# Hess’s Law

Hess’ law, is a relationship in physical chemistry named after Germain Hess, a Swiss-born Russian chemist and physician who published it in 1840. The law states that the total enthalpy change during the complete course of a chemical reaction is independent of the number of steps taken.

Hess’ law is now understood as an expression of the principle of conservation of energy, also expressed in the first law of thermodynamics, and the fact that the enthalpy of a chemical process is independent of the path taken from the initial to the final state (i.e. enthalpy is a state function).

Reaction enthalpy changes can be determined by calorimetry for many reactions. The values are usually stated for processes with the same initial and final temperatures and pressures, although the conditions can vary during the reaction.

Hess’ law can be used to determine the overall energy required for a chemical reaction, when it can be divided into synthetic steps that are individually easier to characterize. This affords the compilation of standard enthalpies of formation, that may be used as a basis to design complex syntheses.

Examples:

1) (a) Cgraphite + O2 → CO2 (g) ;(ΔH = –393.5 kJ/mol) (direct step)

(b) Cgraphite + 1/2 O2 → CO (g) ; (ΔH = –110.5 kJ/mol)

(c) CO (g) +1/2 O2 → CO2 (g); (ΔH = –283.02 kJ/mol)

Reaction (a) is the sum of reactions (b) and (c), for which the total ΔH = –393.5 kJ/mol which is equal to ΔH in (a).

The difference in the value of ΔH is 0.02 kJ/mol which is due to measurement errors .

2) Given:

• B2O3 (s) + 3H2O (g) → 3O2 (g) + B2H6 (g) (ΔH = 2035 kJ/mol)
• H2O (l) → H2O (g) (ΔH = 44 kJ/mol)
• H2 (g) + 1/2 O2 (g) → H2O (l) (ΔH = –286 kJ/mol)
• 2B (s) + 3H2 (g) → B2H6 (g) (ΔH = 36 kJ/mol)

The concepts of Hess’ law can be expanded to include changes in entropy and in Gibbs free energy, which are also state functions. The Bordwell thermodynamic cycle is an example of such an extension which takes advantage of easily measured equilibria and redox potentials to determine experimentally inaccessible Gibbs free energy values.

Combining ΔGvalues from Bordwell thermodynamic cycles and ΔHo values found with Hess’ law can be helpful in determining entropy values which are not measured directly, and therefore must be calculated through alternative paths.

Hess’ law is useful in the determination of enthalpies of the following:

• Heats of formation of unstable intermediates like CO(g) and NO(g).
• Heat changes in phase transitions and allotropic transitions.
• Lattice energies of ionic substances by constructing Born–Haber cycles if the electron affinity to form the anion is known, or
• Electron affinities using a Born–Haber cycle with a theoretical lattice energy