Chemical equilibrium

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Chemical equilibrium

In a chemical process

Chemical process

In a "Process " sense, a chemical process is a method or means of somehow changing one or more chemicals or chemical compounds. Such a chemical process can occur by itself or be caused by somebody....
, chemical equilibrium is the state in which the chemical activities

Activity (chemistry)

In chemical thermodynamics activity is a measure of the ?effective concentration? of a species in a mixture. By convention, it is a dimensionless quantity....
or concentrations of the reactants and products have no net change over time. Usually, this would be the state that results when the forward chemical process

Chemical process

In a "Process " sense, a chemical process is a method or means of somehow changing one or more chemicals or chemical compounds. Such a chemical process can occur by itself or be caused by somebody....
proceeds at the same rate as their reverse reaction

Reversible reaction

A reversible reaction is a chemical reaction that results in an chemical equilibrium mixture of reactants and Product . For a reaction involving two reactants and two products this can be expressed symbolically asA and B can react to form C and D or, in the reverse reaction, C and D can react to form A and B....
. The reaction rate

Reaction rate

The reaction rate or rate of reaction for a reactant or product in a particular chemical reaction is intuitively defined as how fast a reaction takes place....
s of the forward and reverse reactions are generally not zero but, being equal, there are no net changes in any of the reactant or product concentrations.

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Encyclopedia

In a chemical process

Chemical process

Activity (chemistry)

Chemical process

In a "Process " sense, a chemical process is a method or means of somehow changing one or more chemicals or chemical compounds. Such a chemical process can occur by itself or be caused by somebody....
proceeds at the same rate as their reverse reaction

Reversible reaction

Reaction rate

Dynamic equilibrium

Introduction

In a chemical reaction

Chemical reaction

A chemical reaction is a process that always results in the interconversion of chemical substances. The substance or substances initially involved in a chemical reaction are called reactants....
, when reactants are mixed together in a reaction vessel (and heated if needed), the whole of reactants do not get converted into the products. After some time (which may be shorter than millionths of a second or longer than the age of the universe), the opposing reactions will have equal reaction rates, creating a dynamic equilibrium in which the ratio between reactants and products will appear fixed. This is called chemical equilibrium.

The concept of chemical equilibrium was developed after Berthollet (1803) found that some chemical reaction

Chemical reaction

Reversible reaction

Reaction rate

The reaction rate or rate of reaction for a reactant or product in a particular chemical reaction is intuitively defined as how fast a reaction takes place....
of the forward and backward (reverse) reactions have to be equal. In this chemical equation

Chemical equation

A chemical equation may be described as a chemical reaction or a means of writing out and describing such a phenomenon. The coefficients next to the symbols and formulae of entities are the absolute values of the stoichiometric coefficient....
with harpoon arrows pointing both ways to indicate equilibrium, A and B are reactant chemical species, S and T are product species, and a

Alpha (letter)

Alpha is the first letter of the Greek alphabet. In the system of Greek numerals it has a value of 1. It was derived from the Phoenician alphabet Aleph ....
, ß

Beta (letter)

Beta is the second letter of the Greek alphabet. In the system of Greek numerals it has a value of 2. It was derived from the Phoenician alphabet Beth ....
, s

Sigma

Sigma is the eighteenth letter of the Greek alphabet, and carries the /s/ sound. In the system of Greek numerals it has a value of 200. When used at the end of a word, and the word is not all upper case, the final form is used....
, and t

Tau

Tau is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300. This letter in English is pronounced , but in Modern Greek, this letter's name is pronounced ....
are the stoichiometric coefficients of the respective reactants and products. The equilibrium position of a reaction is said to lie far to the right if, at equilibrium, nearly all the reactants are used up and far to the left if hardly any product is formed from the reactants.

Guldberg

Cato Maximilian Guldberg

Cato Maximilian Guldberg was a Norway mathematician and chemist....
and Waage

Peter Waage

Peter Waage was a significant Norway chemist and professor at the University of Oslo. Along with Cato Guldberg, he co-discovered and developed the law of mass action between 1864 and 1879....
(1865), building on Berthollet’s ideas, proposed the law of mass action:

where A, B, S and T are active masses

Activity (chemistry)

In chemical thermodynamics activity is a measure of the ?effective concentration? of a species in a mixture. By convention, it is a dimensionless quantity....
and k₊ and k_- are rate constants. Since forward and backward rates are equal:

and the ratio of the rate constants is also a constant, now known as an equilibrium constant

Equilibrium constant

For a general chemical equilibriumthe equilibrium constant can be defined bywhere is the activity of the chemical species A etc . It is conventional to put the activities of the products in the numerator and those of the reactants in the denominator....
.

