Enthalpy change

What you'll learn

How to distinguish exothermic and endothermic reactions.
What enthalpy change, $ΔH\Delta H$ , means at constant pressure.
What standard conditions and standard states mean.
How to define $ΔcH⊖\Delta_c H^\ominus$ and $ΔfH⊖\Delta_f H^\ominus$ accurately.

The basic idea: energy moves between the reaction and the surroundings

In energetics, we usually focus on a chemical reaction as the system. Everything outside it — the solution, container, thermometer and air nearby — is the surroundings.

When a reaction happens, energy may be transferred between the system and the surroundings, often as heat.

Definition

System and surroundings

The system is the chemical reaction being studied. The surroundings are everything outside the reaction that can gain or lose energy.

At A-Level, you need to be very comfortable describing the direction of heat transfer: from the reaction to the surroundings, or from the surroundings into the reaction.

Exothermic reactions

An exothermic reaction transfers heat energy to the surroundings. The surroundings usually get warmer, so a thermometer placed in the reaction mixture often shows a temperature rise.

Definition

Exothermic reaction

An exothermic reaction is a reaction that releases heat energy to the surroundings. Its enthalpy change is negative: $ΔH<0\Delta H < 0$ .

The products have less enthalpy than the reactants. The “missing” energy has been transferred to the surroundings.

Endothermic reactions

An endothermic reaction takes in heat energy from the surroundings. The surroundings usually get cooler, so a thermometer often shows a temperature fall.

Definition

Endothermic reaction

An endothermic reaction is a reaction that absorbs heat energy from the surroundings. Its enthalpy change is positive: $ΔH>0\Delta H > 0$ .

The products have more enthalpy than the reactants. Energy has been absorbed from the surroundings and stored in the products.

The reaction profile diagrams below show the sign of $ΔH\Delta H$ for exothermic and endothermic reactions.

Reaction profile diagrams for exothermic and endothermic reactions

Key Idea

Sign of ΔH

For exothermic reactions, products are lower in enthalpy than reactants, so $ΔH\Delta H$ is negative. For endothermic reactions, products are higher in enthalpy than reactants, so $ΔH\Delta H$ is positive.

Example

Deciding whether a reaction is exothermic or endothermic

A reaction mixture starts at 21.0 °C and reaches 34.5 °C. Decide whether the reaction is exothermic or endothermic, and state the sign of $ΔH\Delta H$ .

Compare the initial and final temperatures: the temperature increases from 21.0 °C to 34.5 °C, so the surroundings have gained heat energy.
If the surroundings gain heat energy, the reaction must have transferred heat energy to the surroundings.
Therefore the reaction is exothermic, so its enthalpy change is negative: $ΔH<0\Delta H < 0$ .

Common Mistake

Mixing up temperature change and ΔH sign

A temperature rise means the surroundings gained energy, so the reaction lost energy. That is why a temperature rise usually means $ΔH\Delta H$ is negative.

What enthalpy change means

Enthalpy is a measure of the heat energy content of a system at constant pressure. You do not need to measure the absolute enthalpy of a substance; in chemistry, we measure changes in enthalpy.

Definition

Enthalpy change

The enthalpy change, $ΔH\Delta H$ , is the heat energy change measured under conditions of constant pressure.

The symbol $Δ\Delta$ means “change in”. So $ΔH\Delta H$ means:

ΔH=Hproducts−Hreactants\Delta H = H_{\text{products}} - H_{\text{reactants}}

This explains the sign convention:

If products have lower enthalpy than reactants, $Hproducts−HreactantsH_{\text{products}} - H_{\text{reactants}}$ is negative.
If products have higher enthalpy than reactants, $Hproducts−HreactantsH_{\text{products}} - H_{\text{reactants}}$ is positive.

Enthalpy changes are usually given in kJ mol⁻¹. The “per mole” part depends on the balanced equation being used.

