Hess's law - AbsoluteAstronomy.com

Hess' law is a relationship in physical chemistry

Physical chemistry

Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of physical laws and concepts...

named for Germain Hess

Germain Henri Hess

Germain Henri Hess was a Swiss-born Russian chemist and doctor who formulated Hess's Law, an early principle of thermochemistry.-Early days:...

, a Swiss-born Russia

Russia

Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

n chemist

Chemist

A chemist is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties such as density and acidity. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component atoms...

and physician

Physician

A physician is a health care provider who practices the profession of medicine, which is concerned with promoting, maintaining or restoring human health through the study, diagnosis, and treatment of disease, injury and other physical and mental impairments...

.

The law states that the enthalpy

Enthalpy

Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...

change for a reaction that is carried out in a series of steps is equal to the sum of the enthalpy changes for the individual steps.

The law is an expression of the principle of conservation of energy, also expressed in the first law of thermodynamics

First law of thermodynamics

The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

, and that the enthalpy

Enthalpy

of a chemical process is independent of the path taken from the initial to the final state. 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.

Definition

Hess' law states that the energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

change for any chemical or physical process is independent of the pathway or number of steps required to complete the process provided that the final and initial reaction conditions are the same. 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 function

State function

In thermodynamics, a state function, function of state, state quantity, or state variable is a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state . A state function describes the equilibrium state of a system...

s.

Hess' law allows the enthalpy

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 equation

Chemical equation

A chemical equation is the symbolic representation of a chemical reaction where the reactant entities are given on the left hand side and the product entities on the right hand side. The coefficients next to the symbols and formulae of entities are the absolute values of the stoichiometric numbers...

of reactions using previously determined values for the enthalpies of formation.

Addition of chemical equations may lead to a net 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

Endothermic

In thermodynamics, the word endothermic describes a process or reaction in which the system absorbs energy from the surroundings in the form of heat. Its etymology stems from the prefix endo- and the Greek word thermasi,...

reactions. Entropy

Entropy

Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

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 can be calculated from the difference between the heat of formation of the products

Product (chemistry)

Product are formed during chemical reactions as reagents are consumed. Products have lower energy than the reagents and are produced during the reaction according to the second law of thermodynamics. The released energy comes from changes in chemical bonds between atoms in reagent molecules and...

and the heat of formation of the reactants:

where the ^o superscript indicates standard state values.

Use

Table of data for a Hess' law calculation:

Substance	ΔH^o_f kJ mol⁻¹
CH₄ (g)	-75
O₂ (g)	0
CO₂ (g)	-394
H₂O (l)	-286

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/mol

Example

Given:

B₂O₃ (s) + 3 H₂O (g) → 3 O₂ (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)
2 B (s) + 3 H₂ (g) → B₂H₆ (g) (ΔH = 36 kJ/mol)

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

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/mol)

Extension to entropy and free energy

The concepts of Hess' law can be expanded to include changes in entropy

Entropy

and in Gibbs free energy

Gibbs free energy

In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...

, which are also state functions

State function

. The Bordwell thermodynamic cycle

Bordwell thermodynamic cycle

A Bordwell thermodynamic cycle use experimentally determined and reasonable estimates of Gibbs free energy values to determine unknown and experimentally inaccessible values.- Overview :...

is an example of such an extension which takes advantage of easily measured equilibrium

Chemical equilibrium

In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...

s and redox potentials to determine experimentally inaccessible Gibbs free energy

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:

For entropy

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 for an "entropy of formation"; one simply uses the actual entropies for products and reactants:

External links

Hess' paper (1840) on which his law is based (at ChemTeam site)
Hess' Law - The principle of conservation of energy
a Hess’ Law experiment

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