By convention the products form the numerator

Numerator

Numerator may refer to:* A numeral used to indicate a count, particularly of the equal parts in a fraction . A numerator is the number on top of the fraction....
. However, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state

Transition state

The transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest energy along this reaction coordinate....
and is not valid in general because rate equations

Reaction rate

The reaction rate or rate of reaction for a reactant or product in a particular chemical reaction is intuitively defined as how fast a reaction takes place....
do not, in general, follow the stoichiometry

Stoichiometry

Stoichiometry is the calculation of quantitative relationships of the reactants and Product in a balanced chemical reaction .Etymology...
of the reaction as Guldberg and Waage had proposed (see, for example, nucleophilic aliphatic substitution by S_N1 or reaction of hydrogen

Hydrogen

Hydrogen is the chemical element with atomic number 1. It is represented by the chemical symbol H. At standard temperature and pressure, hydrogen is a colorless, odorless, nonmetallic, tasteless, highly combustion and explosive Diatomic molecule gas with the molecular formula H2....
and bromine

Bromine

Bromine , , meaning "stench " ), is a chemical element with the symbol Br and atomic number 35. A halogen element, bromine is a reddish-brown Volatility liquid at Standard conditions for temperature and pressure that is intermediate in reactivity between chlorine and iodine....
to form hydrogen bromide

Hydrogen bromide

Hydrogen bromide is the diatomic molecule HydrogenBromine. Under standard conditions, HBr is a gas, but it can be liquified. The aqueous solution hydrobromic acid forms upon dissolving HBr in water....
). Equality of forward and backward reaction rates, however, is a necessary condition

Necessary and sufficient conditions

In logic, the words necessity and sufficiency refer to the implicational relationships between Statement . The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true....
to explain why equilibrium occurs.

Despite the failure of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van 't Hoff equation. Adding a catalyst will affect both the forward reaction and the reverse reaction in the same way and will not have an effect on the equilibrium constant. The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached.

Although the macroscopic equilibrium concentrations are constant in time reactions do occur at the molecular level. For example, in the case of ethanoic acid dissolved in water and forming ethanoate and hydronium

Hydronium

In chemistry, hydronium is the common name for the aqueous cation hydrogen3oxygen+ derived from protonation of water. It is the simplest type of an oxonium ion....
ions,

CH₃CO₂H + H₂O CH₃CO₂^- + H₃O⁺

a proton may hop from one molecule of ethanoic acid on to a water molecule and then on to an ethanoate ion to form another molecule of ethanoic acid and leaving the number of ethanoic acid molecules unchanged. This is an example of dynamic equilibrium

Dynamic equilibrium

A system in dynamic equilibrium is a particular example of a system in a steady state. In a steady state the rate of inputs is equal to the rate of outputs so that the composition of the system is unchanging in time....
. Equilibria, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior.

Le Chatelier's principle
Le Châtelier's principle

In chemistry, Le Chatelier's Principle, also called the Le Chatelier-Braun principle, can be used to predict the effect of a change in conditions on a chemical equilibrium....
(1884) is a useful principle that gives a qualitative idea of an equilibrium system's response to changes in reaction conditions. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward (though the equilibrium constant will stay the same).

If mineral acid

Mineral acid

A mineral acid is an acid derived from one or more inorganic chemistry compounds. A mineral acid does not contain any carbon atoms and all mineral acids release hydrogen ions when dissolved in water....
is added to the ethanoic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. This can also be deduced from the equilibrium constant expression for the reaction: if increases must increase and must decrease.

A quantitative version is given by the reaction quotient

Reaction quotient

In chemistry, reaction quotient is a quantitative measure of the extent of reaction, the relative proportion of products and reactants present in the reaction mixture at some instant of time....
.

J.W. Gibbs suggested in 1873 that equilibrium is attained when the Gibbs energy

Chemical potential

In thermodynamics, physics and chemistry, chemical potential, symbolized by ?, is a term introduced by the American engineer, chemist and mathematical physicist Willard Gibbs, which he defined as follows:...
of the system is at its minimum value (assuming the reaction is carried out under constant pressure). What this means is that the derivative of the Gibbs energy with respect to reaction coordinate

Reaction coordinate

In chemistry, a reaction coordinate is an abstract one-dimensional coordinate which represents progress along a reaction pathway. It is usually a geometric parameter that changes during the conversion of one or more molecular entity....
(a measure of the extent of reaction that has occurred, ranging from zero for all reactants to a maximum for all products) vanishes, signalling a stationary point

Stationary point

In mathematics, particularly in calculus, a stationary point is an input to a function where the derivative is zero : where the function "stops" increasing or decreasing ....
. This derivative is usually called, for certain technical reasons, the Gibbs energy change. This criterion is both necessary and sufficient. If a mixture is not at equilibrium, the liberation of the excess Gibbs energy (or Helmholtz energy at constant volume reactions) is the “driving force” for the composition of the mixture to change until equilibrium is reached. The equilibrium constant can be related to the standard Gibbs energy change for the reaction by the equation

where R is the universal gas constant and T the temperature

Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
.