Example

Finding ΔH from enthalpy levels

A reaction has reactants at an enthalpy level of 250 kJ mol⁻¹ and products at 90 kJ mol⁻¹. Calculate $ΔH\Delta H$ and classify the reaction.

Use the definition of enthalpy change:
$ΔH=Hproducts−Hreactants\Delta H = H_{\text{products}} - H_{\text{reactants}}$
Substitute the enthalpy levels, keeping the units:
$mol−1\Delta H = 90 - 250 = -160\ \text{kJ mol}^{-1}$
Since $ΔH\Delta H$ is negative, the reaction is exothermic.

Tip

Quick sign check

Think “products lower means negative”. On an energy-level diagram, a downward arrow for $ΔH\Delta H$ means an exothermic reaction.

Standard enthalpy changes

Enthalpy changes depend on conditions such as pressure, temperature and physical state. For example, forming liquid water and forming steam are not the same enthalpy change.

To make values comparable, chemists use standard enthalpy changes.

Definition

Standard conditions

Standard conditions for enthalpy changes are a pressure of 100 kPa and a stated temperature, often 298 K.

You may see a standard enthalpy change written with the symbol $⊖\ominus$ , for example $ΔH⊖\Delta H^\ominus$ or $ΔH298⊖\Delta H_{298}^\ominus$ .

The 298 tells you the temperature is 298 K. If the temperature is different, it should be stated.

Standard states

A standard state is the physical state of a substance under the stated standard conditions. For example, at 100 kPa and 298 K:

hydrogen is H₂(g)
oxygen is O₂(g)
water is H₂O(l)
carbon is C(s, graphite), not diamond

For solutions, a standard concentration of 1.00 mol dm⁻³ is commonly used.

Definition

Standard enthalpy change

A standard enthalpy change is an enthalpy change measured under standard conditions, with substances in their standard states.

Common Mistake

Forgetting the state symbols

Definitions of standard enthalpy changes rely on substances being in their standard states, so equations should include state symbols such as (s), (l), (g) and (aq).

Standard enthalpy of combustion

Combustion means burning in oxygen. For the AQA definition, you must include one mole, complete combustion, oxygen, and standard conditions.

Definition

Standard enthalpy of combustion

The standard enthalpy of combustion, $ΔcH⊖\Delta_c H^\ominus$ , is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions, with all substances in their standard states.

Combustion reactions are usually exothermic, so values of $ΔcH⊖\Delta_c H^\ominus$ are usually negative.

For example, the standard enthalpy of combustion of methane refers to:

CH4(g)+2O2(g)→CO2(g)+2H2O(l)\text{CH}_4(g) + 2\text{O}_2(g) \to \text{CO}_2(g) + 2\text{H}_2\text{O}(l)

This equation shows one mole of methane being completely burned in oxygen.

Example

Writing a combustion equation for ΔcH⦵

Write the equation that represents the standard enthalpy of combustion of ethanol, C₂H₅OH(l).

Start with exactly one mole of the substance being burned:
$C2H5OH(l)+O2(g)→\text{C}_2\text{H}_5\text{OH}(l) + \text{O}_2(g) \to$
Complete combustion of a compound containing carbon and hydrogen forms carbon dioxide and water:
$C2H5OH(l)+O2(g)→2CO2(g)+3H2O(l)\text{C}_2\text{H}_5\text{OH}(l) + \text{O}_2(g) \to 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l)$
Balance oxygen atoms. The products contain 7 oxygen atoms in total. Ethanol already contains 1 oxygen atom, so 6 more are needed from oxygen gas, requiring 3 molecules of O₂:
$C2H5OH(l)+3O2(g)→2CO2(g)+3H2O(l)\text{C}_2\text{H}_5\text{OH}(l) + 3\text{O}_2(g) \to 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l)$

Standard enthalpy of formation

Formation means making a compound from its elements. For the AQA definition, you must include one mole of compound, formed from its elements, standard conditions, and standard states.

