Breaking one mole of H–H bonds requires roughly 436 kJ; breaking one mole of Cl–Cl bonds requires about 243 kJ. Forming two moles of H–Cl bonds releases roughly 864 kJ when a tabulated 432 kJ/mol value is used. The broken-minus-formed estimate for H₂(g)+Cl₂(g)→2HCl(g) is therefore −185 kJ—close to, but not numerically identical with, the standard formation-enthalpy result near −184.6 kJ.
The difference teaches an important distinction: bond-energy tables are powerful estimates and explanatory tools, but average entries, chemical environment, gas-phase definitions, stoichiometric coefficients and reference-state corrections determine whether a numerical estimate can be treated as a rigorous reaction enthalpy.
Find the question you need
All teaching chapters remain open. Follow the calculation route or jump to the limitations, common errors and exercises.
Define bonds and the reaction
Chapters 1–3. Start this route.
Calculate and compare ΔH
Chapters 4–6. Start this route.
Check chemical context and limitations
Chapters 7–10. Start this route.
Practise and report
Chapters 11–12. Start this route.
Chapter index · Practice with answers · Thermochemistry subject root
Chapter index
Define bonds and the reaction · Chapters 1–3
Calculate and compare ΔH · Chapters 4–6
Check chemical context and limitations · Chapters 7–10
Practise and report · Chapters 11–12
Take the balanced gas-phase reaction H₂(g)+Cl₂(g)→2HCl(g). Two atoms of hydrogen and two atoms of chlorine appear on each side. The product coefficient two matters: the reaction creates two H–Cl bonds for every one H–H and one Cl–Cl bond consumed.
We want an approximate enthalpy change for the reaction as written. It is not enough to list three bond strengths without counting their occurrences. An H–Cl bond strength is an energy per mole of such bonds, while the reported reaction enthalpy is an energy per mole of the written chemical reaction.
The standard enthalpy change is a state-function difference between specified reactants and products under a reference convention. An approximate bond-energy method constructs a conceptual path through separated gas-phase atoms and accounts for the energies of breaking reactant bonds and forming product bonds.
The path is a thermochemical accounting device, not necessarily the elementary molecular mechanism followed in an actual reacting vessel. Reaction kinetics and transition states are different questions from the net enthalpy difference.
Contents · Next · Subject root
Stable bonded atoms typically lie at lower energy than separated fragments under the reference conditions used for a bond dissociation enthalpy. To separate a gas-phase H₂ molecule into two H atoms requires adding energy; its illustrative bond dissociation enthalpy is about +436 kJ per mole of H–H bonds broken.
The reverse transformation—two gas-phase H atoms forming H₂—releases the same magnitude of energy under compatible state definitions. In the ordinary enthalpy sign convention, bond breaking contributes positively to the reaction energy ledger and bond formation negatively.
A frequent misconception is that ‘the energy stored in a bond is released when you break it’. Breaking a stable bond is instead an energy-consuming step. The net release from an exothermic reaction occurs because newly formed product bonds, considered along with other state changes, release more energy than was required to break the original bonds.
The enthalpy estimate is therefore written ΔH≈ΣD(bonds broken)−ΣD(bonds formed). The minus sign in front of the formed-bond subtotal carries the energy release.
Contents · Previous · Next · Subject root
One H₂ molecule contains one H–H bond, so one mole of H₂ contains one mole of H–H bonds. One Cl₂ molecule similarly contributes one Cl–Cl bond. The reactant side therefore calls for breaking one mole of each bond.
Each HCl molecule contains one H–Cl bond, but the target equation forms two HCl molecules per H₂ consumed. Hence two moles of H–Cl bonds are formed per mole of reaction as written.
The gas-phase bond ledger is therefore: bonds broken—1 H–H and 1 Cl–Cl; bonds formed—2 H–Cl. Writing this count before substituting numbers prevents an error of hundreds of kilojoules caused by omitting the coefficient two.
For larger molecules, draw or inspect structural formulas and multiply the number of each bond by the stoichiometric coefficient of the species. A reaction equation counts molecules; a bond-energy ledger counts bonds across those molecules.
