta H$ for reactions that can't be measured directly.

Using Enthalpy of Formation Data ($\Delta H_f^\ominus$)

One of the most common applications of Hess's Law involves using standard enthalpy changes of formation. We can imagine a hypothetical route where reactants are first broken down into their constituent elements in their standard states, and then these elements are reassembled to form the products. The enthalpy cycle helps us visualise this.

$\Delta H_{reaction}^\ominus = \sum n\Delta H_f^\ominus(\text{products}) - \sum m\Delta H_f^\ominus(\text{reactants})$

In this formula, 'n' and 'm' are the stoichiometric coefficients from the balanced equation. The cycle works because the 'down' arrow from reactants to elements is the negative of their formation enthalpy, and the 'up' arrow from elements to products is their formation enthalpy.

Using Enthalpy of Combustion Data ($\Delta H_c^\ominus$)

Alternatively, we can use standard enthalpy changes of combustion. This method is particularly useful for reactions involving organic compounds. The hypothetical route involves combusting both the reactants and the products to form common combustion products, typically carbon dioxide and water. Notice how the formula differs slightly from the formation method.

$\Delta H_{reaction}^\ominus = \sum m\Delta H_c^\ominus(\text{reactants}) - \sum n\Delta H_c^\ominus(\text{products})$

EXAM TIP

Pay close attention to the formula when using combustion data! It's Reactants - Products, the opposite of the formation data formula. A common mistake is to mix these up. Drawing the cycle with arrows pointing DOWN to combustion products helps to derive this correctly every time.

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

EXAMPLE 1

Calculate the standard enthalpy change of reaction, $\Delta H_r^\ominus$ , for the thermal decomposition of calcium carbonate. $\text{CaCO}_3(\text{s}) \rightarrow \text{CaO}(\text{s}) + \text{CO}_2(\text{g})$

Use the following standard enthalpy of formation data: $\Delta H_f^\ominus[\text{CaCO}_3(\text{s})] = -1207 \text{ kJ mol}^{-1}$ $\Delta H_f^\ominus[\text{CaO}(\text{s})] = -635 \text{ kJ mol}^{-1}$ $\Delta H_f^\ominus[\text{CO}_2(\text{g})] = -394 \text{ kJ mol}^{-1}$

1
Identify the formula: We are using formation data, so we use $\Delta H_r^\ominus = \sum \Delta H_f^\ominus(\text{products}) - \sum \Delta H_f^\ominus(\text{reactants})$ .

EXAMPLE 2

Calculate the standard enthalpy change for the hydrogenation of ethene to ethane. $\text{C}_2\text{H}_4(\text{g}) + \text{H}_2(\text{g}) \rightarrow \text{C}_2\text{H}_6(\text{g})$

Use the following standard enthalpy of combustion data: $\Delta H_c^\ominus[\text{C}_2\text{H}_4(\text{g})] = -1411 \text{ kJ mol}^{-1}$ $\Delta H_c^\ominus[\text{H}_2(\text{g})] = -286 \text{ kJ mol}^{-1}$ $\Delta H_c^\ominus[\text{C}_2\text{H}_6(\text{g})] = -1560 \text{ kJ mol}^{-1}$

1
Identify the formula: We are using combustion data, so we use $\Delta H_r^\ominus = \sum \Delta H_c^\ominus(\text{reactants}) - \sum \Delta H_c^\ominus(\text{products})$ .

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAHess's law

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Try to recall each definition before you reveal it.

Quick check

Answer in your head first — then tap to check. No pressure.

Revision flashcards

Flip the card. Test yourself before the exam.

QUESTION · 1 / 11

What is Hess's Law?

TAP OR SPACE TO FLIP

ANSWER

Hess's Law states that the total enthalpy change for a chemical reaction is independent of the route taken, provided the initial and final conditions are the same.

TAP OR SPACE TO FLIP BACK

1 / 11 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

✓
Core Principle: Total enthalpy change is route-independent.
✓
Foundation: Based on the First Law of Thermodynamics (conservation of energy).
✓
Application: Allows calculation of $\Delta H$ for reactions that can't be measured directly.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Real past paper[0]

Test Your Knowledge on Hess's Law

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

✓

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do Test Your Knowledge on Hess's Law on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS5.1 Enthalpy change, ΔH NEXT →6.1 Redox processes: electron transfer and changes in oxidation number (oxidation state)

Hess's law

BY THE END, YOU CAN…

1State Hess's Law and explain its basis in the conservation of energy.
2Construct and interpret enthalpy cycles to calculate unknown enthalpy changes.
3Calculate enthalpy changes of reaction from standard enthalpy changes of formation ( $\Delta H_f^\ominus$ ).
4Calculate enthalpy changes of reaction from standard enthalpy changes of combustion ( $\Delta H_c^\ominus$ ).

