Library / Foundations: Chemistry / FCH-17
Foundations: Chemistry
Hess’s law from formation enthalpies
Reaction enthalpy from the enthalpies of formation of products and reactants.
- Ref
- FCH-17
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- ΔH [kJ/mol]
Subscripts p and r mean products and reactants. Multiply each ΔHf by its coefficient in the balanced equation before adding. Elements in their standard states have ΔHf = 0. The defaults are for CH₄ + 2O₂ → CO₂ + 2H₂O: products −393.5 + 2(−285.8) = −965.1; reactants −74.8.
The energy change of a reaction depends only on the start and end, so you can find it by going via the elements.
Calculator
- Heat released (positive)890.3 kJ/mol
- Energy released for 0.5 mol445.2 kJ
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Methane burning releases about 890 kJ per mole, a standard fuel benchmark.
- Reversing a reaction changes the sign of ΔH.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kJ/mol) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ΣΔHf (products) Sum of ΔHf of products | −5,000 to 5,000 kJ/mol | −4,925 | 5,075 | 10,000 | +10% | +10.8 % |
| ΣΔHf (reactants) Sum of ΔHf of reactants | −5,000 to 5,000 kJ/mol | −5,965 | 4,035 | 10,000 | +10% | −0.84 % |
Sweep of Sum of ΔHf of products
| Sum of ΔHf of products (kJ/mol) | Enthalpy of reaction (kJ/mol) |
|---|---|
| −5,000 | −4,925 |
| −3,750 | −3,675 |
| −2,500 | −2,425 |
| −1,250 | −1,175 |
| 0 | 74.8 |
| 1,250 | 1,325 |
| 2,500 | 2,575 |
| 3,750 | 3,825 |
| 5,000 | 5,075 |
Sweep one variable
Variables and how each one contributes
Enthalpy of reaction
What the equation gives you. Everything else feeds it.
Sum of ΔHf of products
Total formation enthalpy of the products, with coefficients. Raises ΔH one-for-one.
Sum of ΔHf of reactants
Total formation enthalpy of the reactants, with coefficients. Lowers ΔH one-for-one.
Worked example with the values above
- Products: −965.1 kJ/mol.
- Reactants: −74.8 kJ/mol.
- ΔH = −965.1 − (−74.8) = −890.3 kJ/mol.
Assumptions and limits
- Standard conditions.
- Balanced equation used for coefficients.
Common mistakes
- Forgetting to multiply by the coefficients.
- Subtracting the wrong way round.
Statistics and uncertainty
Tabulated enthalpies are rounded to 0.1 kJ/mol, so the result is accurate to about that level.
Where it is used
- Fuel energy comparisons.
- Energy budgets of explosives and propellants.
Maths you need
- Enthalpy of formation: from elements
- Balanced equations: coefficients