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In a
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breakin ...
, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The
reaction rate The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit ...
s of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.


Historical introduction

The
concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by sev ...
of chemical equilibrium was developed in 1803, after Berthollet found that some
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breakin ...
s are reversible. For any reaction mixture to exist at equilibrium, the
rates Rate or rates may refer to: Finance * Rates (tax), a type of taxation system in the United Kingdom used to fund local government * Exchange rate, rate at which one currency will be exchanged for another Mathematics and science * Rate (mathema ...
of the forward and backward (reverse) reactions must be equal. In the following
chemical equation A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between ...
, arrows point both ways to indicate equilibrium. A and B are reactant chemical species, S and T are product species, and ''α'', ''β'', ''σ'', and ''τ'' are the
stoichiometric coefficient A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between ...
s of the respective reactants and products: :''α'' A + ''β'' B ''σ'' S + ''τ'' T The equilibrium concentration position of a reaction is said to lie "far to the right" if, at equilibrium, nearly all the reactants are consumed. Conversely the equilibrium position is said to be "far to the left" if hardly any product is formed from the reactants. Guldberg and
Waage Waage is a Norwegian surname. Notable people with the surname include: * Anita Waage (born 1971), Norwegian footballer * Elsa Waage (born 1959), Icelandic opera singer * Geir Waage (born 1967), Norwegian politician * Hilde Waage (born 1959), Norweg ...
(1865), building on Berthollet's ideas, proposed the law of mass action: :\begin \text &= k_ \ce^\alpha\ce^\beta \\ \text &= k_ \ce^\sigma\ce^\tau \end where A, B, S and T are active masses and ''k''+ and ''k'' are
rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction. For a reaction between reactants A and B to form product C the reaction rate is often found to have the f ...
s. Since at equilibrium forward and backward rates are equal: : k_+ \left\^\alpha \left\^\beta = k_ \left\^\sigma\left\^\tau and the ratio of the rate constants is also a constant, now known as an equilibrium constant. :K_c=\frac=\frac By convention, the products form the numerator. However, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state and is not valid in general because rate equations do not, in general, follow the
stoichiometry Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
of the reaction as Guldberg and Waage had proposed (see, for example,
nucleophilic aliphatic substitution In chemistry, a nucleophilic substitution is a class of chemical reactions in which an electron-rich chemical species (known as a nucleophile) replaces a functional group within another electron-deficient molecule (known as the electrophile). The ...
by SN1 or reaction of hydrogen and
bromine Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table (halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a simila ...
to form
hydrogen bromide Hydrogen bromide is the inorganic compound with the formula . It is a hydrogen halide consisting of hydrogen and bromine. A colorless gas, it dissolves in water, forming hydrobromic acid, which is saturated at 68.85% HBr by weight at room tempe ...
). Equality of forward and backward reaction rates, however, is a
necessary condition In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth o ...
for chemical equilibrium, though it is not
sufficient In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of ...
to explain why equilibrium occurs. Despite the limitations 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 Catalysis () is the process of increasing the reaction rate, rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the ...
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 The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena a ...
equilibrium concentrations are constant in time, reactions do occur at the molecular level. For example, in the case of
acetic acid Acetic acid , systematically named ethanoic acid , is an acidic, colourless liquid and organic compound with the chemical formula (also written as , , or ). Vinegar is at least 4% acetic acid by volume, making acetic acid the main component ...