Contents · Previous · Next · Subject root
Use representative values given in the OpenStax chemistry treatment: D(H–H)=436 kJ/mol, D(Cl–Cl)=243 kJ/mol and D(H–Cl)=432 kJ/mol. These are energies for bonds under the relevant gas-phase reference assumptions.
Breaking the reactant bonds requires 436+243=679 kJ for the written reaction. Forming two moles of H–Cl bonds releases 2×432=864 kJ.
Subtracting gives the estimated reaction enthalpy ΔH≈679−864=−185 kJ. The negative sign predicts an exothermic transformation: in this accounting, formation releases 185 kJ more than bond breaking absorbs.
The result’s precision should reflect rounded input energies. Reporting −185.000000 kJ would give a false impression of certainty about tabulated bonds, especially when the values are used as general averages rather than exact molecule-specific constants.
Contents · Previous · Next · Subject root
The same reaction can be evaluated using a consistent standard formation-enthalpy table. By convention, H₂(g) and Cl₂(g) in their elemental reference states each have zero standard formation enthalpy. For HCl(g), an illustrative tabulated standard formation enthalpy is −92.307 kJ/mol.
With two HCl molecules produced, the formation-enthalpy route gives ΔH°=2(−92.307)−[0+0]=−184.614 kJ for the reaction as written.
The bond-energy approximation −185 kJ differs from this representative standard-state result by about 0.386 kJ. That is close agreement for the chosen gas-phase diatomic reaction, but a numerical difference is expected when input tables have different rounding or definitions.
The agreement is an independent check that the signs and coefficients were handled sensibly. It does not prove every reaction computed from average bond enthalpies will have such a small discrepancy.
| Energy component | Count | Bond enthalpy | Subtotal |
|---|---|---|---|
| H–H broken | 1 | 436 kJ/mol | +436 kJ |
| Cl–Cl broken | 1 | 243 kJ/mol | +243 kJ |
| H–Cl formed | 2 | 432 kJ/mol | −864 kJ |
| Approximate ΔH | Reaction as written | 679−864 | −185 kJ |
| Formation-enthalpy result | 2 HCl(g) | 2×(−92.307) | −184.614 kJ |
Contents · Previous · Next · Subject root
A bond dissociation enthalpy depends on the molecular environment in which the bond is broken. A carbon–hydrogen bond in methane is not necessarily identical in dissociation enthalpy to a carbon–hydrogen bond in an aromatic molecule or a different radical environment.
Tables of average bond enthalpies combine information across different compounds or contexts to supply convenient representative values. Those averages are valuable for estimating whether a reaction is exothermic and for obtaining an approximate energy scale, but they cannot be treated as guaranteed molecule-specific measurements in every case.
For simple diatomic bonds such as H–H, Cl–Cl or H–Cl, a bond dissociation can be defined unambiguously for a gas-phase molecular species. Complex molecules may have multiple nonequivalent bonds of the same apparent structural type, and successive removal of atoms changes the species.
The key lesson is to ask whether the table provides a specific dissociation energy or a general average. The numbers may be similar enough for a useful estimate, but the meaning is not the same.
Contents · Previous · Next · Subject root
Consider a molecule with several carbon–hydrogen bonds. Removing one hydrogen atom leaves a radical, so the next C–H dissociation occurs from a different chemical species. Subsequent bond dissociation enthalpies can differ, even if the original structural drawing displays several similar-looking bonds.
An average C–H entry is therefore not necessarily the correct precise energy for breaking the first particular C–H bond in methane. OpenStax’s organic chemistry discussion gives an illustrative first C–H dissociation energy for methane around 439.3 kJ/mol, different from some broadly averaged C–H table values.
This matters when someone multiplies one generic bond energy by four and calls the result an experimentally exact atomisation enthalpy. The approximation may be useful, but a precise calculation of successive dissociations must follow the actual sequence of molecular species.
For a rigorous molecule-specific enthalpy, look for suitable experimental thermochemical data rather than silently treating every similar symbol in a line drawing as a chemically identical bond.
Contents · Previous · Next · Subject root
Ordinary bond dissociation enthalpies describe processes involving gas-phase molecules and separated gas-phase atoms or fragments. A reaction involving liquid water, solid salts or graphite includes phase and lattice effects not captured merely by adding gas-phase covalent bond averages.