In simple terms

A friendly intro before the formal notes — no formulas yet.

The Chemical Detour

THINK OF IT LIKE…

1
Hess’s law: total ΔH is independent of the route taken.
2
Enthalpy cycles: reverse a step → sign of ΔH reverses.
3
Use formation/combustion data tables with careful sign and stoichiometry.
4
State the cycle clearly in exams — examiners award diagram marks.

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Key formulas

Tap any symbol to reveal exactly what it means and its units.

$\Delta H_{reaction}^\ominus = \sum n\Delta H_f^\ominus(\text{products}) - \sum m\Delta H_f^\ominus(\text{reactants})$

$\Delta H_{reaction}^\ominus = \sum m\Delta H_c^\ominus(\text{reactants}) - \sum n\Delta H_c^\ominus(\text{products})$

Full topic notes

Formal explanation with the rigour you need for the exam.

Hess's Law: The First Law of Thermodynamics in Disguise

Core Principle: Total enthalpy change is route-independent.
Foundation: Based on the First Law of Thermodynamics (conservation of energy).
Application: Allows calculation of $\Delta H$ for reactions that can't be measured directly.

Using Enthalpy of Formation Data ($\Delta H_f^\ominus$)

$\Delta H_{reaction}^\ominus = \sum n\Delta H_f^\ominus(\text{products}) - \sum m\Delta H_f^\ominus(\text{reactants})$

Using Enthalpy of Combustion Data ($\Delta H_c^\ominus$)

$\Delta H_{reaction}^\ominus = \sum m\Delta H_c^\ominus(\text{reactants}) - \sum n\Delta H_c^\ominus(\text{products})$

EXAM TIP

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

EXAMPLE 1

1
Identify the formula: We are using formation data, so we use $\Delta H_r^\ominus = \sum \Delta H_f^\ominus(\text{products}) - \sum \Delta H_f^\ominus(\text{reactants})$ .

EXAMPLE 2

Calculate the standard enthalpy change for the hydrogenation of ethene to ethane. $\text{C}_2\text{H}_4(\text{g}) + \text{H}_2(\text{g}) \rightarrow \text{C}_2\text{H}_6(\text{g})$

1
Identify the formula: We are using combustion data, so we use $\Delta H_r^\ominus = \sum \Delta H_c^\ominus(\text{reactants}) - \sum \Delta H_c^\ominus(\text{products})$ .

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAHess's law

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Try to recall each definition before you reveal it.

Quick check

Answer in your head first — then tap to check. No pressure.

Revision flashcards

Flip the card. Test yourself before the exam.

QUESTION · 1 / 11

What is Hess's Law?

TAP OR SPACE TO FLIP

ANSWER

Hess's Law states that the total enthalpy change for a chemical reaction is independent of the route taken, provided the initial and final conditions are the same.

TAP OR SPACE TO FLIP BACK

1 / 11 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

✓
Core Principle: Total enthalpy change is route-independent.
✓
Foundation: Based on the First Law of Thermodynamics (conservation of energy).
✓
Application: Allows calculation of $\Delta H$ for reactions that can't be measured directly.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Real past paper[0]

Test Your Knowledge on Hess's Law

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

✓

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do Test Your Knowledge on Hess's Law on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS5.1 Enthalpy change, ΔH NEXT →6.1 Redox processes: electron transfer and changes in oxidation number (oxidation state)

Revise Hess's law for Cambridge 9701 (5.2)

In simple terms

Explore the concept

Key formulas

Full topic notes

Hess's Law: The First Law of Thermodynamics in Disguise

Using Enthalpy of Formation Data ($\Delta H_f^\ominus$)

Using Enthalpy of Combustion Data ($\Delta H_c^\ominus$)

Worked examples

How it all connects

Glossary

Quick check

Revision flashcards

Key takeaways

Practice — then mark it

Test Your Knowledge on Hess's Law

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

In simple terms

Explore the concept

Key formulas

Full topic notes

Hess's Law: The First Law of Thermodynamics in Disguise

Using Enthalpy of Formation Data ($\Delta H_f^\ominus$)

Using Enthalpy of Combustion Data ($\Delta H_c^\ominus$)

Worked examples

How it all connects

Glossary

Quick check

Revision flashcards

Key takeaways

Practice — then mark it

Test Your Knowledge on Hess's Law

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Hess's law