When the reactants are dissolved

Solution

In chemistry, a solution is a homogeneous mixture composed of two or more substances. In such a mixture, a solute is dissolved in another substance, known as a solvent....
in a medium of high ionic strength

Ionic strength

The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions....
the quotient of activity coefficient

Activity coefficient

An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture the interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed directly in terms...
s may be taken to be constant. In that case the concentration quotient, K_c, where [A] is the concentration

Concentration

In chemistry, concentration is the measure of how much of a given chemical substance there is mixed with another substance. This can apply to any sort of chemical mixture, but most frequently the concept is limited to homogeneous solutions, where it refers to the amount of solute in the solvent....
of A, etc., is independent of the analytical concentration of the reactants. For this reason, equilibrium constants for solution

Solution

In chemistry, a solution is a homogeneous mixture composed of two or more substances. In such a mixture, a solute is dissolved in another substance, known as a solvent....
s are usually determined

Determination of equilibrium constants

Equilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant is expressed as a concentration quotient,...
in media of high ionic strength. K_c varies with ionic strength, temperature and pressure (or volume). Likewise K_p for gases depends on partial pressure

Partial pressure

In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
. These constants are easier to measure and encountered in high-school chemistry courses.

Thermodynamics

The relationship between the Gibbs energy and the equilibrium constant can be found by considering chemical potentials. At constant temperature and pressure the fonction G 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 an isothermal, Isobaric process thermodynamic system....
for the reaction, depends only with the extent of reaction: ? and can only decrease according to the second law of thermodynamics

Second law of thermodynamics

The second law of thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in Thermodynamic equilibrium will tend to increase over time, approaching a maximum value at equilibrium....
. It means that the derivative of G with ? must be negative if the reaction happens; at the equilibrium the derivative being equal to zero.

equilibrium

At constant volume, one must consider the Helmholtz free energy

Helmholtz free energy

In thermodynamics, the Helmholtz free energy is a thermodynamic potential which measures the ?useful? work obtainable from a closed system thermodynamic thermodynamic system at a constant temperature and volume....
for the reaction: A.

In this article only the constant pressure case is considered. The constant volume case is important in geochemistry

Geochemistry

The field of geochemistry involves study of the chemistry composition of the Earth and other planets, chemical processes and reactions that govern the composition of Rock s and soils, and the cycles of matter and energy that transport the Earth's chemical components in time and space, and their interaction with the hydrosphere and the atmosph...
and atmospheric chemistry

Atmospheric chemistry

Atmospheric chemistry is a branch of atmospheric science in which the chemistry of the Earth's atmosphere and that of other planets is studied....
where pressure variations are significant. Note that, if reactants and products were in standard state (completely pure), then there would be no reversibility and no equilibrium. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing

Entropy of mixing

The entropy of mixing is the change in the configuration entropy, an extensive quantity thermodynamics quantity, when two different chemical substances or components are mixed....
) to states containing equal mixture of products and reactants. The combination of the standard Gibbs energy change and the Gibbs energy of mixing determines the equilibrium state.

In general an equilibrium system is defined by writing an equilibrium equation for the reaction

In order to meet the thermodynamic condition for equilibrium, the Gibbs energy must be stationary, meaning that the derivative of G with respect to the extent of reaction : ?, must be zero. It can be shown that in this case, the sum of chemical potential

Chemical potential

In thermodynamics, physics and chemistry, chemical potential, symbolized by ?, is a term introduced by the American engineer, chemist and mathematical physicist Willard Gibbs, which he defined as follows:...
s of the products is equal to the sum of those corresponding to the reactants. Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products.

where µ

Mu (letter)

Mu is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water which had been simplified by the Phoenicians and named after their word for water, to become Mem ....
is in this case a partial molar Gibbs energy, a chemical potential

Chemical potential

Activity (chemistry)

In chemical thermodynamics activity is a measure of the ?effective concentration? of a species in a mixture. By convention, it is a dimensionless quantity....
, of that reagent.

, ( is the standard chemical potential ).

Substituting expressions like this into the Gibbs energy equation:

in the case of a closed system
Closed system

A closed system is a system in the state of being isolated from its surrounding. It is often used to refer to a theoretical system where perfect closure is an assumption, however in practice no system can be completely closed; there are only varying degrees of closure....
. or
( corresponds to the stoechiometric coefficient and is the differential
Differential

Differential may refer to:...
of the extent of reaction ).

at constant pressure and temperature is obtained:

which corresponds to the Gibbs free energy change for the reaction .

results in:

By substituting the chemical potentials:

the relationship becomes:

which is the standard Gibbs energy change for the reaction. It is a constant at a given temperature, which can be calculated, using thermodynamical tables.

.

Therefore

At equilibrium

; the reaction quotient becomes equal to the equilibrium constant
Equilibrium constant

For a general chemical equilibriumthe equilibrium constant can be defined bywhere is the activity of the chemical species A etc . It is conventional to put the activities of the products in the numerator and those of the reactants in the denominator....
.

leading to:

and

Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant

Equilibrium change with addition of reactant or product

For a reactionnal system at equilibrium: ; .

If are modified activities of constituants, the value of the reaction quotient changes and becomes different from the equilibrium constant:

and

then

If activity of a reagent increases

, the reaction quotient decreases.

then

and : The reaction will shift to the right (i.e. in the forward direction, and thus more products will form).

If activity of a product increases

then

and : The reaction will shift to the left (i.e. in the reverse direction, and thus less products will form).