dissolved in water and forming
acetate An acetate is a salt formed by the combination of acetic acid with a base (e.g. alkaline, earthy, metallic, nonmetallic or radical base). "Acetate" also describes the conjugate base or ion (specifically, the negatively charged ion called an ...
and
hydronium In chemistry, hydronium (hydroxonium in traditional British English) is the common name for the aqueous cation , the type of oxonium ion produced by protonation of water. It is often viewed as the positive ion present when an Arrhenius acid is d ...
ions, : a proton may hop from one molecule of acetic acid onto a water molecule and then onto an acetate anion to form another molecule of acetic acid and leaving the number of acetic acid molecules unchanged. This is an example of dynamic equilibrium. Equilibria, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior. Le Châtelier's principle (1884) predicts the behavior of an equilibrium system when changes to its reaction conditions occur. ''If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse 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 A mineral acid (or inorganic acid) is an acid derived from one or more inorganic compounds, as opposed to organic acids which are acidic, organic compounds. All mineral acids form hydrogen ions and the conjugate base when dissolved in water. Cha ...
is added to the acetic 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: :K=\frac \ce If increases must increase and must decrease. The H2O is left out, as it is the solvent and its concentration remains high and nearly constant. A quantitative version is given by the reaction quotient.
J. W. Gibbs Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in t ...
suggested in 1873 that equilibrium is attained when the
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and p ...
of the system is at its minimum value (assuming the reaction is carried out at a constant temperature and pressure). What this means is that the derivative of the Gibbs energy with respect to
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 entities. In molecu ...
(a measure of the
extent of reaction In physical chemistry and chemical engineering, extent of reaction is a quantity that measures the extent to which the reaction has proceeded. Often, it refers specifically to the value of the extent of reaction when equilibrium has been reached. It ...
that has occurred, ranging from
zero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by multiplying digits to the left of 0 by the radix, usuall ...
for all reactants to a maximum for all products) vanishes, signaling a
stationary point In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" in ...
. This derivative is called the reaction Gibbs energy (or energy change) and corresponds to the difference between the
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
s of reactants and products at the composition of the reaction mixture. 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 free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and p ...
change for the reaction by the equation :\Delta_rG^\ominus = -RT \ln K_\mathrm where ''R'' is the
universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment pe ...
and ''T'' the temperature. When the reactants are dissolved in a medium of high
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 total electrolyte concentration in solution will affect important properties such a ...
the quotient of
activity coefficient In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same ...
s may be taken to be constant. In that case the concentration quotient, ''K''c, :K_\ce=\frac where is the concentration of A, etc., is independent of the
analytical concentration Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of so ...
of the reactants. For this reason, equilibrium constants for
solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solutio ...
s are usually
determined Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and simi ...
in media of high ionic strength. ''Kc'' varies with
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 total electrolyte concentration in solution will affect important properties such a ...
, temperature and pressure (or volume). Likewise ''Kp'' for gases depends on partial pressure. These constants are easier to measure and encountered in high-school chemistry courses.