For example, methane combustion to water vapour and methane combustion to liquid water have different reaction enthalpies even though the H–O covalent bonds within the water molecules are of the same nominal type. The difference involves condensation of the water products.
The earlier HHV–LHV methane guide calculates how the water phase changes the reference combustion enthalpy. A bond-energy estimate for gas-phase water should not be advertised as the corresponding liquid-water combustion result.
Likewise, the energetic contributions of melting, vaporisation, sublimation or ionic lattice formation require appropriate terms in a thermochemical cycle. Ignoring them can produce a plausible-looking but physically mismatched answer.
Contents · Previous · Next · Subject root
A C–C single bond differs from a C=C double bond and a C≡C triple bond. Likewise O–O and O=O represent distinct bond types with different dissociation energies. A student cannot count every connection between two atoms as one generic bond of the same energy.
In a polyatomic molecule, a double bond may be influenced by resonance and its surroundings. Carbon dioxide, for example, should not automatically be assigned the generic C=O bond-average value used for every carbonyl compound without checking whether a suitable CO₂-specific entry is available.
Counting formulas alone is insufficient; use correct structural information and the exact species. Then calculate the number of each bond type in reactants and products, including every stoichiometric multiplier.
These choices are particularly important when a model claims high numerical accuracy. A few percent error from using inappropriate bond entries may be much larger than the decimal rounding in the calculator.
Contents · Previous · Next · Subject root
The bond-energy ledger imagines all relevant reactant bonds separated and all product bonds formed, but that is a state-function pathway for accounting. It does not assert that a real H₂/Cl₂ reaction proceeds by dissociating all the molecules into a common pool of isolated atoms first.
The reaction mechanism can involve chain processes or other intermediates, depending on conditions. The net enthalpy may remain negative while the rate depends on activation barriers, light, temperature, concentrations and other kinetic factors.
One should also not infer that a larger magnitude negative ΔH necessarily means a faster reaction. Rate and net energy change are related through physical chemistry but are not interchangeable quantities.
For parents and students, the useful distinction is: enthalpy says how initial and final energy states compare; kinetics asks how the system moves between them. A worked bond-energy sum addresses primarily the first question.
Contents · Previous · Next · Subject root
Exercise A: For H₂+Cl₂→2HCl, a student writes 436+243−432=247 kJ. The error is omitting the second H–Cl bond in the products. The correct formed-bond contribution is 2×432=864, giving −185 kJ.
Exercise B: Another student computes 864−679=+185 kJ and calls the reaction endothermic. The order was reversed. The bond-enthalpy estimate is bonds broken minus bonds formed, so the answer is negative for this example.
Exercise C: A standard formation-enthalpy reference gives −92.307 kJ/mol HCl(g). Find the reaction enthalpy to produce two moles of HCl(g) from elements. Answer: 2×(−92.307)=−184.614 kJ.
Exercise D: A reaction forms liquid water, but only gas-phase bond averages were used. Name the missing question: which phase-change or formation-enthalpy information is required to compare with a liquid-product standard reaction enthalpy?
Contents · Previous · Next · Subject root
Write and balance the reaction with phases. Draw structures or otherwise identify exact bonding, then count each bond type multiplied by the reaction’s stoichiometric coefficients. Separate a subtotal for bonds broken from one for bonds formed.
Use a consistent table, preserve the sign convention and compute ΔH≈broken−formed. State whether entries are averages or molecule-specific dissociation values, and resist quoting more digits than the data justify.
Check an independently available formation-enthalpy result when useful. If the two methods disagree significantly, investigate incorrect bond types, molecular context, species phase, stoichiometric errors and rounding before declaring a thermodynamic paradox.
Continue with The Gold Standard of Thermochemistry, Hess’s Law and reversed equations and Kirchhoff’s Law. Each asks a different question about how energy values are combined and interpreted.
Applied bond-energy lab
A two-route thermochemical consistency check
Route one is broken minus formed: H–H plus Cl–Cl requires 679 kJ, while two H–Cl bonds release 864 kJ, giving −185 kJ for the reaction.
Route two is products minus reactants using standard formation enthalpies: 2×(−92.307)−0=−184.614 kJ. The results differ by only a few tenths of one kilojoule at the tabulated precision.