Note that activities and equilibrium constants are dimensionless numbers.

Treatment of activity

The expression for the equilibrium constant can be rewritten as the product of a concentration quotient, K_c and an activity coefficient

Activity coefficient

An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture the interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed directly in terms...
quotient, G.

[A] is the concentration of reagent A, etc. It is possible in principle to obtain values of the activity coefficients, ?. For solutions, equations such as the Debye-Hückel equation

Debye-Hückel equation

The Debye-H?ckel limiting law, named for its developers Peter Debye and Erich H?ckel, provides one way to obtain activity coefficients. activity , rather than concentrations, are needed in many chemical calculations because solutions that contain ionic solutes do not behave ideally even at very low concentrations....
or extensions such as Davies equation or Pitzer equations may be used.^{Software (below)}. However this is not always possible. It is common practice to assume that G is a constant, and to use the concentration quotient in place of the thermodynamic equilibrium constant. It is also general practice to use the term equilibrium constant instead of the more accurate concentration quotient. This practice will be followed here.

For reactions in the gas phase partial pressure

Partial pressure

In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
is used in place of concentration and fugacity coefficient in place of activity coefficient. In the real world, for example, when making ammonia

Haber process

The Haber process, also called the Haber?Bosch process, is the nitrogen fixation reaction of nitrogen and hydrogen, over an enriched iron Catalysis, to produce ammonia....
in industry, fugacity coefficients must be taken into account. Fugacity, f, is the product of partial pressure and fugacity coefficient. The chemical potential of a species in the gas phase is given by so the general expression defining an equilibrium constant is valid for both solution and gas phases.

Justification for the use of concentration quotients

In aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as sodium nitrate

Sodium nitrate

Sodium nitrate is the chemical compound with the chemical formula NaNO3. This salts, also known as "Chile saltpeter" or "Peru saltpeter" , is a white solid which is very soluble in water....
NaNO₃ or Potassium perchlorate

Potassium perchlorate

Potassium perchlorate is the inorganic salt with the chemical formula potassiumchlorineoxygen. Like other a perchlorates, this salt is a strong oxidizing agent....
KClO₄. The ionic strength

Ionic strength

The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions....
, I, of a solution containing a dissolved salt, X⁺Y^-, is given by where c stands for concentration, z stands for ionic charge and the sum is taken over all the species in equilibrium. When the concentration of dissolved salt is much higher than the analytical concentrations of the reagents, the ionic strength is effectively constant. Since activity coefficients depend on ionic strength the activity coefficients of the species are effectively independent of concentration. Thus, the assumption that G

Gamma

Gamma is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. It was derived from the Phoenician alphabet Gimel ....
is constant is justified. The concentration quotient is a simple multiple of the equilibrium constant. However, K_c will vary with ionic strength. If it is measured at a series of different ionic strengths the value can be extrapolated to zero ionic strength. The concentration quotient obtained in this manner is known, paradoxically, as a thermodynamic equilibrium constant.

To use a published value of an equilibrium constant in conditions of ionic strength different from the conditions used in its determination, the value should be adjusted^{Software (below)}.

Metastable mixtures

A mixture may be appear to have no tendency to change, though it is not at equilibrium. For example, a mixture of SO₂

Sulfur dioxide

Sulfur dioxide is the chemical compound with the formula SO2. It is produced by volcanoes and in various industrial processes. Since coal and petroleum often contain sulfur compounds, their combustion generates sulfur dioxide....
and O₂

Oxygen

Oxygen no O2 produced; 2) O2 produced, but absorbed in oceans & seabed rock; 3) O2 starts to gas out of the oceans, but is absorbed by land surfaces and formation of ozone layer; 4-5) O2 sinks filled and the gas accumulates]]...
is metastable as there is a kinetic barrier

Activation energy

In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined as the energy that must be overcome in order for a chemical reaction to occur....
to formation of the product, SO₃

Sulfur trioxide

Sulfur trioxide is the chemical compound with the formula SO3. In the gaseous form, this species is a significant pollutant, being the primary agent in acid rain....
.

2SO₂ + O₂ 2SO₃

The barrier can be overcome when a catalyst

Catalysis

Catalysis is the process in which the reaction rate of a chemical reaction is either increased or decreased by means of a chemical substance known as a catalyst....
is also present in the mixture as in the contact process

Contact process

The contact process is the current method of producing sulfuric acid in the high concentrations needed for industrial processes. Vanadium oxide is the catalyst employed....
, but the catalyst does not affect the equilibrium concentrations.