Thermodynamics

At constant temperature and pressure, one must consider the
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and p ...
, ''G'', while at constant temperature and volume, one must consider the Helmholtz free energy, ''A'', for the reaction; and at constant internal energy and volume, one must consider the entropy, ''S'', for the reaction. The constant volume case is important in
geochemistry Geochemistry is the science that uses the tools and principles of chemistry to explain the mechanisms behind major geological systems such as the Earth's crust and its oceans. The realm of geochemistry extends beyond the Earth, encompassing the e ...
and
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. It is a multidisciplinary approach of research and draws on environmental chemistry, physics, meteoro ...
where pressure variations are significant. Note that, if reactants and products were in
standard state In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is use ...
(completely pure), then there would be no reversibility and no equilibrium. Indeed, they would necessarily occupy disjoint volumes of space. The mixing of the products and reactants contributes a large entropy increase (known as
entropy of mixing In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the therm ...
) to states containing equal mixture of products and reactants and gives rise to a distinctive minimum in the Gibbs energy as a function of the extent of reaction.Atkins, P.; de Paula, J.; Friedman, R. (2014). ''Physical Chemistry – Quanta, Matter and Change'', 2nd ed., Fig. 73.2. Freeman. The standard Gibbs energy change, together with the Gibbs energy of mixing, determine the equilibrium state. In this article only the constant pressure case is considered. The relation between the Gibbs free energy and the equilibrium constant can be found by considering
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
s. At constant temperature and pressure in the absence of an applied voltage, the
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and p ...
, ''G'', for the reaction depends only on the
extent of reaction In physical chemistry and chemical engineering, extent of reaction is a quantity that measures the extent to which the reaction has proceeded. Often, it refers specifically to the value of the extent of reaction when equilibrium has been reached. It ...
: ''ξ'' (Greek letter xi), and can only decrease according to the second law of thermodynamics. It means that the derivative of ''G'' with respect to ''ξ'' must be negative if the reaction happens; at the equilibrium this derivative is equal to zero. :\left(\frac \right)_ = 0~:equilibrium 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, ''ξ'', must be zero. It can be shown that in this case, the sum of
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
s times the stoichiometric coefficients of the products is equal to the sum of those corresponding to the reactants. Mortimer, R. G. ''Physical Chemistry'', 3rd ed., p. 305, Academic Press, 2008. Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products. : \alpha \mu_\mathrm + \beta \mu_\mathrm = \sigma \mu_\mathrm + \tau \mu_\mathrm \, where ''μ'' is in this case a partial molar Gibbs energy, a
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
. The chemical potential of a reagent A is a function of the activity, of that reagent. : \mu_\mathrm = \mu_^ + RT \ln\ \, (where ''μ'' is the standard chemical potential). The definition of the
Gibbs energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and p ...
equation interacts with the
fundamental thermodynamic relation In thermodynamics, the fundamental thermodynamic relation are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentiall ...
to produce : dG = Vdp-SdT+\sum_^k \mu_i dN_i . Inserting ''dNi'' = ''νi dξ'' into the above equation gives a
stoichiometric coefficient A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between ...
( \nu_i~) and a differential that denotes the reaction occurring to an infinitesimal extent (''dξ''). At constant pressure and temperature the above equations can be written as :\left(\frac \right)_ = \sum_^k \mu_i \nu_i = \Delta_\mathrmG_ which is the "Gibbs free energy change for the reaction . This results in: : \Delta_\mathrmG_ = \sigma \mu_\mathrm + \tau \mu_\mathrm - \alpha \mu_\mathrm - \beta \mu_\mathrm \,. By substituting the chemical potentials: : \Delta_\mathrmG_ = ( \sigma \mu_\mathrm^ + \tau \mu_\mathrm^ ) - ( \alpha \mu_\mathrm^ + \beta \mu_\mathrm^ ) + ( \sigma RT \ln\ + \tau RT \ln\ ) - ( \alpha RT \ln\ + \beta RT \ln \ ) , the relationship becomes: : \Delta_\mathrmG_=\sum_^k \mu_i^\ominus \nu_i + RT \ln \frac :\sum_^k \mu_i^\ominus \nu_i = \Delta_\mathrmG^: which is the standard Gibbs energy change for the reaction that can be calculated using thermodynamical tables. The reaction quotient is defined as: : Q_\mathrm = \frac Therefore, :\left(\frac \right)_ = \Delta_\mathrmG_= \Delta_\mathrmG^ + RT \ln Q_\mathrm At equilibrium: :\left(\frac \right)_ = \Delta_\mathrmG_ = 0 leading to: : 0 = \Delta_\mathrmG^ + RT \ln K_\mathrm and : \Delta_\mathrmG^ = -RT \ln K_\mathrm Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant.