That small difference is a useful example of how an estimate can agree with an independently defined reference without being algebraically identical to it. Preserve the input tables and definitions so readers can reproduce both routes.
Show why products can have stronger total bonding
In the estimate, reactant bond breaking requires 679 kJ, while the product bond formation contributes 864 kJ of energy release. The product bonding thus stabilises the chemical state by a larger magnitude than the initial bonds required to be broken.
The net difference is negative, but that does not mean a bond releases energy while being broken. The release belongs to bond formation on the product side of the conceptual cycle.
Students can highlight broken bonds in one colour and formed bonds in another, then label each subtotal with an energy sign. That physical interpretation is more durable than memorising a one-line formula.
A context-sensitive bond-strength thought experiment
Suppose two different molecules each contain a structural C–H bond but their other attached groups differ. A generic C–H average can provide a rough estimate for both, yet the precise homolytic dissociation enthalpy can differ because the radical products have different stability.
Thus molecular identity is part of the definition of a bond dissociation, not an inconvenient detail that a general table magically removes.
When precision matters, seek molecule-specific thermochemistry and explicitly state any averaging approximation. This avoids misleading comparisons where the apparent discrepancy comes from using unlike bond data.
A careful note about actual laboratory heat
A gas-phase reference reaction enthalpy is not identical to the rise in temperature of an arbitrary beaker. An experimental heat balance includes sample amount, reaction extent, heat capacities, losses and potentially incomplete conversion.
The bond-energy estimate is useful for predicting the approximate sign and magnitude of a defined reaction. Measuring useful heat delivered by equipment is a different task with its own boundary and state assumptions.
Keeping theoretical enthalpy, observed heat transfer and practical rate separate makes the explanation helpful without encouraging unsafe chemical experimentation.
Frequently asked questions
Does breaking a bond release its energy?
No. Bond breaking requires energy; bond formation releases energy. Exothermicity occurs when energy released in forming bonds and other state changes exceeds energy absorbed in breaking bonds.
Are average bond enthalpies exact for every molecule?
No. Molecular environment and the specific fragments formed can change dissociation enthalpies. Averages are estimates.
Do gas-phase bond sums include condensing water?
Not automatically. Phase changes require the corresponding enthalpy terms or a complete formation-enthalpy treatment.
Sources and connected reading
The worked values are rounded educational bond-energy estimates and reference formation data for gas-phase species; no laboratory experiment is being reported.
- OpenStax Chemistry: Atoms First 2e — Bond Strengths and Average Enthalpies
- OpenStax Organic Chemistry — Bond Dissociation Energies
- OpenStax Chemistry 2e — Standard Enthalpy
- The Gold Standard of Thermochemistry | Hess’s Law
Advanced thermochemistry lab: methane bonds, tabular differences and uncertainty
Extend the method to methane combustion with gaseous water
Take the balanced gas-phase reaction CH₄(g)+2O₂(g)→CO₂(g)+2H₂O(g). As a deliberately approximate teaching exercise, choose average bond enthalpies C–H=413, O=O=498, O–H=463 and C=O in CO₂=799 kJ per mole of bonds. The special CO₂ entry is important: not every carbon–oxygen double-bond environment has the same value.
Breaking four C–H bonds and two O=O bonds requires 4(413)+2(498)=1652+996=2648 kJ per mole of methane reaction. Forming two C=O bonds in CO₂ and four O–H bonds across two H₂O molecules releases 2(799)+4(463)=1598+1852=3450 kJ.
The approximate gas-product reaction enthalpy is therefore ΔH≈2648−3450=−802 kJ/mol methane. This is close to the representative gas-water standard reaction enthalpy around −802.3 kJ/mol calculated in the separate methane heating-value article. Such numerical agreement is a check, not proof that the averages are universally exact.
If the water product were liquid rather than vapour, the thermochemical comparison would include condensation. The reference enthalpy would have larger negative magnitude, around −890.3 kJ/mol in that earlier model. An all-gas bond ledger does not automatically include the roughly 88 kJ per mole of methane from condensing two water molecules.