Likewise, the formation of bicarbonate

Bicarbonate

In inorganic chemistry, bicarbonate is an intermediate form in the deprotonation of carbonic acid. Its chemical formula is HCO3−....
from carbon dioxide

Carbon dioxide

Carbon dioxide is a chemical compound composed of two oxygen atoms covalent bond to a single carbon atom. It is a gas at standard temperature and pressure and exists in Earth's atmosphere in this state....
and water

Water

Water is a common chemical substance that is essential for the survival of all known forms of life. In typical usage, water refers only to its liquid form or States of matter, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam....
is very slow under normal conditions

CO₂ + 2H₂O HCO₃^- +H₃O⁺

but almost instantaneous in the presence of the catalytic enzyme

Enzyme

Enzymes are biomolecules that catalysis chemical reactions. Almost all enzymes are proteins. In enzymatic reactions, the molecules at the beginning of the process are called Substrate , and the enzyme converts them into different molecules, the products....
carbonic anhydrase

Carbonic anhydrase

The carbonic anhydrases form a family of enzymes that catalyst the rapid conversion of carbon dioxide to bicarbonate and Hydronium ions, a reaction that occurs rather slowly in the absence of a catalyst....
.

Pure compounds in equilibria

When pure substances (liquids or solids) are involved in equilibria they do not appear in the equilibrium equation

Applying the general formula for an equilibrium constant to the specific case of ethanoic acid one obtains

It may be assumed that the concentration of water is constant. This assumption will be valid for all but very concentrated solutions. The equilibrium constant expression is therefore usually written as

where now

a constant factor is incorporated into the equilibrium constant.

A particular case is the self-ionization of water

Self-ionization of water

The self-ionization of water is the chemical reaction in which two water molecules react to produce a hydronium ion and a hydroxide ion :It is an example of autoprotolysis, and relies on the amphoteric nature of water....
itself

The self-ionization constant of water is defined as

It is perfectly legitimate to write [H⁺] for the hydronium ion concentration, since the state of solvation

Solvation

Solvation, commonly called dissolution, is the process of attraction and association of molecules of a solvent with molecules or ions of a solute....
of the proton is constant (in dilute solutions) and so does not affect the equilibrium concentrations. K_w varies with variation in ionic strength and/or temperature.

The concentrations of H⁺ and OH^- are not independent quantities. Most commonly [OH^-] is replaced by K_w[H⁺]^-1 in equilibrium constant expressions which would otherwise hydroxide

Hydroxide

In chemistry, hydroxide is the name for the Diatomic molecule anion OH-, consisting of oxygen and hydrogen atoms, usually derived from the Dissociation of a base ....
.

Solids also do not appear in the equilibrium equation. An example is the Boudouard reaction

Boudouard reaction

The Boudouard reaction is the redox reaction of a chemical equilibrium mixture of carbon monoxide and carbon dioxide at a given temperature. It is the disproportionation of carbon monoxide into carbon dioxide and graphite or its reverse...
:

for which the equation (without solid carbon) is written as:

Multiple equilibria

Consider the case of a dibasic acid H₂A. When dissolved in water, the mixture will contain H₂A, HA^- and A^2-. This equilibrium can be split into two steps in each of which one proton is liberated. K₁ and K₂ are examples of stepwise equilibrium constants. The overall equilibrium constant,, is product of the stepwise constants. Note that these constants are dissociation constants

Acid dissociation constant

An acid dissociation constant, Ka, is a quantitative measure of the strong acid in solution. It is the equilibrium constant for a chemical reaction known as Dissociation in the context of acid-base reactions....
because the products on the right hand side of the equilibrium expression are dissociation products. In many systems, it is preferable to use association constants. ß₁ and ß₂ are examples of association constants. Clearly ß₁ = 1/K₂ and ß₂ = 1/ß_D; lg ß₁ = pK₂ and lg ß₂ = pK₂ + pK₁

Effect of temperature change on an equilibrium constant

The effect of changing temperature on an equilibrium constant is given by the van 't Hoff equation Thus, for exothermic

Exothermic

File:Explosion1.JPG In thermodynamics, the term exothermic describes a process or reaction that releases energy usually in the form of heat, but also in form of light , electricity , or sound....
reactions, (?H is negative) K decreases with an increase in temperature, but, for endothermic

Endothermic

In thermodynamics, the word endothermic "within-heating" describes a process or reaction that absorbs energy in the form of heat. Its etymology stems from the Greek prefix endo-, meaning ?inside? and the Greek suffix ?thermic, meaning ?to heat?....
reactions, (?H is positive) K increases with an increase temperature. An alternative formulation is At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of K with temperature. In practice, however, the method is unreliable because error propagation almost always gives very large errors on the values calculated in this way.

Types of equilibrium and some applications

In the gas phase. Rocket engine
Rocket engine

A rocket engine or simply rocket is a jet engineRocket Propulsion Elements; 7th edition- chapter 1 that uses only propellant mass for forming its high speed propulsive Jet ....
s
The industrial synthesis such as ammonia
Ammonia

Ammonia is a chemical compound with the chemical formula nitrogenhydrogen. It is normally encountered as a gas with a characteristic pungent odor....
in the Haber-Bosch process (depicted right) takes place through a succession of equilibrium steps including adsorbtion processes.# atmospheric chemistry
Atmospheric chemistry

Atmospheric chemistry is a branch of atmospheric science in which the chemistry of the Earth's atmosphere and that of other planets is studied....
Seawater and other natural waters: Chemical oceanography
Chemical oceanography