Definition

Standard enthalpy of formation

The standard enthalpy of formation, $ΔfH⊖\Delta_f H^\ominus$ , is the enthalpy change when one mole of a compound is formed from its constituent elements under standard conditions, with all substances in their standard states.

For example, the standard enthalpy of formation of carbon dioxide is represented by:

graphite)+O2(g)→CO2(g)\text{C}(s,\text{ graphite}) + \text{O}_2(g) \to \text{CO}_2(g)

This forms exactly one mole of CO₂ from carbon and oxygen in their standard states.

Key Idea

Elements have zero ΔfH⦵

The standard enthalpy of formation of an element in its standard state is zero, because no formation reaction is needed to make it from itself.

So:

$ΔfH⊖\Delta_f H^\ominus$ for O₂(g) is zero.
$ΔfH⊖\Delta_f H^\ominus$ for H₂(g) is zero.
$ΔfH⊖\Delta_f H^\ominus$ for C(s, graphite) is zero.
$ΔfH⊖\Delta_f H^\ominus$ for C(s, diamond) is not zero, because diamond is not carbon’s standard state at 298 K and 100 kPa.

Example

Writing a formation equation for ΔfH⦵

Write the equation that represents the standard enthalpy of formation of liquid water, H₂O(l).

Formation must make exactly one mole of the compound, so put one H₂O(l) on the product side:
$→H2O(l)\to \text{H}_2\text{O}(l)$
Use the elements in their standard states as reactants: hydrogen is H₂(g) and oxygen is O₂(g).
$H2(g)+O2(g)→H2O(l)\text{H}_2(g) + \text{O}_2(g) \to \text{H}_2\text{O}(l)$
Balance the equation while keeping one mole of water as the product:
$H2(g)+12O2(g)→H2O(l)\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \to \text{H}_2\text{O}(l)$

Common Mistake

Fractions are allowed in formation equations

Formation equations often contain fractions, such as $12O2(g)\frac{1}{2}\text{O}_2(g)$ . That is fine because the definition requires exactly one mole of compound to be formed.

Comparing combustion and formation

These two definitions are easy to mix up, but they focus on different substances.

For combustion, the “one mole” is the substance being burned. Oxygen is a reactant, and complete combustion products are formed.

For formation, the “one mole” is the compound being made. The reactants must be elements in their standard states.

Tip

Spot the definition quickly

Combustion: one mole burned in oxygen. Formation: one mole made from elements.

Example

Choosing the correct enthalpy definition

Consider this equation:

graphite)+2H2(g)→CH4(g)\text{C}(s,\text{ graphite}) + 2\text{H}_2(g) \to \text{CH}_4(g)

Decide whether it represents a standard enthalpy of combustion or formation.

Check what is happening to the substance: methane is being made, not burned.
Check the reactants: carbon and hydrogen are elements in their standard states.
Check the amount of product: exactly one mole of CH₄(g) is formed, so the equation represents the standard enthalpy of formation of methane, $ΔfH⊖\Delta_f H^\ominus$ .

Exam technique

In the exam

For exothermic/endothermic questions, link the sign of $ΔH\Delta H$ to the direction of heat transfer and the relative enthalpy of reactants and products.
In definitions, include the crucial phrases: one mole, standard conditions, and standard states where needed.
When writing equations for $ΔcH⊖\Delta_c H^\ominus$ or $ΔfH⊖\Delta_f H^\ominus$ , include state symbols and make sure the equation forms or burns exactly one mole of the named substance.

Self review

Check yourself

Why is $ΔH\Delta H$ negative for an exothermic reaction?
What conditions are meant by “standard conditions” for enthalpy changes?
Write the equation for the standard enthalpy of formation of MgO(s).

What you'll learn

How to distinguish exothermic and endothermic reactions.
What enthalpy change, $ΔH\Delta H$ , means at constant pressure.
What standard conditions and standard states mean.
How to define $ΔcH⊖\Delta_c H^\ominus$ and $ΔfH⊖\Delta_f H^\ominus$ accurately.

