Chemical equilibrium

In a chemical reaction, chemical equilibrium is the state in which both 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.[1] Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium.[2][3]

Historical introduction

The concept of chemical equilibrium was developed after Berthollet (1803) found that some chemical reactions are reversible.[4] For any reaction mixture to exist at equilibrium, the rates of the forward and backward (reverse) reactions are equal. In the following chemical equation with arrows pointing both ways to indicate equilibrium,[5] A and B are reactant chemical species, S and T are product species, and α, β, σ, and τ are the stoichiometric coefficients 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 (1865), building on Berthollet's ideas, proposed the law of mass action:

where A, B, S and T are active masses and k+ and k are rate constants. Since at equilibrium forward and backward rates are equal:

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

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 of the reaction as Guldberg and Waage had proposed (see, for example, nucleophilic aliphatic substitution by SN1 or reaction of hydrogen and bromine to form hydrogen bromide). Equality of forward and backward reaction rates, however, is a necessary condition for chemical equilibrium, though it is not sufficient 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.[2][6]

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

CH3CO2H + H2O ⇌ CH
+ H3O+

a proton may hop from one molecule of acetic acid on to a water molecule and then on to 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 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:

If {H3O+} increases {CH3CO2H} must increase and CH
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 suggested in 1873 that equilibrium is attained when the Gibbs free energy of the system is at its minimum value (assuming the reaction is carried out at constant temperature and pressure). What this means is that the derivative of the Gibbs energy with respect to reaction coordinate (a measure of the extent of reaction that has occurred, ranging from zero for all reactants to a maximum for all products) vanishes, signaling a stationary point. This derivative is called the reaction Gibbs energy (or energy change) and corresponds to the difference between the chemical potentials of reactants and products at the composition of the reaction mixture.[1] 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 change for the reaction by the equation

where R is the universal gas constant and T the temperature.

When the reactants are dissolved in a medium of high ionic strength the quotient of activity coefficients may be taken to be constant. In that case the concentration quotient, Kc,

where [A] is the concentration of A, etc., is independent of the analytical concentration of the reactants. For this reason, equilibrium constants for solutions are usually determined in media of high ionic strength. Kc varies with ionic strength, 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.


At constant temperature and pressure, one must consider the Gibbs free energy, 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 and atmospheric chemistry 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. Indeed, they would necessarily occupy disjoint volumes of space. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing) to states containing equal mixture of products and reactants. The standard Gibbs energy change, together with the Gibbs energy of mixing, determine the equilibrium state.[7][8]

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 potentials.[1]

At constant temperature and pressure, the Gibbs free energy, G, for the reaction depends only on the extent of reaction: ξ (Greek letter xi), and can only decrease according to the second law of thermodynamics. It means that the derivative of G with ξ must be negative if the reaction happens; at the equilibrium the derivative being equal to zero.

:     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 potentials 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 is in this case a partial molar Gibbs energy, a chemical potential. The chemical potential of a reagent A is a function of the activity, {A} of that reagent.

(where μo
is the standard chemical potential).

The definition of the Gibbs energy equation interacts with the fundamental thermodynamic relation to produce


Inserting dNi = νi dξ into the above equation gives a Stoichiometric coefficient () and a differential that denotes the reaction occurring once (). At constant pressure and temperature the above equations can be written as

which is the "Gibbs free energy change for the reaction .

This results in:


By substituting the chemical potentials:


the relationship becomes:


which is the standard Gibbs energy change for the reaction that can be calculated using thermodynamical tables. The reaction quotient is defined as:


At equilibrium:

leading to:


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

Diag eq

Addition of reactants or products

For a reactional system at equilibrium: Qr = Keq; ξ = ξeq.

  • If are modified activities of constituents, the value of the reaction quotient changes and becomes different from the equilibrium constant: Qr ≠ Keq
  • If activity of a reagent i increases
, the reaction quotient decreases.
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
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, Kc and an activity coefficient quotient, Γ.

[A] 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[9] Specific ion interaction theory or Pitzer equations[10] 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 place of activity coefficient. In the real world, for example, when making 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.

Concentration quotients

In aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as sodium nitrate NaNO3 or potassium perchlorate KClO4. The ionic strength of a solution is given by

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.[11]

However, Kc 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.[10] 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 adjustedSoftware (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 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 is also present in the mixture as in the contact process, but the catalyst does not affect the equilibrium concentrations.

Likewise, the formation of bicarbonate from carbon dioxide and water is very slow under normal conditions

CO2 + 2 H2O ⇌ HCO
+ H3O+

but almost instantaneous in the presence of the catalytic enzyme carbonic anhydrase.