Addition of reactants or products

For a reactional system at equilibrium: ''Q''r = ''K''eq; ''ξ'' = ''ξ''eq. *If the activities of constituents are modified, the value of the reaction quotient changes and becomes different from the equilibrium constant: ''Q''r ≠ ''K''eq \left(\frac \right)_ = \Delta_\mathrmG^ + RT \ln Q_\mathrm~ and \Delta_\mathrmG^ = - RT \ln K_~ then \left(\frac \right)_ = RT \ln \left(\frac \right)~ *If activity of a reagent ''i'' increases Q_\mathrm = \frac~, the reaction quotient decreases. Then Q_\mathrm < K_\mathrm~ and \left(\frac \right)_ < 0~ The reaction will shift to the right (i.e. in the forward direction, and thus more products will form). *If activity of a product ''j'' increases, then Q_\mathrm > K_\mathrm~ and \left(\frac \right)_ >0~ 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 In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same ...
quotient, ''Γ''. :K=\frac \times \frac = K_\mathrm \Gamma is the concentration of reagent A, etc. It is possible in principle to obtain values of the activity coefficients, γ. For solutions, equations such as the Debye–Hückel equation or extensions such as
Davies equation The Davies equation is an empirical extension of Debye–Hückel theory which can be used to calculate activity coefficients of electrolyte solutions at relatively high concentrations at 25 °C. The equation, originally published in 1938, was ...
Specific ion interaction theory In theoretical chemistry, Specific ion Interaction Theory (SIT theory) is a theory used to estimate single-ion activity coefficients in electrolyte solutions at relatively high concentrations. It does so by taking into consideration ''interaction ...
or
Pitzer equations Pitzer equations are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. They were first described by physical chemist Kenneth Pitzer. The parameters of the Pitzer equations ar ...
may be used. Software (below) However this is not always possible. It is common practice to assume that ''Γ'' 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 is used in place of concentration and
fugacity coefficient In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas wh ...
in place of activity coefficient. In the real world, for example, when making
ammonia Ammonia is an inorganic compound of nitrogen and hydrogen with the formula . A stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous wa ...
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
real gas Real gases are nonideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behaviour of real gases, the following must be taken into account: *compressibility effects ...
phase is given by :\mu = \mu^ + RT \ln \left( \frac \right) = \mu^ + RT \ln \left( \frac \right) + RT \ln \gamma so the general expression defining an equilibrium constant is valid for both solution and gas phases.


Concentration quotients

In aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as
sodium nitrate Sodium nitrate is the chemical compound with the formula . This alkali metal nitrate salt is also known as Chile saltpeter (large deposits of which were historically mined in Chile) to distinguish it from ordinary saltpeter, potassium nitrate. ...
, NaNO3, or
potassium perchlorate Potassium perchlorate is the inorganic salt with the chemical formula K Cl O4. Like other perchlorates, this salt is a strong oxidizer although it usually reacts very slowly with organic substances. This, usually obtained as a colorless, crysta ...
, KClO4. The
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 total electrolyte concentration in solution will affect important properties such a ...
of a solution is given by : I = \frac12\sum_^N c_i z_i^2 where ''ci'' and ''zi'' stand for the concentration and ionic charge of ion type ''i'', and the sum is taken over all the ''N'' types of charged species in solution. When the concentration of dissolved salt is much higher than the analytical concentrations of the reagents, the ions originating from the dissolved salt determine the ionic strength, and 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 ''Γ'' is constant is justified. The concentration quotient is a simple multiple of the equilibrium constant. : K_\mathrm = \frac 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. Before using 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 appear to have no tendency to change, though it is not at equilibrium. For example, a mixture of SO2 and O2 is
metastable In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball i ...
as there is a kinetic barrier to formation of the product, SO3. :2 SO2 + O2 2 SO3 The barrier can be overcome when a
catalyst Catalysis () is the process of increasing the reaction rate, rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the ...
is also present in the mixture as in the
contact process The contact process is the current method of producing sulfuric acid in the high concentrations needed for industrial processes. Platinum was originally used as the catalyst for this reaction; however, as it is susceptible to reacting with arseni ...
, but the catalyst does not affect the equilibrium concentrations. Likewise, the formation of
bicarbonate In inorganic chemistry, bicarbonate (IUPAC-recommended nomenclature: hydrogencarbonate) is an intermediate form in the deprotonation of carbonic acid. It is a polyatomic anion with the chemical formula . Bicarbonate serves a crucial biochemic ...
from carbon dioxide and water is very slow under normal conditions : but almost instantaneous in the presence of the catalytic enzyme
carbonic anhydrase The carbonic anhydrases (or carbonate dehydratases) () form a family of enzymes that catalyze the interconversion between carbon dioxide and water and the dissociated ions of carbonic acid (i.e. bicarbonate and hydrogen ions). The active sit ...
.


