Chemistry • Year 11 • Module 4 • Lesson 10
Hess’s Law Applied — Heat of Combustion & Consolidation
Lock in the vocabulary, the three-method selection rules, and the energy-per-gram formula before moving to application questions.
1. Term–definition match
Match each term to its correct definition. Write the matching term from the word bank in the right-hand column. 10 marks
Word bank: standard enthalpy of combustion (ΔH°c) • indirect determination • enthalpy of formation (ΔH°f) • Hess’s Law • energy per gram • bond energy method • average bond enthalpy • state symbol • stoichiometric coefficient • consolidation strategy
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The enthalpy change when one mole of a substance burns completely in O2 under standard conditions (25°C, 100 kPa). | |
| 1.2 | The principle that the total enthalpy change of a reaction is independent of the pathway taken — only the initial and final states matter. | |
| 1.3 | The enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. | |
| 1.4 | The approach of calculating ΔHc° for a substance that cannot be burned cleanly by combining known thermochemical equations to cancel intermediates and yield the target reaction. | |
| 1.5 | The number used to multiply each ΔH°f value when applying ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants); it comes from the balanced equation. | |
| 1.6 | A calculation method for ΔH that uses tabulated average values for breaking and forming specific bond types; approximate because it assumes gaseous species throughout. | |
| 1.7 | The energy absorbed or released per gram of fuel burned; calculated as |ΔHc| ÷ M (kJ g−1). Used to compare fuels on a mass basis. | |
| 1.8 | The average energy required to break one mole of a given type of bond across many molecular environments; used in the bond energy method. | |
| 1.9 | A letter in parentheses after a chemical formula indicating whether the substance is solid (s), liquid (l), gas (g) or aqueous (aq) — essential for accurate ΔH calculations. | |
| 1.10 | The problem-solving approach: identify target equation; write known equations; reverse and/or scale to cancel intermediates; sum the ΔH values. |
2. True or false — with correction
Circle T or F. If false, write the corrected statement. 10 marks (1 T/F + 1 correction where needed)
2.1 When a table of standard enthalpies of formation (ΔH°f) is provided, the bond energy method is the most appropriate calculation method to use. T / F
2.2 The standard enthalpy of formation of any element in its standard state equals zero. T / F
2.3 A fuel with a larger |ΔHc| per mole always delivers more energy per gram than a fuel with a smaller |ΔHc| per mole. T / F
2.4 In the ΔH°f method, the formula is: ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants). T / F
2.5 In Hess’s Law calculations, reversing a thermochemical equation requires you to change the sign of ΔH and also change the magnitude of ΔH. T / F
3. Function recall
Answer each in 1–2 sentences using precise lesson terms. 8 marks (2 each)
3.1 What is the purpose of the “energy per gram” comparison, and when is it more useful than comparing ΔHc per mole?
3.2 Why does the bond energy method give a less accurate ΔH value than the ΔH°f method for the same reaction?
3.3 What is the function of “cancelling intermediates” in a Hess’s Law calculation?
3.4 Why must you show the state symbol for water — H2O(l) vs H2O(g) — when applying the ΔH°f method to a combustion reaction?
4. Method selection grid
Each row describes the data available for a particular question. Write the correct method name in the “Method to use” column and a one-line justification. 6 marks (1 method + 0.5 justification per row)
| # | Data provided in the question | Method to use | One-line justification |
|---|---|---|---|
| 4.1 | A table listing ΔH°f values for CO2(g), H2O(l), and CH3OH(l). | ||
| 4.2 | Bond enthalpies (kJ mol−1) for C–H, O=O, C=O, and O–H. | ||
| 4.3 | Three balanced thermochemical equations with ΔH values, from which intermediate species cancel to give the target reaction. | ||
| 4.4 | A mixture: the ΔH°f of the fuel is unknown, but the combustion ΔH values of the fuel’s component formation reactions are each given individually. |
5. Complete the cloze paragraph
Fill each blank with the correct word or phrase from the word bank below. 8 marks
Word bank: path-independent • enthalpy of formation • bond energies • products minus reactants • intermediates • energy per gram • state symbols • accurate
Hess’s Law states that the total enthalpy change for a reaction is (1) ______________, meaning it depends only on the initial and final states, not the pathway. When the question provides a table of ΔH°f values, the most (2) ______________ method is to apply the formula ΔH°rxn = ΣΔH°f( (3) ______________). This method uses experimentally measured (4) ______________ values for each specific substance. When only bond enthalpy data is available, the (5) ______________ method is used, though it introduces more error because it assumes gaseous species and uses average values. When a set of thermochemical equations is given, Hess’s Law steps are used: the equations are scaled and reversed so that (6) ______________ cancel. The (7) ______________ formula is then used to compare fuels on the basis of mass rather than moles. In all three methods, (8) ______________ must be specified for water because the value of ΔH°f[H2O(l)] differs from ΔH°f[H2O(g)].