The basic idea: energy moves between the reaction and the surroundings

In energetics, we usually focus on a chemical reaction as the system. Everything outside it — the solution, container, thermometer and air nearby — is the surroundings.

When a reaction happens, energy may be transferred between the system and the surroundings, often as heat.

Definition

System and surroundings

The system is the chemical reaction being studied. The surroundings are everything outside the reaction that can gain or lose energy.

At A-Level, you need to be very comfortable describing the direction of heat transfer: from the reaction to the surroundings, or from the surroundings into the reaction.

Exothermic reactions

An exothermic reaction transfers heat energy to the surroundings. The surroundings usually get warmer, so a thermometer placed in the reaction mixture often shows a temperature rise.

Definition

Exothermic reaction

An exothermic reaction is a reaction that releases heat energy to the surroundings. Its enthalpy change is negative: $ΔH<0\Delta H < 0$ .

The products have less enthalpy than the reactants. The “missing” energy has been transferred to the surroundings.

Endothermic reactions

An endothermic reaction takes in heat energy from the surroundings. The surroundings usually get cooler, so a thermometer often shows a temperature fall.

Definition

Endothermic reaction

An endothermic reaction is a reaction that absorbs heat energy from the surroundings. Its enthalpy change is positive: $ΔH>0\Delta H > 0$ .

The products have more enthalpy than the reactants. Energy has been absorbed from the surroundings and stored in the products.

The reaction profile diagrams below show the sign of $ΔH\Delta H$ for exothermic and endothermic reactions.

Reaction profile diagrams for exothermic and endothermic reactions

Key Idea

Sign of ΔH

Example

Deciding whether a reaction is exothermic or endothermic

A reaction mixture starts at 21.0 °C and reaches 34.5 °C. Decide whether the reaction is exothermic or endothermic, and state the sign of $ΔH\Delta H$ .

Compare the initial and final temperatures: the temperature increases from 21.0 °C to 34.5 °C, so the surroundings have gained heat energy.
If the surroundings gain heat energy, the reaction must have transferred heat energy to the surroundings.
Therefore the reaction is exothermic, so its enthalpy change is negative: $ΔH<0\Delta H < 0$ .

Common Mistake

Mixing up temperature change and ΔH sign

A temperature rise means the surroundings gained energy, so the reaction lost energy. That is why a temperature rise usually means $ΔH\Delta H$ is negative.

What enthalpy change means

Definition

Enthalpy change

The enthalpy change, $ΔH\Delta H$ , is the heat energy change measured under conditions of constant pressure.

The symbol $Δ\Delta$ means “change in”. So $ΔH\Delta H$ means:

ΔH=Hproducts−Hreactants\Delta H = H_{\text{products}} - H_{\text{reactants}}

This explains the sign convention:

If products have lower enthalpy than reactants, $Hproducts−HreactantsH_{\text{products}} - H_{\text{reactants}}$ is negative.
If products have higher enthalpy than reactants, $Hproducts−HreactantsH_{\text{products}} - H_{\text{reactants}}$ is positive.

Enthalpy changes are usually given in kJ mol⁻¹. The “per mole” part depends on the balanced equation being used.

Example

Finding ΔH from enthalpy levels

A reaction has reactants at an enthalpy level of 250 kJ mol⁻¹ and products at 90 kJ mol⁻¹. Calculate $ΔH\Delta H$ and classify the reaction.

Use the definition of enthalpy change:
$ΔH=Hproducts−Hreactants\Delta H = H_{\text{products}} - H_{\text{reactants}}$
Substitute the enthalpy levels, keeping the units:
$mol−1\Delta H = 90 - 250 = -160\ \text{kJ mol}^{-1}$
Since $ΔH\Delta H$ is negative, the reaction is exothermic.

Tip

Quick sign check

Think “products lower means negative”. On an energy-level diagram, a downward arrow for $ΔH\Delta H$ means an exothermic reaction.