Pure substances

When pure substances (liquids or solids) are involved in equilibria their activities do not appear in the equilibrium constant because their numerical values are considered one. Applying the general formula for an equilibrium constant to the specific case of a dilute solution of acetic acid in water one obtains :CH3CO2H + H2O CH3CO2 + H3O+ :K_\mathrm=\frac \mathrm \mathrm For all but very concentrated solutions, the water can be considered a "pure" liquid, and therefore it has an activity of one. The equilibrium constant expression is therefore usually written as :K=\frac \mathrm \mathrm = K_\mathrm. A particular case is the self-ionization of water :2 H2O H3O+ + OH Because water is the solvent, and has an activity of one, the self-ionization constant of water is defined as :K_\mathrm = \mathrm It is perfectly legitimate to write +for the
hydronium ion In chemistry, hydronium (hydroxonium in traditional British English) is the common name for the aqueous cation , the type of oxonium ion produced by protonation of water. It is often viewed as the positive ion present when an Arrhenius acid is d ...
concentration, since the state of solvation 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 His replaced by ''K''w +sup>−1 in equilibrium constant expressions which would otherwise include hydroxide ion. Solids also do not appear in the equilibrium constant expression, if they are considered to be pure and thus their activities taken to be one. An example is the
Boudouard reaction The Boudouard reaction, named after Octave Leopold Boudouard, 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 ...
: :2 CO CO2 + C for which the equation (without solid carbon) is written as: :K_\mathrm=\frac \mathrm \mathrm


Multiple equilibria

Consider the case of a dibasic acid H2A. When dissolved in water, the mixture will contain H2A, HA and A2−. This equilibrium can be split into two steps in each of which one proton is liberated. :\begin \ce : & K_1=\frac \ce \ce \\ \ce : & K_2=\frac \ce \ce \end ''K''1 and'' K''2 are examples of ''stepwise'' equilibrium constants. The ''overall'' equilibrium constant, ''β''D, is product of the stepwise constants. : <=> + :\beta_\ce = \frac \ce \ce=K_1K_2 Note that these constants are dissociation constants 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. :\begin \ce:&\beta_1=\frac \ce \ce \\ \ce:&\beta_2=\frac \ce \ce \end ''β''1 and ''β''2 are examples of association constants. Clearly and ; and For multiple equilibrium systems, also see: theory of Response reactions.


Effect of temperature

The effect of changing temperature on an equilibrium constant is given by the van 't Hoff equation :\frac = \frac Thus, for exothermic reactions (Δ''H'' is negative), ''K'' decreases with an increase in temperature, but, for
endothermic In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. p. ...
reactions, (ΔH is positive) ''K'' increases with an increase temperature. An alternative formulation is :\frac = -\frac 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.


Effect of electric and magnetic fields

The effect of electric field on equilibrium has been studied by
Manfred Eigen Manfred Eigen (; 9 May 1927 – 6 February 2019) was a German biophysical chemist who won the 1967 Nobel Prize in Chemistry for work on measuring fast chemical reactions. Eigen's research helped solve major problems in physical chemistry and ...
among others.


