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Calculating Heat from Molar Enthalpy (Optional)

Optional enrichment: scale a supplied molar enthalpy, distinguish signed heat from energy released, and use the balanced equation’s reacting amount.

  • SEC G3 Pure Chemistry 2027

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Optional enrichment

The required K324 energetics work is qualitative: explain exothermic and endothermic changes, draw energy profiles, and compare bond breaking with bond making. Numerical molar-enthalpy calculations are not required for that work. Use it if you want additional numerical practice.

Read the supplied quantity before calculating

A molar enthalpy change gives an energy change per mole of reaction as written. For example, -120 kJ mol⁻¹ means the reacting system transfers 120 kJ to the surroundings for each mole of the specified reaction. The negative sign describes the system’s change; “120 kJ released” reports its magnitude and direction in words.

For a reaction written with one mole of the named reactant, multiply its reacting amount by the supplied molar enthalpy. Units cancel to leave kJ:

signed heat change of system = amount of reaction × Δ H

At constant pressure, the surroundings’ heat transfer has the opposite sign, when other transfers are excluded. Do not confuse a reaction’s heat transfer with all the energy a furnace needs to heat the apparatus and materials.

Keep extra digits while calculating, then round the final answer to the precision of the supplied quantities. The worked carbon and calcium-carbonate examples use reacting amounts given to two significant figures.

Scale a supplied value

Guided practice 1

Use Δ H to Find Energy Released

About 6 min

Out-of-syllabus enrichment

A reaction has Δ H = -120 kJ mol⁻¹. If 0.50 mol of reaction occurs, how much heat energy is released?

Scale and choose the reporting convention

Transfer wording

Hints

Hint 1: scale the per-mole value
Half a mole gives half of the 120 kJ mol⁻¹ magnitude.
View solution step by step

  1. Scale the magnitude

    Method

    Multiply amount by the per-mole energy.

    Reason

    The supplied value applies to one mole of reaction as written.

    Working

    0.50 mol × 120 kJ mol⁻¹ = 60 kJ.

  2. Report the direction

    Method

    State 60 kJ released.

    Reason

    The question asks for the amount released; the negative sign is already represented by the transfer direction.

    Working

    60 kJ released. If a signed system energy change is requested, write -60 kJ.

Apply the same method to combustion

Challenge 2

Use ΔH to Find Energy Released

Minimal support

Out-of-syllabus enrichment

For C(s) + O₂(g) → CO₂(g), the supplied enthalpy change is Δ H = -394 kJ mol⁻¹ for the reaction as written. How much heat is released when 0.25 mol of carbon burns completely?

Scale the energy per mole

Scaling operation
Requested energy

Hints

Hint 1: unit meaning
394 kJ mol⁻¹ means 394 kJ is released per mole of reaction as written.
View solution step by step

  1. Scale by the reacting amount

    Method

    Multiply the amount by the magnitude of the molar enthalpy.

    Reason

    Only one quarter of a mole reacts, so it releases one quarter of the per-mole energy.

    Working

    0.25 mol × 394 kJ mol⁻¹ = 98.5 kJ.

  2. Report the requested quantity

    Method

    State the positive amount of heat released, rounded to two significant figures.

    Reason

    The negative sign belongs to Δ H; “how much heat is released” asks for its magnitude.

    Working

    99 kJ released (2 significant figures).

Apply the same method to decomposition

Challenge 3

Use ΔH to Find Energy Absorbed

Minimal support

Out-of-syllabus enrichment

For CaCO₃(s) → CaO(s) + CO₂(g), the supplied enthalpy change is Δ H = +178 kJ mol⁻¹ for the reaction as written. How much heat is absorbed when 0.40 mol of CaCO₃ decomposes?

Scale the energy per mole

Scaling operation
Energy statement

Hints

Hint 1: unit meaning
178 kJ mol⁻¹ means 178 kJ is absorbed per mole of reaction as written.
View solution step by step

  1. Scale by the decomposed amount

    Method

    Multiply the amount by the molar enthalpy.

    Reason

    Only 0.40 of the per-mole reaction occurs.

    Working

    0.40 mol × 178 kJ mol⁻¹ = 71.2 kJ.

  2. State the transfer direction

    Method

    Report the energy as absorbed, rounded to two significant figures.

    Reason

    The positive enthalpy change means energy enters the reacting system from the surroundings.

    Working

    71 kJ absorbed (2 significant figures).

Check the equation as well as the units

Try independently: For the reaction 2CO(g) + O₂(g) → 2CO₂(g), the supplied Δ H is -566 kJ mol⁻¹ of reaction as written. What is the signed heat change when 1.00 mol of carbon monoxide reacts? How much heat is released?

Show answer and reasoning

One mole of the reaction as written consumes 2 mol of carbon monoxide. Reacting 1.00 mol of carbon monoxide therefore represents 0.500 mol of reaction:

0.500 × (-566) = -283 kJ

The system’s signed heat change is −283 kJ; 283 kJ is released. Multiplying 1.00 × (-566) would incorrectly apply the two-mole reaction value to one mole of carbon monoxide.

Try independently: A learner says an endothermic reaction with a supplied Δ H = +80 kJ mol⁻¹ releases 20 kJ when 0.25 mol of reaction occurs. Which part is correct and which part needs repair?

Show answer and reasoning

The magnitude is correct: 0.25 × 80 = 20 kJ. The direction is wrong. Positive Δ H means the system absorbs 20 kJ, so its signed heat change is +20 kJ.

Return to Chemical Energetics for the required qualitative sequence, or use the topic check to practise and check those concepts. These optional numerical questions are answered within this lesson.

Syllabus and review details

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