Chemical oceanography is the study of the behavior of the chemical elements within the Earth's oceans. The ocean is unique in that it contains - in greater or lesser quantities - nearly every chemical element in the periodic table....
Distribution between two phases

LogD-Distribution coefficient: Important for pharmaceuticals where lipophilicity is a significant property of a drug
Liquid-liquid extraction
Liquid-liquid extraction

Liquid-liquid extraction, also known as solvent extraction and partitioning, is a method to separate compounds based on their relative solubility in two different miscible liquids, usually Water and an solvent....
, Ion exchange
Ion exchange

Ion exchange is an exchange of ions between two electrolytes or between an electrolyte solution and a complex . In most cases the term is used to denote the processes of purification, separation, and decontamination of aqueous and other ion-containing solutions with solid polymeric or mineralic 'ion exchangers'....
, Chromatography
Chromatography

Chromatography is the collective term for a family of laboratory techniques for the separation of mixtures. It involves passing a mixture dissolved in a "mobile phase" through a stationary phase, which separates the analyte to be measured from other molecules in the mixture and allows it to be isolated....
Solubility product
Solubility equilibrium

Solubility equilibrium is any type chemical equilibrium between solid and dissolved states of a compound at saturation .Solubility equilibria involve application of chemical principles and constants to predict solubility of substances under specific conditions ....
Uptake and release of oxygen by haemoglobin in blood

Acid/base equilibria: Acid dissociation constant
Acid dissociation constant

An acid dissociation constant, Ka, is a quantitative measure of the strong acid in solution. It is the equilibrium constant for a chemical reaction known as Dissociation in the context of acid-base reactions....
, hydrolysis
Hydrolysis

Hydrolysis is a chemical reaction during which one or more water are split into hydrogen and hydroxide ions which may go on to participate in further reactions....
, buffer solution
Buffer solution

A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. It has the property that the pH of the solution changes very little when a small amount of acid or base is added to it....
s, indicators
PH indicator

A pH indicator is a halochromism chemical chemical compound that is added in small amounts to a solution so that the pH of the solution can be determined easily....
, acid-base homeostasis
Acid-base homeostasis

Acid-base homeostasis is the part of human homeostasis concerning the proper balance between acids and Chemical base, in other words the pH. The body is very sensitive to its pH level....
Metal-ligand complexation: sequestering agents
Chelation

Chelation is the binding or complex of a bi- or multidentate ligand. These ligands, which are often organic compounds, are called chelants, chelators, chelating agents, or sequestration....
, chelation therapy
Chelation therapy

Chelation therapy is the administration of chelations to remove heavy metals from the body. For the most common forms of heavy metal intoxication?those involving lead, arsenic or Mercury ?the standard of care in the USA dictates the use of dimercaptosuccinic acid ....
, MRI contrast reagents
Magnetic resonance imaging

GaneshMagnetic resonance imaging , or nuclear magnetic resonance imaging , is primarily a medical imaging technique most commonly used in radiology to visualize the structure and function of the body....
, Schlenk equilibrium
Schlenk equilibrium

The Schlenk equilibrium is a chemical equilibrium named after its discoverer Wilhelm Schlenk taking place in solutions of Grignard reagents.The process described is an equilibrium between two equivalents of an alkyl or aryl magnesium halide on the left of the equation and on the right side, one equivalent of the dialkyl or diaryl magnesium...
Adduct formation: Host-guest chemistry
Host-guest chemistry

In supramolecular chemistry, host-guest chemistry describes complex that are composed of two or more molecules or ions held together in unique structural relationships by hydrogen bonding or by ion pairing or by Van der Waals force other than those of full covalent bonds....
, supramolecular chemistry
Supramolecular chemistry

Supramolecular chemistry refers to the area of chemistry beyond the molecules focuses on the chemical systems made up of a discrete number of assembled molecular subunits or components....
, molecular recognition
Molecular recognition

The term molecular recognition refers to the specific interaction between two or more molecules through noncovalent bonding such as including hydrogen bonding, metal coordination, hydrophobic effect, van der Waals forces, pi-pi interactions, electrostatic and/or electromagnetic effects....
, dinitrogen tetroxide
Dinitrogen tetroxide

Dinitrogen tetroxide is the chemical compound N2O4. It forms an Chemical equilibrium with nitrogen dioxide; some call this mixture dinitrogen tetroxide, some call it nitrogen dioxide....
In certain oscillating reactions, the approach to equilibrium is not asymptotically but in the form of a damped oscillation .
The related Nernst equation
Nernst equation

In electrochemistry, the Nernst equation is an equation which can be used to determine the equilibrium reduction potential of a half-cell in an electrochemical cell....
in electrochemistry gives the difference in electrode potential as a function of redox concentrations.
When molecules on each side of the equilibrium are able to further react irreversibly in secondary reactions, the final product ratio is determined according to the Curtin-Hammett principle
Curtin-Hammett principle

The Curtin?Hammett principle is a principle in chemical kinetics that was proposed by David Yarrow Curtin and Louis Plack Hammett. It states that, for a reaction that has a pair of reactive intermediates or reactants that interconvert rapidly , each going irreversibly to a different product, the Product ratio will depend only on the differe...
.