6. Complete the consolidation comparison table
Fill in the missing cells. Use the lesson’s three-method comparison cards and the formula panel. 8 marks
| Feature | Bond energy method | ΔH°f method | Hess’s Law (multi-step) |
|---|---|---|---|
| Data required | Table of ___________ | Table of ΔH°f values | Set of ___________ equations |
| Core formula | ΔH = ΣB(___________) − ΣB(products) | ΔH = ΣΔH°f(products) − ΣΔH°f(__________) | Add manipulated equations; cancel __________; sum ΔH |
| Accuracy | ___________ (uses average values, assumes gaseous state) | More accurate (uses ___________ measured values) | Depends on quality of ___________ |
| State symbols required? | Often not critical (all gaseous) | ___________ — ΔH°f[H2O(l)] ≠ ΔH°f[H2O(g)] | Yes — included in given ___________ |
Q1 — Term–definition match
1.1 standard enthalpy of combustion (ΔH°c) • 1.2 Hess’s Law • 1.3 enthalpy of formation (ΔH°f) • 1.4 indirect determination • 1.5 stoichiometric coefficient • 1.6 bond energy method • 1.7 energy per gram • 1.8 average bond enthalpy • 1.9 state symbol • 1.10 consolidation strategy.
Q2 — True / false with correction
2.1 False. When ΔH°f data is provided, the ΔH°f method (enthalpy of formation method) is the most appropriate; it uses those values directly and is more accurate than bond energy calculations.
2.2 True. By definition, the standard state of each element is its reference state; no energy is required to “form” it from itself, so ΔH°f = 0.
2.3 False. A fuel with larger |ΔHc| per mole does not automatically deliver more energy per gram. Energy per gram = |ΔHc| ÷ M; a large molar mass can offset a large |ΔHc|. Always calculate both separately.
2.4 True.
2.5 False. Reversing an equation changes only the sign of ΔH; the magnitude stays the same. (Scaling changes the magnitude.)
Q3 — Function recall
3.1 Energy per gram compares fuels on a mass basis (kJ g−1). It is more useful than per-mole when fuels are compared by mass or volume — e.g., for aircraft, ships, or any application where the tank is loaded by weight rather than by moles.
3.2 Bond energy values are averages across many molecular environments, not exact values for a specific bond in a specific molecule. They also assume all species are gaseous, which is incorrect for liquid reactants or products (e.g. liquid water product in combustion). Both sources of error accumulate, making the bond energy result approximate (±5–20%).
3.3 Intermediate species that appear on both sides of the added equations cancel, confirming that the manipulated equations combine to give exactly the target reaction. If intermediates do not cancel, the equations have been manipulated incorrectly.
3.4 ΔH°f[H2O(l)] = −285.8 kJ mol−1 but ΔH°f[H2O(g)] = −241.8 kJ mol−1 — a difference of 44 kJ mol−1 (the latent heat of vaporisation). Using the wrong state propagates an error of 44n kJ mol−1 for n moles of water, which is significant.
Q4 — Method selection grid
4.1 ΔH°f method — because ΔH°f data is directly provided for all species in the reaction.
4.2 Bond energy method — because only bond enthalpies (not ΔH°f values or thermochemical equations) are given.
4.3 Hess’s Law (multi-step) — because a set of thermochemical equations is provided and the target can be obtained by manipulating and adding these equations.
4.4 Hess’s Law (multi-step) — the ΔH°f of the fuel is unknown, so the ΔH°f formula cannot be applied directly; the given formation-step equations must be combined via Hess’s Law to determine the unknown formation enthalpy first.
Q5 — Cloze paragraph
(1) path-independent • (2) accurate • (3) products minus reactants • (4) enthalpy of formation • (5) bond energies • (6) intermediates • (7) energy per gram • (8) state symbols.
Q6 — Consolidation comparison table
Row 1 (Data): Bond energy — average bond enthalpies • Hess’s Law — thermochemical (equations).
Row 2 (Formula): Bond energy — ΣB(reactants) − ΣB(products) • ΔH°f — ΣΔH°f(reactants) • Hess’s Law — cancel intermediates.
Row 3 (Accuracy): Bond energy — approximate • ΔH°f — experimentally • Hess’s Law — input data.
Row 4 (State symbols): ΔH°f — Yes, critical • Hess’s Law — equations.