Chemistry · General chemistry I · Concept
Hess’s law and enthalpies of formation
Hess’s law says that if chemical equations add up to a target equation, their enthalpy changes add up to its ΔH, because enthalpy is a state function. Reversing an equation flips the sign of ΔH and multiplying it multiplies ΔH. Standard enthalpies of formation turn this into one formula: ΔH°rxn = Σ n ΔHf°(products) − Σ n ΔHf°(reactants).
Only the start and the end matter
Enthalpy is a state function: ΔH depends on the substances you start with and end with, not on the route between them. So a reaction that is hard to measure directly can be reached through steps whose enthalpies are known.
Three rules for thermochemical equations
A thermochemical equation’s ΔH belongs to the equation exactly as written, with its coefficients and physical states. Changing the equation changes ΔH in step.
| Change to the equation | Change to ΔH |
|---|---|
| Reverse it | Change the sign |
| Multiply every coefficient by k | Multiply ΔH by k |
| Add equations | Add their ΔH values |
Cancel only identical species
When equations are added, a substance on both sides cancels only if its physical state matches. H₂O(l) and H₂O(g) are different substances for this purpose, with different enthalpies.
Standard enthalpy of formation
ΔHf° is the enthalpy change to form one mole of a substance from its elements in their standard states, at 1 bar and a stated temperature, usually 25 °C. An element already in its standard state, such as O₂(g), H₂(g) or Mg(s), has ΔHf° = 0 by definition. For liquid water the formation equation is H₂(g) + ½O₂(g) → H₂O(l).
Products minus reactants
Formation enthalpies turn Hess’s law into one formula. Take the reactants apart into their elements, the reverse of their formation, then build the products from those elements. Multiply each ΔHf° by its coefficient.
Say what the ΔH is for
Report ΔH per reaction as written, in kJ, or per mole of a named substance, in kJ/mol. The same reaction written with doubled coefficients has twice the ΔH.
Common mistakes
- Reversing an equation but keeping the sign of its ΔH.
- Multiplying the coefficients but not ΔH, or ΔH but not every coefficient.
- Cancelling substances in different states, such as H₂O(l) against H₂O(g).
- Giving an element in its standard state a nonzero ΔHf°: O₂(g), H₂(g) and Mg(s) are all zero.
- Subtracting in the wrong order: the formula is products minus reactants.
Key terms
- Hess’s law
- If a reaction is the sum of other reactions, its ΔH is the sum of their ΔH values, because enthalpy is a state function. Reversing a reaction flips the sign of ΔH; multiplying it scales ΔH by the same factor.
- Thermochemical equation
- A balanced chemical equation, with physical states, together with its enthalpy change for the reaction as written. Reversing the equation changes the sign of ΔH; multiplying its coefficients multiplies ΔH.
- Standard formation enthalpy
- ΔH°f: the enthalpy change to form one mole of a substance from its elements in their standard states, such as C(s, graphite) + O₂(g) → CO₂(g). It is zero for an element in its standard state.
- State function
- A property that depends only on a system’s current state, not on how it got there, such as enthalpy or entropy. Heat and work depend on the path, so they are not state functions.
- Standard state
- The reference conditions behind tabulated thermodynamic values: a pure gas at 1 atm (1 bar in newer tables), a solute at 1 M, and a pure liquid or solid in its most stable form. Temperature isn’t fixed by it, though tables usually use 25 °C.
- Enthalpy
- H = U + PV, a state function. At constant pressure its change, ΔH, equals the heat the system absorbs (positive) or releases (negative).
Work through an example
A student measures ΔH₁ = −467 kJ for Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g) and ΔH₂ = −151 kJ for MgO(s) + 2HCl(aq) → MgCl₂(aq) + H₂O(l). With ΔH₃ = −285.83 kJ for H₂(g) + ½O₂(g) → H₂O(l), find ΔH for Mg(s) + ½O₂(g) → MgO(s).
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