Types of equilibrium

Equilibrium can be broadly classified as heterogeneous and homogeneous equilibrium. Homogeneous equilibrium consists of reactants and products belonging in the same phase whereas heterogeneous equilibrium comes into play for reactants and products in different phases. * In the gas phase: rocket engines * The industrial synthesis such as
ammonia Ammonia is an inorganic compound of nitrogen and hydrogen with the formula . A stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous wa ...
in the
Haber–Bosch process The Haber process, also called the Haber–Bosch process, is an artificial nitrogen fixation process and is the main industrial procedure for the production of ammonia today. It is named after its inventors, the German chemists Fritz Haber and C ...
(depicted right) takes place through a succession of equilibrium steps including
adsorption Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a ...
processes *
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. It is a multidisciplinary approach of research and draws on environmental chemistry, physics, meteoro ...
* Seawater and other natural waters:
chemical oceanography Marine chemistry, also known as ocean chemistry or chemical oceanography, is influenced by plate tectonics and seafloor spreading, turbidity currents, sediments, pH levels, atmospheric constituents, metamorphic activity, and ecology. The field ...
* Distribution between two phases ** log ''D'' distribution coefficient: important for pharmaceuticals where lipophilicity is a significant property of a drug **
Liquid–liquid extraction Liquid–liquid extraction (LLE), also known as solvent extraction and partitioning, is a method to separate compounds or metal complexes, based on their relative solubilities in two different immiscible liquids, usually water (polar) and an orga ...
,
Ion exchange Ion exchange is a reversible interchange of one kind of ion present in an insoluble solid with another of like charge present in a solution surrounding the solid with the reaction being used especially for softening or making water demineralised, ...
, Chromatography **
Solubility product Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical reac ...
** Uptake and release of oxygen by hemoglobin in blood * Acid–base equilibria:
acid dissociation constant In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction :HA ...
, hydrolysis,
buffer solution A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small amount of strong acid or base is ...
s,
indicators Indicator may refer to: Biology * Environmental indicator of environmental health (pressures, conditions and responses) * Ecological indicator of ecosystem health (ecological processes) * Health indicator, which is used to describe the health o ...
,
acid–base homeostasis Acid–base homeostasis is the homeostatic regulation of the pH of the body's extracellular fluid (ECF). The proper balance between the acids and bases (i.e. the pH) in the ECF is crucial for the normal physiology of the body—and for cellula ...
* Metal–ligand complexation: sequestering agents,
chelation therapy Chelation therapy is a medical procedure that involves the administration of chelating agents to remove heavy metals from the body. Chelation therapy has a long history of use in clinical toxicology and remains in use for some very specific medi ...
, MRI contrast reagents,
Schlenk equilibrium Schlenk can refer to: People * Wilhelm Schlenk (1879-1943), German chemist In chemistry * Schlenk flask * Schlenk line The Schlenk line (also vacuum gas manifold) is a commonly used chemistry apparatus developed by Wilhelm Schlenk. It consist ...
* Adduct formation:
host–guest chemistry In supramolecular chemistry, host–guest chemistry describes complexes that are composed of two or more molecules or ions that are held together in unique structural relationships by forces other than those of full covalent bonds. Host–guest ch ...
,
supramolecular chemistry Supramolecular chemistry refers to the branch of chemistry concerning chemical systems composed of a discrete number of molecules. The strength of the forces responsible for spatial organization of the system range from weak intermolecular forces, ...
,
molecular recognition The term molecular recognition refers to the specific interaction between two or more molecules through noncovalent bonding such as hydrogen bonding, metal coordination, hydrophobic forces, van der Waals forces, π-π interactions, halogen ...
, dinitrogen tetroxide * In certain oscillating reactions, the approach to equilibrium is not asymptotically but in the form of a damped oscillation . * The related
Nernst equation In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction (half-cell or full cell reaction) from the standard electrode potential, absolute tempera ...
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. In these applications, terms such as stability constant, formation constant, binding constant, affinity constant, association constant and 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 a mixture

When the only equilibrium is that of the formation of a 1:1 adduct as the composition of a mixture, there are many ways that the composition of a mixture can be calculated. For example, see
ICE table An ICE table or RICE box or RICE chart is a tabular system of keeping track of changing concentrations in an equilibrium reaction. ICE stands for ''initial, change, equilibrium''. It is used in chemistry to keep track of the changes in amount of su ...
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 In physics, a mass balance, also called a material 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 b ...
. 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 In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass ca ...
.