Why different textbooks can produce slightly different bond totals
Our H₂+Cl₂ example uses H–Cl=432 kJ/mol from the selected OpenStax discussion. Another source may give a representative H–Cl value of 431 kJ/mol. With the latter input, the formed subtotal is 862 rather than 864 kJ, giving ΔH≈679−862=−183 kJ instead of −185.
Neither calculation is arithmetically inconsistent with its supplied table. The difference arises from different rounded bond data. A student should use the values provided for a particular examination or reference problem, keep the table internally consistent, and explain the estimate’s precision.
The standard formation-enthalpy check, using −92.307 kJ/mol HCl(g), gives −184.614 kJ for the written reaction. Both representative bond-ledger results are approximations around that reference figure; claiming one must equal it to every decimal place overstates the tabular method.
This is why an apparently meticulous solution can still be scientifically misleading if it combines numbers drawn from different reference tables without noting what they mean. Data provenance is part of the chemistry explanation, not merely a footnote.
Propagate hypothetical bond-data uncertainty instead of hiding it
Suppose for teaching that the H–H, Cl–Cl and H–Cl entries each carried an independent illustrative standard uncertainty of 5 kJ per mole of bonds. The estimated reaction enthalpy is a linear combination D(H–H)+D(Cl–Cl)−2D(H–Cl).
Under the stated independence assumption, the variance of the estimate is 5²+5²+(2×5)²=150 in squared kilojoule units, so the standard uncertainty is about 12.2 kJ. It is much larger than the roughly 0.4 kJ difference between our one chosen approximation and the standard-state result.
Those ±5 inputs are invented for instruction and are not claimed uncertainty specifications for the actual OpenStax table. In real averages, systematic biases and correlated molecular-environment effects can matter, so treating deviations as independent measurement errors may be inappropriate.
The exercise nevertheless demonstrates why quoting an average-bond estimate to a tenth of a kilojoule without an uncertainty discussion can imply precision that the underlying method has not earned.
Separate atomisation bookkeeping from an elementary reaction mechanism
The conceptual bond ledger can be understood as a Hess-law route: imagine dissociating reactant gas molecules into suitable gas-phase atoms, then allowing atoms to form the product bonds. The total enthalpy difference equals the sum of those hypothetical steps under consistent state definitions.
A real gas reaction need not follow that route. For example, the chemistry of H₂ and Cl₂ under particular conditions involves kinetic pathways and may be affected by initiation processes. A calculated exothermic ΔH does not specify its activation energy, reaction speed, chain mechanism or safe experimental conditions.
Likewise, a table’s high bond strength does not mean a molecule will necessarily react or dissociate on an ordinary classroom timescale. Thermodynamics, kinetics and safety are separate questions, even when they concern the same bonds.
This distinction keeps a theoretical calculation useful for learners without turning it into a recipe for mixing reactive chemicals. The correct educational objective is to understand the energy balance, not to attempt the reaction.
A reliable way to compare two reporting bases
Scale the gas-phase target H₂+Cl₂→2HCl by a factor of two: 2H₂+2Cl₂→4HCl. The approximate bond-energy result scales from −185 to −370 kJ for the doubled reaction as written. The standard formation-enthalpy result scales from −184.614 to −369.228 kJ.
If the question instead asks for approximate energy per mole of HCl produced, divide the original −185 kJ by two, giving −92.5 kJ/mol HCl. That normalisation differs from energy per mole of the original written reaction, even though both use kJ/mol.
One should also distinguish a gas-phase reaction from one involving solvated hydrochloric acid. Dissolving HCl(g) in water introduces additional enthalpy changes and solution conditions; the gas-phase bond ledger is not a complete calculation for that process.
End the calculation by writing the balanced equation, states, energy sign and basis on one line. A well-defined chemical result is easier to compare with literature data and much harder to misuse.
Preserve source-table consistency when checking chemistry work
Two legitimate educational data tables can list slightly different rounded bond energies. The correct exam or teaching calculation is based on the set supplied for that question, not a mixture selected after the result is known. State the source of each input, count each bond with the balanced-equation coefficients, and explain why the final number is an estimate.
Cross-checking against formation enthalpies provides an independent chemical reference when states and conditions match. Agreement supports the calculation’s plausibility; disagreement should prompt checks of molecular context, phase, coefficients and data quality before concluding that a fundamental conservation law has failed.