In these applications, terms such as stability constant, formation constant, binding constant, affinity constant, association/dissociation constant are used. In biochemistry, it is common to give units for binding constants, which serve to define the concentration units used when the constant’s value was determined.

Composition of an equilibrium mixture

When the only equilibrium is that of the formation of a 1:1 adduct as the composition of a mixture, there are any number of ways that the composition of a mixture can be calculated. For example, see ICE table

ICE table

An ICE table or ICE chart is a tabular system of keeping track of changing concentrations in an equilibrium reaction. ICE stands for "Initial, Change, Equilibrium"....
for a traditional method of calculating the pH of a solution of a weak acid.

There are three approaches to the general calculation of the composition of a mixture at equilibrium.

The most basic approach is to manipulate the various equilibrium constants until the desired concentrations are expressed in terms of measured equilibrium constants (equivalent to measuring chemical potentials) and initial conditions.
Minimize the Gibbs energy of the system.
Satisfy the equation of mass balance
Mass balance

A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique....
. The equations of mass balance are simply statements that demonstrate that the total concentration of each reactant must be constant by the law of conservation of mass
Conservation of mass

The law of conservation of mass/matter, also known as law of mass/matter conservation says that the mass of a closed system will remain constant, regardless of the processes acting inside the system....
.

Solving the equations of mass-balance

In general, the calculations are rather complicated. For instance, in the case of a dibasic acid, H₂A dissolved in water the two reactants can be specified as the conjugate base, A^2-, and the proton

Hydronium

In chemistry, hydronium is the common name for the aqueous cation hydrogen3oxygen+ derived from protonation of water. It is the simplest type of an oxonium ion....
, H⁺. The following equations of mass-balance could apply equally well to a base such as 1,2-diaminoethane, in which case the base itself is designated as the reactant A:

With T_A the total concentration of species A. Note that it is customary to omit the ionic charges when writing and using these equations.

When the equilibrium constants are known and the total concentrations are specified there are two equations in two unknown "free concentrations" [A] and [H]. This follows from the fact that [HA]= ß₁[A][H], [H₂A]= ß₂[A][H]² and [OH] = K_w[H]^-1

so the concentrations of the "complexes" are calculated from the free concentrations and the equilibrium constants. General expressions applicable to all systems with two reagents, A and B would be It is easy to see how this can be extended to three or more reagents.

Composition for polybasic acids as a function of pH

The composition of solutions containing reactants A and H is easy to calculate as a function of p[H

pH is a measure of the Acid or Base of a solution. It is defined as the cologarithm of the Activity of dissolved hydrogen ions . Hydrogen ion activity coefficients cannot be measured experimentally, so they are based on theoretical calculations....
]. When [H] is known, the free concentration [A] is calculated from the mass-balance equation in A. Here is an example of the results that can be obtained.

This diagram, for the hydrolysis of the aluminium

Aluminium

Aluminium or aluminum is a silvery white and ductile member of the boron group of chemical elements. It has the symbol Al; its atomic number is 13....
Lewis acid

Lewis acid

A Lewis acid is a chemical compound, A, that can accept a pair of electrons from a Lewis base, B, that acts as an electron-pair donor, forming an adduct, AB.Gilbert N....
Al³⁺_aq shows the species concentrations for a 5×10^-6M solution of an aluminium salt as a function of pH. Each concentration is shown as a percentage of the total aluminium.

Solution equilibria with precipitation

The diagram above illustrates the point that a precipitate

Precipitation (chemistry)

Precipitation is the formation of a solid in a solution during a chemical reaction. When the reaction occurs, the solid formed is called the precipitate, and the liquid remaining above the solid is called the supernate....
that is not one of the main species in the solution equilibrium may be formed. At pH just below 5.5 the main species present in a 5µM solution of Al³⁺ are aluminium hydroxide

Aluminium hydroxide

Aluminium hydroxide, Al3, is the most stable form of aluminium in normal conditions. It is found in nature as the mineral gibbsite and its three, much more rare, polymorphs: bayerite, doyleite and nordstrandite....
s Al(OH)²⁺, Al(OH)₂⁺ and Al₁₃(OH)₃₂⁷⁺, but on raising the pH Al(OH)₃

Aluminium hydroxide

Aluminium hydroxide, Al3, is the most stable form of aluminium in normal conditions. It is found in nature as the mineral gibbsite and its three, much more rare, polymorphs: bayerite, doyleite and nordstrandite....
precipitates from the solution. This occurs because Al(OH)₃ has a very large lattice energy

Lattice energy

The lattice energy of an Ionic bond solid is a measure of the strength of bonds in that ionic compound. It is usually defined as the enthalpy of formation of the ionic compound from gaseous ions and as such is invariably exothermic....
. As the pH rises more and more Al(OH)₃ comes out of solution. This is an example of Le Chatelier's principle

Le Châtelier's principle

In chemistry, Le Chatelier's Principle, also called the Le Chatelier-Braun principle, can be used to predict the effect of a change in conditions on a chemical equilibrium....
in action: Increasing the concentration of the hydroxide ion causes more aluminium hydroxide to precipitate, which removes hydroxide from the solution. When the hydroxide concentration becomes sufficiently high the soluble aluminate, Al(OH)₄^-, is formed.