Mass-balance equations

In general, the calculations are rather complicated or complex. For instance, in the case of a dibasic acid, H2A dissolved in water the two reactants can be specified as the
conjugate base A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid donates a proton () to a base—in other words, it is a base with a hydrogen ion added to it, as in the reverse reaction it loses a ...
, A2−, and the proton, 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: :T_\mathrm = \mathrm \, :T_\mathrm = \mathrm \, with TA 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" and This follows from the fact that Anbsp;= ''β''1 H], 2Anbsp;= ''β''2 H]2 and Hnbsp;= ''K''w sup>−1 : T_\mathrm = \mathrm + \beta_1\mathrm + \beta_2\mathrm^2 \, : T_\mathrm = \mathrm + \beta_1\mathrm + 2\beta_2\mathrm^2 - K_w mathrm H \, 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 :T_\mathrm= mathrm A\sum_i p_i \beta_i mathrm A mathrm B :T_\mathrm= mathrm B\sum_i q_i \beta_i mathrm A mathrm B It is easy to see how this can be extended to three or more reagents.


Polybasic acids

The composition of solutions containing reactants A and H is easy to calculate as a function of p When is known, the free concentration is calculated from the mass-balance equation in A. The diagram alongside, shows an example of the hydrolysis of the
aluminium Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It has ...
Lewis acid A Lewis acid (named for the American physical chemist Gilbert N. Lewis) is a chemical species that contains an empty orbital which is capable of accepting an electron pair from a Lewis base to form a Lewis adduct. A Lewis base, then, is any sp ...
Al3+(aq)The diagram was created with the progra
HySS
/ref> shows the species concentrations for a 5 × 10−6 M solution of an aluminium salt as a function of pH. Each concentration is shown as a percentage of the total aluminium.


Solution and precipitation

The diagram above illustrates the point that a precipitate 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 5 μM solution of Al3+ are
aluminium hydroxide Aluminium hydroxide, Al(OH)3, is found in nature as the mineral gibbsite (also known as hydrargillite) and its three much rarer polymorphs: bayerite, doyleite, and nordstrandite. Aluminium hydroxide is amphoteric, i.e., it has both basic and ...
s Al(OH)2+, and , but on raising the pH Al(OH)3 precipitates from the solution. This occurs because Al(OH)3 has a very large
lattice energy In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bin ...
. As the pH rises more and more Al(OH)3 comes out of solution. This is an example of Le Châtelier's principle 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, , 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
hydrophobic In chemistry, hydrophobicity is the physical property of a molecule that is seemingly repelled from a mass of water (known as a hydrophobe). In contrast, hydrophiles are attracted to water. Hydrophobic molecules tend to be nonpolar and, t ...
, it will precipitate out of water. This occurs with the nickel ion Ni2+ and
dimethylglyoxime Dimethylglyoxime is a chemical compound described by the formula CH3C(NOH)C(NOH)CH3. Its abbreviation is dmgH2 for neutral form, and dmgH− for anionic form, where H stands for hydrogen. This colourless solid is the di oxime derivative of the di ...
, (dmgH2): in this case the lattice energy of the solid is not particularly large, but it greatly exceeds the energy of solvation of the molecule Ni(dmgH)2.