Standard enthalpy changes

Enthalpy changes depend on conditions such as pressure, temperature and physical state. For example, forming liquid water and forming steam are not the same enthalpy change.

To make values comparable, chemists use standard enthalpy changes.

Definition

Standard conditions

Standard conditions for enthalpy changes are a pressure of 100 kPa and a stated temperature, often 298 K.

You may see a standard enthalpy change written with the symbol $⊖\ominus$ , for example $ΔH⊖\Delta H^\ominus$ or $ΔH298⊖\Delta H_{298}^\ominus$ .

The 298 tells you the temperature is 298 K. If the temperature is different, it should be stated.

Standard states

A standard state is the physical state of a substance under the stated standard conditions. For example, at 100 kPa and 298 K:

hydrogen is H₂(g)
oxygen is O₂(g)
water is H₂O(l)
carbon is C(s, graphite), not diamond

For solutions, a standard concentration of 1.00 mol dm⁻³ is commonly used.

Definition

Standard enthalpy change

A standard enthalpy change is an enthalpy change measured under standard conditions, with substances in their standard states.

Common Mistake

Forgetting the state symbols

Definitions of standard enthalpy changes rely on substances being in their standard states, so equations should include state symbols such as (s), (l), (g) and (aq).

Standard enthalpy of combustion

Combustion means burning in oxygen. For the AQA definition, you must include one mole, complete combustion, oxygen, and standard conditions.

Definition

Standard enthalpy of combustion

Combustion reactions are usually exothermic, so values of $ΔcH⊖\Delta_c H^\ominus$ are usually negative.

For example, the standard enthalpy of combustion of methane refers to:

CH4(g)+2O2(g)→CO2(g)+2H2O(l)\text{CH}_4(g) + 2\text{O}_2(g) \to \text{CO}_2(g) + 2\text{H}_2\text{O}(l)

This equation shows one mole of methane being completely burned in oxygen.

Example

Writing a combustion equation for ΔcH⦵

Write the equation that represents the standard enthalpy of combustion of ethanol, C₂H₅OH(l).

Start with exactly one mole of the substance being burned:
$C2H5OH(l)+O2(g)→\text{C}_2\text{H}_5\text{OH}(l) + \text{O}_2(g) \to$
Complete combustion of a compound containing carbon and hydrogen forms carbon dioxide and water:
$C2H5OH(l)+O2(g)→2CO2(g)+3H2O(l)\text{C}_2\text{H}_5\text{OH}(l) + \text{O}_2(g) \to 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l)$
Balance oxygen atoms. The products contain 7 oxygen atoms in total. Ethanol already contains 1 oxygen atom, so 6 more are needed from oxygen gas, requiring 3 molecules of O₂:
$C2H5OH(l)+3O2(g)→2CO2(g)+3H2O(l)\text{C}_2\text{H}_5\text{OH}(l) + 3\text{O}_2(g) \to 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l)$

Standard enthalpy of formation

Formation means making a compound from its elements. For the AQA definition, you must include one mole of compound, formed from its elements, standard conditions, and standard states.

Definition

Standard enthalpy of formation

For example, the standard enthalpy of formation of carbon dioxide is represented by:

graphite)+O2(g)→CO2(g)\text{C}(s,\text{ graphite}) + \text{O}_2(g) \to \text{CO}_2(g)

This forms exactly one mole of CO₂ from carbon and oxygen in their standard states.

Key Idea

Elements have zero ΔfH⦵

The standard enthalpy of formation of an element in its standard state is zero, because no formation reaction is needed to make it from itself.

So:

$ΔfH⊖\Delta_f H^\ominus$ for O₂(g) is zero.
$ΔfH⊖\Delta_f H^\ominus$ for H₂(g) is zero.
$ΔfH⊖\Delta_f H^\ominus$ for C(s, graphite) is zero.
$ΔfH⊖\Delta_f H^\ominus$ for C(s, diamond) is not zero, because diamond is not carbon’s standard state at 298 K and 100 kPa.