Another common instance where precipitation occurs is when a metal cation interacts with an anionic ligand to form an electrically-neutral complex. If the complex is hydrophopbic, it will precipitate out of water. This occurs with the nickel

Nickel

Nickel is a chemical element, with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge....
ion Ni²⁺ and dimethylglyoxime

Dimethylglyoxime

Dimethylglyoxime is a chemical compound described by the formula CH3CCCH3. This colourless solid is the dioxime derivative of the diketone diacetyl ....
, (dmgH₂): in this case the lattice energy of the solid is not particularly large, but it greatly exceeds the energy of solvation

Solvation

Solvation, commonly called dissolution, is the process of attraction and association of molecules of a solvent with molecules or ions of a solute....
of the molecule Ni(dmgH)₂.

Minimization of Gibbs energy

At equilibrium, G is at a minimum:

For a closed system, no particles may enter or leave, although they may combine in various ways. The total number of atoms of each element will remain constant. This means that the minimization above must be subjected to the constraints:

where is the number of atoms of element i in molecule j and b_i⁰ is the total number of atoms of element i, which is a constant, since the system is closed. If there are a total of k types of atoms in the system, then there will be k such equations.

This is a standard problem in optimisation

Optimization (mathematics)

In mathematics, the simplest case of optimization, or mathematical programming, refers to the study of problems in which one seeks to maxima and minima or maxima and minima a Function of a real variable by systematically choosing the values of Real number or integer variables from within an allowed set....
, known as constrained minimisation. The most common method of solving it is using the method of Lagrange multipliers

Lagrange multipliers

In mathematical optimization , the method of Lagrange multipliers provides a strategy for finding the maximum/minimum of a function subject to constraint ....
, also known as undetermined multipliers (though other methods may be used).

Define:

where the are the Lagrange multipliers, one for each element. This allows each of the to be treated independently, and it can be shown using the tools of multivariate calculus that the equilibrium condition is given by

and

(For proof see Lagrange multipliers

Lagrange multipliers

In mathematical optimization , the method of Lagrange multipliers provides a strategy for finding the maximum/minimum of a function subject to constraint ....
)

This is a set of (m+k) equations in (m+k) unknowns (the and the ) and may, therefore, be solved for the equilibrium concentrations as long as the chemical potentials are known as functions of the concentrations at the given temperature and pressure. (See Thermodynamic databases for pure substances

Thermodynamic databases for pure substances

Thermodynamics databases contain information about List of thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy....
).

This method of calculating equilibrium chemical concentrations is useful for systems with a large number of different molecules. The use of k atomic element conservation equations for the mass constraint is straightforward, and replaces the use of the stoichiometric coefficient equations.

External links

Computer programs for calculating species concentrations

There are n mass-balance equations in n unknown free concentrations. This constitutes a set of non-linear equations that must be solved by a method of successive approximations. The most commonly-used method is the Newton-Raphson method, which has been the subject of numerous publications. Some general computer programs are listed here.

Titration simulation and speciation calculations.
A powerful computer program originally developed for gas-phase equilibria but subsequently extended to general applications. Uses the Gibbs energy minimization approach.
A comprehensive computer program for the calculation of thermodynamic equilibrium concentrations of species in homogeneous and heterogeneous systems. Many geochemical applications.
A Windows version of the SOLGASWATER computer program.
A Windows version of MINTEQA2 (ver 4.0). is a chemical equilibrium model for the calculation of metal speciation, solubility equilibria etc. for natural waters.
A chemical equilibrium modeling system for aqueous systems. Handles a wide range of pH, redox, solubility and sorption scenarios.

Software for chemical equilibria

A set of six computer programs for
Specific Interaction Theory. An editable database of published SIT parameters. Estimation of SIT parameters and adjustment of stability constants for changes in ionic strength.
Calculation of electrolyte activity coefficients, ionic activity coefficients, osmotic coefficients
Calculation of acid-base equilibria in electrolyte solutions and sea water
Calculation of O₂ solubility in water, electrolyte solutions, natural fluids, and seawater as a function of temperature, concentration, salinity, altitude, external pressure, humidity
Prediction of temperature dependence of lg K values using various thermodynamic models
:A powerful research tool for thermodynamic and kinetic modelling of chemical speciation in complex aqueous environments.

Chemical equilibrium

Introduction

Thermodynamics

Equilibrium change with addition of reactant or product

Treatment of activity

Justification for the use of concentration quotients

Metastable mixtures

Pure compounds in equilibria

Multiple equilibria

Effect of temperature change on an equilibrium constant

Types of equilibrium and some applications

Composition of an equilibrium mixture

Solving the equations of mass-balance

Composition for polybasic acids as a function of pH

Solution equilibria with precipitation

Minimization of Gibbs energy

See also

Further reading

External links

Computer programs for calculating species concentrations

Software for chemical equilibria