Minimization of Gibbs energy

At equilibrium, at a specified temperature and pressure, and with no external forces, the
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and p ...
''G'' is at a minimum: :dG= \sum_^m \mu_j\,dN_j = 0 where μj is the
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
of molecular species ''j'', and ''Nj'' is the amount of molecular species ''j''. It may be expressed in terms of
thermodynamic activity In chemical thermodynamics, activity (symbol ) is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depen ...
as: :\mu_j = \mu_j^ + RT\ln where \mu_j^ is the chemical potential in the standard state, ''R'' is the gas constant ''T'' is the absolute temperature, and ''Aj'' is the activity. 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: :\sum_^m a_N_j=b_i^0 where ''aij'' is the number of atoms of element ''i'' in molecule ''j'' and ''b'' 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. If ions are involved, an additional row is added to the aij matrix specifying the respective charge on each molecule which will sum to zero. This is a standard problem in optimisation, known as constrained minimisation. The most common method of solving it is using the method of Lagrange multipliers (although other methods may be used). Define: :\mathcal= G + \sum_^k\lambda_i\left(\sum_^m a_N_j-b_i^0\right)=0 where the ''λi'' are the Lagrange multipliers, one for each element. This allows each of the ''Nj'' and ''λj'' to be treated independently, and it can be shown using the tools of
multivariate calculus Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving several variables, rather th ...
that the equilibrium condition is given by :0 = \frac = \mu_j + \sum_^k \lambda_i a_ :0 = \frac = \sum_^m a_N_j-b_i^0 (For proof see Lagrange multipliers.) This is a set of (''m'' + ''k'') equations in (''m'' + ''k'') unknowns (the ''Nj'' and the ''λi'') and may, therefore, be solved for the equilibrium concentrations ''Nj'' as long as the chemical activities are known as functions of the concentrations at the given temperature and pressure. (In the ideal case, activities are proportional to concentrations.) (See
Thermodynamic databases for pure substances Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calcula ...
.) Note that the second equation is just the initial constraints for minimization. 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. The results are consistent with those specified by chemical equations. For example, if equilibrium is specified by a single chemical equation:, :\sum_^m \nu_j R_j=0 where νj is the stoichiometric coefficient for the ''j'' th molecule (negative for reactants, positive for products) and ''Rj'' is the symbol for the ''j'' th molecule, a properly balanced equation will obey: :\sum_^m a_ \nu_j =0 Multiplying the first equilibrium condition by νj and using the above equation yields: :0 =\sum_^m \nu_j \mu_j + \sum_^m \sum_^k \nu_j \lambda_i a_ = \sum_^m \nu_j \mu_j As above, defining ΔG :\Delta G=\sum_^m \nu_j \mu_j = \sum_^m \nu_j (\mu_j^ + RT \ln(\)) = \Delta G^ + RT \ln\left(\prod_^m \^\right) = \Delta G^ + RT \ln(K_c) where ''Kc'' is the equilibrium constant, and ΔG will be zero at equilibrium. Analogous procedures exist for the minimization of other thermodynamic potentials.


See also

*
Acidosis Acidosis is a process causing increased acidity in the blood and other body tissues (i.e., an increase in hydrogen ion concentration). If not further qualified, it usually refers to acidity of the blood plasma. The term ''acidemia'' describes ...
*
Alkalosis Alkalosis is the result of a process reducing hydrogen ion concentration of arterial blood plasma (alkalemia). In contrast to acidemia (serum pH 7.35 or lower), alkalemia occurs when the serum pH is higher than normal (7.45 or higher). Alkalosis ...
*
Arterial blood gas An arterial blood gas (ABG) test, or arterial blood gas analysis (ABGA) measures the amounts of arterial gases, such as oxygen and carbon dioxide. An ABG test requires that a small volume of blood be drawn from the radial artery with a syringe a ...
* Benesi–Hildebrand method *
Determination of equilibrium constants Equilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant is expressed as a concentration quotient, :K=\frac it is implied that the activity quotient is constant. For this assumption to be vali ...
* Equilibrium constant *
Henderson–Hasselbalch equation In chemistry and biochemistry, the Henderson–Hasselbalch equation :\ce = \ceK_\ce + \log_ \left( \frac \right) relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant, ''K''a, of acid and t ...
*
Michaelis–Menten kinetics In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rat ...
* pCO2 * pH * p''K''a * Redox equilibria *
Steady state (chemistry) In chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, ...
*
Thermodynamic databases for pure substances Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calcula ...
*
Non-random two-liquid model The non-random two-liquid model (abbreviated NRTL model) is an activity coefficient model that correlates the activity coefficients \gamma_i of a compound with its mole fractions x_i in the liquid phase concerned. It is frequently applied in the f ...
(NRTL model) - Phase equilibrium calculations * UNIQUAC model - Phase equilibrium calculations


References


Further reading

* Mainly concerned with gas-phase equilibria. * *


External links

* {{DEFAULTSORT:Chemical Equilibrium * Analytical chemistry Physical chemistry