Hess’ Law Calculator

Last updated: June 2026

This general Hess’ Law equation solver finds the combination of known thermochemical equations that produces a target equation. It determines automatically which equations must be reversed or multiplied, then uses the same multipliers to calculate the unknown enthalpy change.

Key takeaway: Each reaction is treated as a vector of stoichiometric coefficients. The solver finds multipliers x1, x2, ... such that the known equations add exactly to the target equation, then calculates ΔHtarget = ΣxiΔHi.

How the general Hess’ Law solver works

Reactants are assigned negative stoichiometric coefficients and products are assigned positive coefficients. For example, the reaction C(s) + O2(g) → CO2(g) becomes a numerical pattern containing −1 for C, −1 for O2 and +1 for CO2. The solver compares these patterns across every equation.

x1(equation 1) + x2(equation 2) + ... = target equation

A negative multiplier means that a known equation must be reversed. A multiplier such as 2 or ½ means that all coefficients and the corresponding enthalpy change must be multiplied by that factor.

How to enter equations
  1. Write one target equation and at least one known equation.
  2. Put spaces around the plus sign separating different species.
  3. Use an arrow such as -> or →.
  4. Enter coefficients as whole numbers, decimals or fractions such as 1/2.
  5. Keep physical states because H2O(l) and H2O(g) are different thermochemical species.
  6. For ions, forms such as Fe^3+(aq), SO4^2-(aq), NH4+(aq) and e- are accepted.

Worked example: formation of carbon monoxide

The target equation is:

C(s) + ½O2(g) → CO(g)

The supplied equations are:

C(s) + O2(g) → CO2(g), ΔH = −393.5 kJ mol−1
CO(g) + ½O2(g) → CO2(g), ΔH = −283.0 kJ mol−1

The solver finds multipliers +1 and −1. Therefore, the first equation is used as written and the second is reversed.

ΔH = 1(−393.5) + (−1)(−283.0) = −110.5 kJ mol−1

Advanced checks included in the solver

The calculator verifies that the final linear combination reproduces the target stoichiometry. It also attempts to check elemental and charge balance for ordinary formula notation. Physical states remain distinct during the Hess calculation even though they do not affect elemental balance.

If the known equations are redundant, more than one valid mathematical route may exist. The calculator reports this and checks whether every valid route gives the same enthalpy. If different routes give different answers, the supplied thermochemical data are internally inconsistent.

Important input rule: Use spaces around the plus sign that separates species, for example H2(g) + 1/2 O2(g) -> H2O(l). This prevents the solver from confusing a separator with the positive charge on an ion.

What the solver cannot infer

The calculator cannot decide which thermochemical equations should have been supplied in the first place. If the target reaction is outside the span of the known equations, it will explain that the target cannot be constructed. It also treats differently written species as different; therefore, notation and physical states should be consistent.

Common examination traps

Trap 1: Reversing an equation changes the sign of ΔH. Do not reverse the sign a second time during the final sum.
Trap 2: Multiplying a reaction by ½ also multiplies its enthalpy change by ½.
Trap 3: H2O(l) and H2O(g) cannot cancel because they represent different physical states.
Trap 4: A numerical answer is meaningful only when the manipulated equations add exactly to the target equation.

Frequently asked questions

Can the calculator work with formation and combustion data?

Yes. Enter each formation or combustion equation explicitly with its enthalpy change. The solver does not need a separate memorised formula; it obtains the correct products-minus-reactants or reactants-minus-products pattern by combining the equations themselves.

Can it calculate hydration enthalpy?

Yes, provided the target hydration equation and the atomisation, ionisation, electron-affinity or aqueous-ion equations are entered in a consistent form. The cobalt(II) preset demonstrates this type of cycle.

What does a negative equation multiplier mean?

It means the equation must be reversed. For example, a multiplier of −2 means reverse the equation and then multiply every coefficient and its enthalpy change by 2.

Why might the solver report several possible routes?

This occurs when some supplied equations are redundant. Hess’ Law requires all internally consistent routes between the same initial and final states to give the same enthalpy change.

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