Calculate the enthalpy change of a target reaction from known reactions using Hess’s law in kJ/mol, kcal/mol, J/mol, or cal/mol with multipliers.

undefined

Supply balanced reactions with matching phases and conditions. Species labels match exactly; atomic balance is not checked. Units are per mole of reaction as written.

Loads example values only; select Calculate for the answer.

Use -> and spaced + separators; coefficients may be 1/2. Match labels and phases exactly. Charges use a caret, e.g. Fe^3+.

Related Calculators

Hess’s Law Formula

The following formation-enthalpy formula is one application of Hess’s law. The calculator above instead combines 2–4 known reaction equations, solves their multipliers and sums multiplier × reaction enthalpy. Both methods require balanced equations with consistent physical states and conditions.

Δ Hᵣₓₙ = Σ nu Δ Hf(products) - Σ nu Δ Hf(reactants)

Variables:

  • ΔHrxn is the reaction enthalpy change (kJ per mole of reaction, as written)
  • ν is the stoichiometric coefficient for each species in the balanced chemical equation
  • ΔHf is the (molar) enthalpy of formation for each species (typically tabulated in kJ/mol for the species)

To calculate the reaction enthalpy change, multiply each species’ enthalpy of formation by its stoichiometric coefficient (ν), sum these values for the products, and subtract the corresponding stoichiometric sum for the reactants. The result is the reaction enthalpy change for the reaction as written, regardless of the path taken when initial and final states and conditions match. The calculator matches species labels and phases exactly but does not check atomic balance. A reversed known reaction has a negative multiplier; scaling an equation scales its enthalpy. See OpenStax’s Hess’s law examples.

What is Hess’s Law?

Hess’s Law, named after Russian chemist Germain Hess, states that the total enthalpy change during the complete course of a chemical reaction is the same whether the reaction is carried out in one step or in several steps. This is because enthalpy is a state function, meaning its value depends only on the current state of the system and not on the path taken to reach that state. Therefore, the total enthalpy change in a chemical reaction is independent of the route by which the chemical reaction takes place.

How to Calculate Hess’s Law?

The following steps outline how to calculate the total enthalpy change (ΔH) using Hess’s Law:

  1. Determine the enthalpy of formation (ΔHf) for each product involved in the reaction.
  2. Determine the enthalpy of formation (ΔHf) for each reactant involved in the reaction.
  3. Multiply each ΔHf by the stoichiometric coefficient (ν) for that species and sum to get ΣνΔHf(products) and ΣνΔHf(reactants).
  4. Subtract the stoichiometric sum of the reactants from the stoichiometric sum of the products: ΔHrxn = ΣνΔHf(products) − ΣνΔHf(reactants).
  5. For the formation-enthalpy method, subtract the two stoichiometric sums directly. To use the calculator above, enter the known balanced reaction equations and their reaction enthalpies, then enter the target equation.

Example Problem:

Use the following variables as an example problem to test your knowledge:

ΣνΔHf (products) = -120 kJ/mol (of reaction)

ΣνΔHf (reactants) = -80 kJ/mol (of reaction)

Calculate the reaction enthalpy change (ΔHrxn) using the formula: ΔHrxn = ΣνΔHf (products) – ΣνΔHf (reactants) = -120 – (-80) = -40 kJ/mol of reaction as written. This example uses formation-enthalpy sums; the widget uses known reaction equations instead.