Enthalpy Change from Hess's Law

\[\Delta H_{rxn}=(c\Delta H_{f,C}+d\Delta H_{f,D})-(a\Delta H_{f,A}+b\Delta H_{f,B})\]

Variables

dHrxn[ΔHrxn]reaction enthalpy change (kJ/mol)

dHA[ΔHf,A]standard enthalpy of formation of reactant A (kJ/mol)

dHB[ΔHf,B]standard enthalpy of formation of reactant B (kJ/mol)

dHC[ΔHf,C]standard enthalpy of formation of product C (kJ/mol)

dHD[ΔHf,D]standard enthalpy of formation of product D (kJ/mol)

astoichiometric coefficient of reactant A

bstoichiometric coefficient of reactant B

cstoichiometric coefficient of product C

dstoichiometric coefficient of product D

Description

What is this formula?

Hess's Law states that the enthalpy change of a reaction depends only on the initial and final states and is independent of the reaction pathway.

This equation calculates the reaction enthalpy from standard enthalpies of formation.

When to use it

Use this formula when determining reaction enthalpies from tabulated thermodynamic data or evaluating energy balances in chemical processes.

Example

Reaction:

CH4 + 2O2 → CO2 + 2H2O

Given:

ΔHf(CH4) = -74.8 kJ/mol

ΔHf(O2) = 0 kJ/mol

ΔHf(CO2) = -393.5 kJ/mol

ΔHf(H2O) = -285.8 kJ/mol

Formula:

ΔHrxn = Σ(products) − Σ(reactants)

Substitution:

ΔHrxn = [-393.5 + 2(-285.8)] - [-74.8 + 2(0)]

Result:

ΔHrxn = -890.3 kJ/mol

Applications

Chemical thermodynamics

Combustion analysis

Reaction engineering

Process design

Energy balances

Note

The rigorous form of Hess's Law is usually written using summation notation over all reactants and products. Because fCalc requires explicit equations, this implementation uses a fully expanded form for a typical reaction. The same thermodynamic principle applies to reactions containing any number of species.