Hess's law

Hess's law of constant heat summation, also known as 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.^[1]^[2]

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.

Theory

Hess' law states that the change of enthalpy in a chemical reaction is the same regardless of whether the reaction takes place in one step or several steps, provided the initial and final states of the reactions and products are the same.

In other words, if a chemical change takes place by several different routes, the overall enthalpy change is the same, regardless of the route by which the chemical change occurs (provided the initial and final condition are the same). If this were not true, then one could violate the first law of thermodynamics.

Hess' law allows the enthalpy change (ΔH) for a reaction to be calculated even when it cannot be measured directly. This is accomplished by performing basic algebraic operations based on the chemical equations of reactions using previously determined values for the enthalpies of formation.

Combination of chemical equations leads to a net or overall equation. If enthalpy change is known for each equation, the result will be the enthalpy change for the net equation. If the net enthalpy change is negative (ΔH_net < 0), the reaction is exothermic and is more likely to be spontaneous; positive ΔH values correspond to endothermic reactions. Entropy also plays an important role in determining spontaneity, as some reactions with a positive enthalpy change are nevertheless spontaneous.

Hess' law states that enthalpy changes are additive. Thus the ΔH for a single reaction

\Delta H_{\text{reaction}}^{\ominus }=\sum \Delta H_{\mathrm {f} \,({\text{p}})}^{\ominus }-\sum \Delta H_{\mathrm {f} \,({\text{r}})}^{\ominus }

where $\Delta H_{f(p)}$ is the enthalpy of formation of product p, $\Delta H_{f(r)}$ is the enthalpy of formation of reactant r, and the ^o superscript indicates standard state values. This may be considered as the sum of two (real or fictitious) reactions:

Reactants → Elements

\Delta H^{\ominus }=-\sum \Delta H_{\mathrm {f} \,({\text{r}})}^{\ominus }

and Elements → Products

\Delta H^{\ominus }=\sum \Delta H_{\mathrm {f} \,({\text{p}})}^{\ominus }

Examples

1. C_graphite + O₂ → CO₂ (g) ;(ΔH = −393.5 kJ/mol) (direct step)
2. C_graphite + 1/2 O₂ → CO (g) ; (ΔH = −110.5 kJ/mol)
3. 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.
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)
Find the ΔH_f of:
- 2B (s) + 3/2 O₂ (g) → B₂O₃ (s)
After multiplying the equations (and their enthalpy changes) by appropriate factors and reversing the direction when necessary, the result is:
- B₂H₆ (g) + 3O₂ (g) → B₂O₃ (s) + 3H₂O (g) (ΔH = 2035 × (−1) = −2035 kJ/mol)
- 3H₂O (g) → 3H₂O (l) (ΔH = 44 × (−3) = −132 kJ/mol)
- 3H₂O (l) → 3H₂ (g) + (3/2) O₂ (g) (ΔH = −286 × (−3) = 858 kJ/mol)
- 2B (s) + 3H₂ (g) → B₂H₆ (g) (ΔH = 36 kJ/mol)
Adding these equations and canceling out the common terms on both sides, we obtain
- 2B (s) + 3/2 O₂ (g) → B₂O₃ (s) (ΔH = −1273 kJ/mol)

Extension to free energy and entropy

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 ΔG^o values from Bordwell thermodynamic cycles and ΔH^o 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.

For the free energy:

\Delta G_{\text{reaction}}^{\ominus }=\sum \Delta G_{\mathrm {f} \,({\text{p}})}^{\ominus }-\sum \Delta G_{\mathrm {f} \,({\text{r}})}^{\ominus }.

For entropy, the situation is a little different. Because entropy can be measured as an absolute value, not relative to those of the elements in their reference states (as with ΔH^o and ΔG^o), there is no need to use the entropy of formation; one simply uses the absolute entropies for products and reactants:

\Delta S_{\text{reaction}}^{\ominus }=\sum S_{({\text{p}})}^{\ominus }-\sum S_{({\text{r}})}^{\ominus }.

Applications

Hess' law is useful in the determination of enthalpies of the following:^[1]

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

References

^ ^a ^b Mannam Krishnamurthy; Subba Rao Naidu (2012). "7". In Lokeswara Gupta (ed.). Chemistry for ISEET - Volume 1, Part A (2012 ed.). Hyderabad, India: Varsity Education Management Limited. p. 244.
^ "Hess' Law - Conservation of Energy". University of Waterloo. Archived from the original on 9 January 2015. Retrieved 12 January 2014.

Chakrabarty, D.K. (2001). An Introduction to Physical Chemistry. Mumbai: Alpha Science. pp. 34–37. ISBN 1-84265-059-9.

External links

Hess' paper (1840) on which his law is based (at ChemTeam site)
a Hess’ Law experiment

[Aakash1-1] Mannam Krishnamurthy; Subba Rao Naidu (2012). "7". In Lokeswara Gupta (ed.). Chemistry for ISEET - Volume 1, Part A (2012 ed.). Hyderabad, India: Varsity Education Management Limited. p. 244.

[2] "Hess' Law - Conservation of Energy". University of Waterloo. Archived from the original on 9 January 2015. Retrieved 12 January 2014.

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