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Generated on: July 20, 2026 at 09:33 PM

Hess's Law Enthalpy Calculator

Inputs

Sum of products (Σ ΔHf° × coefficient)-393.5 kJ/mol
Sum of reactants (Σ ΔHf° × coefficient)0 kJ/mol

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Chemistry

Hess's Law Enthalpy Calculator

Find the standard enthalpy of reaction with Hess's law: ΔH°rxn = Σ ΔHf°(products) − Σ ΔHf°(reactants). Enter the coefficient-weighted formation-enthalpy sums for the products and reactants and read off ΔH per mole of reaction, with an exothermic or endothermic label.

Inputs

kJ/mol
kJ/mol

Results

Enter a value to see results.

\begin{aligned} \Delta H_{rxn}^{\circ} &= \textstyle\sum \Delta H_f^{\circ}(\text{prod}) - \sum \Delta H_f^{\circ}(\text{react}) \\ &= \left(-393.5\,\text{kJ/mol}\right) - \left(0\,\text{kJ/mol}\right) \\ &= ?\,\text{kJ/mol} \end{aligned}

ΔH is essentially zero — the reaction is thermoneutral as written.

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What Hess's law says

Enthalpy is a state function: its value depends only on the current state of a system, not on how the system got there. Hess's law is the direct consequence for chemical reactions — the enthalpy change of a reaction is the same whether it proceeds in a single step or through any sequence of intermediate steps. This is what makes it possible to calculate a reaction's enthalpy from tabulated data instead of measuring every reaction in a calorimeter.

The formation-enthalpy route

The most common way to apply Hess's law uses standard enthalpies of formation (ΔHf°), the enthalpy change when one mole of a substance forms from its elements in their standard states. The standard enthalpy of reaction is then:

ΔHrxn∘=∑n ΔHf∘(products)−∑n ΔHf∘(reactants)\Delta H_{rxn}^{\circ} = \sum n\,\Delta H_f^{\circ}(\text{products}) - \sum n\,\Delta H_f^{\circ}(\text{reactants})

where each n is the stoichiometric coefficient from the balanced equation. This calculator takes the two coefficient-weighted sums and returns their difference.

SymbolQuantityUnit
ΔH°rxnStandard enthalpy of reactionkJ/mol
ΔHf°(products)Formation enthalpies of productskJ/mol
ΔHf°(reactants)Formation enthalpies of reactantskJ/mol
nStoichiometric coefficientdimensionless

Worked example

Find the standard enthalpy of combustion of methane:

CH4(g)+2 O2(g)→CO2(g)+2 H2O(l)\text{CH}_4(g) + 2\,\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\,\text{H}_2\text{O}(l)

Using standard formation enthalpies (kJ/mol): CH₄ = −74.8, O₂ = 0, CO₂ = −393.5, H₂O(l) = −285.8.

  1. Sum for products: (1)(−393.5) + (2)(−285.8) = −393.5 − 571.6 = −965.1 kJ/mol.
  2. Sum for reactants: (1)(−74.8) + (2)(0) = −74.8 kJ/mol.
  3. Apply Hess's law: ΔH°rxn = −965.1 − (−74.8) = −890.3 kJ/mol.

The large negative value confirms that methane combustion is strongly exothermic, which is why natural gas is a useful fuel.

Reading the sign

The sign of ΔH°rxn tells you the direction of heat flow for the reaction as written.

Sign of ΔHNameHeat flow
NegativeExothermicReleased to the surroundings
PositiveEndothermicAbsorbed from the surroundings
Near zeroThermoneutralLittle net exchange

Because enthalpy scales with the amount of reaction, reversing an equation flips the sign of ΔH, and multiplying the coefficients multiplies ΔH by the same factor.

Why elements drop out

By definition, the most stable form of any pure element in its standard state has ΔHf° = 0 — graphite for carbon, O₂ gas for oxygen, metallic iron for iron. Those species contribute nothing to either sum, so a reaction that consumes or produces elements only needs the formation enthalpies of its compounds. That is why the oxygen in the methane example never appeared in the arithmetic.

Combining reactions directly

When formation enthalpies are not available, Hess's law can still be applied by adding known reactions algebraically. Reverse a reaction and change its ΔH sign; scale a reaction and scale its ΔH; then add the steps so the intermediates cancel and leave the target equation. The summed ΔH values give the target reaction's enthalpy. The formation-enthalpy method used here is simply the most systematic version of that same idea.

Once ΔH°rxn is known, pairing it with the entropy change gives the Gibbs free energy and therefore whether the reaction is spontaneous. A calorimetry measurement offers an independent experimental check on the same enthalpy, and gas-stoichiometry tools translate the per-mole result into the masses or volumes handled in the lab.

Frequently Asked Questions (FAQ)

What is Hess's law?

Hess's law states that the enthalpy change of a reaction is the same whether it happens in one step or several, because enthalpy is a state function — it depends only on the start and end states, not on the path. A practical consequence is that the standard enthalpy of reaction equals the sum of the standard enthalpies of formation of the products minus that of the reactants, each weighted by its coefficient in the balanced equation.

How do I get the two sums from a balanced equation?

Look up the standard enthalpy of formation (ΔHf°, in kJ/mol) of every species from a data table. Multiply each value by the species coefficient in the balanced equation, then add the products together for one sum and the reactants together for the other. Enter those two totals here, and the calculator subtracts reactants from products to give ΔH°rxn.

What does the sign of ΔH mean?

A negative ΔH means the reaction releases heat to its surroundings — it is exothermic, like combustion. A positive ΔH means the reaction absorbs heat — it is endothermic, like thermal decomposition. A value near zero means little net heat is exchanged for the reaction as written.

Why do elements have a formation enthalpy of zero?

The standard enthalpy of formation is defined as the enthalpy change when one mole of a compound forms from its elements in their standard states. Forming an element from itself involves no change, so the most stable form of any element — O₂ gas, solid carbon as graphite, metallic copper — is assigned ΔHf° = 0 by convention. That is why elemental reactants or products drop out of the sums.

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