Hess's law

A representation of Hess's law (H represents enthalpy)

Hess's law is a relationship from physical chemistry named for Germain Hess, a Swiss-born Russian chemist and doctor. The law is based on the principle of conservation of energy and the path independence of energy changes. Hess's law can be used to predict energy changes that are not easily measured.

Explanation

The law states that the energy change for any chemical or physical process is independent of the pathway or number of steps required to complete the process. In other words, an energy change is path independent, only the initial and final states being of importance. This path independence is true for all state functions.

Hess's law allows the enthalpy change (ΔH) for a reaction to be calculated even when it cannot be measured directly. This is accomplished by performing arithmetic operations on chemical equations and known ΔH values. Chemical equations may be multiplied (or divided) by a whole number. When an equation is multiplied by a constant, its ΔH must be multiplied by the same number as well. If an equation is reversed, ΔH for the reaction must also be reversed (i.e. -ΔH).

Addition of chemical equations can lead to a net equation. If enthalpy change is included for each equation and added, the result will be the enthalpy change for the net equation. If the net enthalpy change is negative (ΔH_net < 0), the reaction will be exothermic and is more likely to be spontaneous; positive ΔH values correspond to endothermic reactions. Note that entropy also plays an important role in determining spontaneity, so some reactions with a positive enthalpy change are nevertheless spontaneous.

Hess's Law says that enthalpy changes are additive. Thus the ΔH for a single reaction can be calculated from the difference between the heat of formation of the products minus the heat of formation of the reactants. In mathematical terms:

where the ^o superscript indicates standard state values.

Use

Typical use

Table of data for a Hess's law calculation:

Using this data, ΔH^o_c for the reaction below can be found:

CH₄ (g) + 2 O₂ (g) → CO₂ (g) + 2 H₂O (l)

ΔH^o_c = [-394 + 2(-286)] - [-75 + 2(0)] = -891 kJ

Example

Given:

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

Find the ΔH_f of:

• 2 B (s) + (3/2) O₂ (g) → B₂O₃ (s)

After the multiplication and reversing of the equations (and their enthalpy changes), the result is:

• B₂H₆ (g) + 3 O₂ (g) → B₂O₃ (s) + 3 H₂O (g) (ΔH = -2035 kJ)
• 3 H₂O (g) → 3 H₂O (l) (ΔH = -132 kJ)
• 3 H₂O (l) → 3 H₂ (g) + (3/2) O₂ (g) (ΔH = 858 kJ)
• 2 B (s) + 3 H₂ (g) → B₂H₆ (g) (ΔH = 36 kJ)

Adding these equations and canceling out the common terms on both sides, we get

• 2 B (s) + (3/2) O₂ (g) → B₂O₃ (s) (ΔH = -1273 kJ)

Extension to entropy and free energy

The concepts of Hess's law can be expanded to include changes in entropy and in free energy, which are also state functions. For example the Bordwell thermodynamic cycle is an example of such an extension which takes advantage of easily measured equilibriums 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's law can be helpful in determining entropy values which are not measured directly, and therefore must be calculated through alternative paths.

For free energy:

For entropy, the situation is a little different. Because entropy can not 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 for an "entropy of formation"; one simply uses the actual entropies for products and reactants :

See also

• Thermochemistry
• Thermodynamics

Further reading

• Leicester, Henry M. (1951). "Germain Henri Hess and the Foundations of Thermochemistry". The Journal of Chemical Education 28: 581 – 583. 

References

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

External links

• Hess's Law - The principle of conservation of energy