Hess's Law Calculator

Combine known reactions to find the enthalpy change of a target reaction.

Known Reactions

1.ΔH =kJ
Add at least one known reaction with a ΔH value.

How Hess's Law Works

Hess's Law states that the total enthalpy change for a chemical reaction is independent of the pathway taken. This means you can combine known thermochemical equations — multiplying them by coefficients and reversing them as needed — to determine the enthalpy change of a target reaction that may be difficult or impossible to measure directly.

This calculator sets up a system of linear equations where each known reaction contributes a row of species coefficients. The solver then finds the linear combination of known reactions that produces the target reaction, using a least-squares approach with Gaussian elimination. The resulting coefficients are multiplied by each known ΔH and summed to give the target enthalpy.

FAQ: Common Questions
How do I enter subscripts?

Use Unicode subscripts (₂, ₃, etc.) or just type regular numbers: H2O works the same as H₂O.

What does a negative coefficient mean?

A negative coefficient means the known reaction must be reversed. For example, if the solver outputs −1.0, flip the reaction and negate its ΔH.

Why do I get a "underdetermined" error?

You need at least as many known reactions as unique chemical species in your target. Add more known reactions to constrain the system.

Example: Formation of Liquid Water

Known reactions:

1. 2H₂ + O₂ → 2H₂O(g), ΔH = −483.6 kJ

2. 2H₂O(g) → 2H₂O(l), ΔH = −88.0 kJ

Target: 2H₂ + O₂ → 2H₂O(l)

The solver finds coefficients 1.0 and 1.0, giving ΔH = (1.0 × −483.6) + (1.0 × −88.0) = −571.6 kJ.