Example

Writing a formation equation for ΔfH⦵

Write the equation that represents the standard enthalpy of formation of liquid water, H₂O(l).

Formation must make exactly one mole of the compound, so put one H₂O(l) on the product side:
$→H2O(l)\to \text{H}_2\text{O}(l)$
Use the elements in their standard states as reactants: hydrogen is H₂(g) and oxygen is O₂(g).
$H2(g)+O2(g)→H2O(l)\text{H}_2(g) + \text{O}_2(g) \to \text{H}_2\text{O}(l)$
Balance the equation while keeping one mole of water as the product:
$H2(g)+12O2(g)→H2O(l)\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \to \text{H}_2\text{O}(l)$

Common Mistake

Fractions are allowed in formation equations

Formation equations often contain fractions, such as $12O2(g)\frac{1}{2}\text{O}_2(g)$ . That is fine because the definition requires exactly one mole of compound to be formed.

Comparing combustion and formation

These two definitions are easy to mix up, but they focus on different substances.

For combustion, the “one mole” is the substance being burned. Oxygen is a reactant, and complete combustion products are formed.

For formation, the “one mole” is the compound being made. The reactants must be elements in their standard states.

Tip

Spot the definition quickly

Combustion: one mole burned in oxygen. Formation: one mole made from elements.

Example

Choosing the correct enthalpy definition

Consider this equation:

graphite)+2H2(g)→CH4(g)\text{C}(s,\text{ graphite}) + 2\text{H}_2(g) \to \text{CH}_4(g)

Decide whether it represents a standard enthalpy of combustion or formation.

Check what is happening to the substance: methane is being made, not burned.
Check the reactants: carbon and hydrogen are elements in their standard states.
Check the amount of product: exactly one mole of CH₄(g) is formed, so the equation represents the standard enthalpy of formation of methane, $ΔfH⊖\Delta_f H^\ominus$ .

Exam technique

In the exam

For exothermic/endothermic questions, link the sign of $ΔH\Delta H$ to the direction of heat transfer and the relative enthalpy of reactants and products.
In definitions, include the crucial phrases: one mole, standard conditions, and standard states where needed.
When writing equations for $ΔcH⊖\Delta_c H^\ominus$ or $ΔfH⊖\Delta_f H^\ominus$ , include state symbols and make sure the equation forms or burns exactly one mole of the named substance.

Self review

Check yourself

Why is $ΔH\Delta H$ negative for an exothermic reaction?
What conditions are meant by “standard conditions” for enthalpy changes?
Write the equation for the standard enthalpy of formation of MgO(s).

What you'll learn

The basic idea: energy moves between the reaction and the surroundings

Exothermic reactions

Endothermic reactions

What enthalpy change means

Standard enthalpy changes

Standard states

Standard enthalpy of combustion

Standard enthalpy of formation

Comparing combustion and formation

Review Enthalpy change by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Enthalpy change

What you'll learn

The basic idea: energy moves between the reaction and the surroundings

Exothermic reactions

Endothermic reactions

What enthalpy change means

Standard enthalpy changes

Standard states

Standard enthalpy of combustion

Standard enthalpy of formation

Comparing combustion and formation

Review Enthalpy change by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Enthalpy change

What you'll learn

The basic idea: energy moves between the reaction and the surroundings

Exothermic reactions

Endothermic reactions

What enthalpy change means

Standard enthalpy changes

Standard states

Standard enthalpy of combustion

Standard enthalpy of formation

Comparing combustion and formation

Review Enthalpy change by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Enthalpy change Revision Guide

Enthalpy change

What you'll learn

The basic idea: energy moves between the reaction and the surroundings

Exothermic reactions

Endothermic reactions

What enthalpy change means

Standard enthalpy changes

Standard states

Standard enthalpy of combustion

Standard enthalpy of formation

Comparing combustion and formation

Review Enthalpy change by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Enthalpy change Revision Guide