Pure substances

When pure substances (liquids or solids) are involved in equilibria their activities do not appear in the equilibrium constant[12] 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+

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


A particular case is the self-ionization of water itself

2 H2O ⇌ H3O+ + OH

Because water is the solvent, and has an activity of one, 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 of the proton is constant (in dilute solutions) and so does not affect the equilibrium concentrations. Kw 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 Kw[H+]−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:[12]

2 CO ⇌ CO2 + C

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 A2−. 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, βD, is product of the stepwise constants.


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.

β1 and β2 are examples of association constants. Clearly β1 = 1/K2 and β2 = 1/βD; log β1 = pK2 and log β2 = pK2 + pK1[13] 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

Thus, for exothermic reactions (ΔH is negative), K decreases with an increase in temperature, but, for endothermic reactions, (ΔH 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.

Effect of electric and magnetic fields

The effect of electric field on equilibrium has been studied by Manfred Eigen among others.

Types of equilibrium

Equilibrium can be broadly classified as heterogeneous and homogeneous equilibrium[14]. 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 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 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 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.

  1. 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.
  2. Minimize the Gibbs energy of the system.[16][17]
  3. Satisfy the equation of mass balance. 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.

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, 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:

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" [A] and [H]. This follows from the fact that [HA] = β1[A][H], [H2A] = β2[A][H]2 and [OH] = Kw[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.

Polybasic acids

Al hydrolysis
Species concentrations during hydrolysis of the aluminium.

The composition of solutions containing reactants A and H is easy to calculate as a function of p[H]. When [H] is known, the free concentration [A] is calculated from the mass-balance equation in A.

The diagram alongside, shows an example of the hydrolysis of the aluminium Lewis acid Al3+(aq)[18] 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 hydroxides Al(OH)2+, AlOH+
and Al
, but on raising the pH Al(OH)3 precipitates from the solution. This occurs because Al(OH)3 has a very large lattice energy. 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, Al(OH)
, 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, it will precipitate out of water. This occurs with the nickel ion Ni2+ and dimethylglyoxime, (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 G is at a minimum:

where μj is the chemical potential of molecular species j, and Nj is the amount of molecular species j. It may be expressed in terms of thermodynamic activity as:

where 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:

where aij is the number of atoms of element i in molecule j and b0
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[19][15] (although other methods may be used).


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 that the equilibrium condition is given by

(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.) 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.[15] The results are consistent with those specified by chemical equations. For example, if equilibrium is specified by a single chemical equation:,[20]

where νj is the stochiometric 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:

Multiplying the first equilibrium condition by νj yields

As above, defining ΔG

where Kc is the equilibrium constant, and ΔG will be zero at equilibrium.

Analogous procedures exist for the minimization of other thermodynamic potentials.[15]

See also


  1. ^ a b c Atkins, Peter; De Paula, Julio (2006). Atkins' Physical Chemistry (8th ed.). W. H. Freeman. pp. 200–202. ISBN 0-7167-8759-8.
  2. ^ a b Atkins, Peter W.; Jones, Loretta. Chemical Principles: The Quest for Insight (2nd ed.). ISBN 0-7167-9903-0.
  3. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "chemical equilibrium". doi:10.1351/goldbook.C01023
  4. ^ Berthollet, C.L. (1803). Essai de statique chimique [Essay on chemical statics] (in French). Paris, France: Firmin Didot. On pp. 404–407, Berthellot mentions that when he accompanied Napoleon on his expedition to Egypt, he (Berthellot) visited Lake Natron and found sodium carbonate along its shores. He realized that this was a product of the reverse of the usual reaction Na2CO3 + CaCl2 → 2NaCl + CaCO3↓ and therefore that the final state of a reaction was a state of equilibrium between two opposing processes. From p. 405: " … la décomposition du muriate de soude continue donc jusqu'à ce qu'il se soit formé assez de muriate de chaux, parce que l'acide muriatique devant se partager entre les deux bases en raison de leur action, il arrive un terme où leurs forces se balancent." ( … the decomposition of the sodium chloride thus continues until enough calcium chloride is formed, because the hydrochloric acid must be shared between the two bases in the ratio of their action [i.e., capacity to react]; it reaches an end [point] at which their forces are balanced.)
  5. ^ The notation ⇌ was proposed in 1884 by the Dutch chemist Jacobus Henricus van 't Hoff. See: van 't Hoff, J.H. (1884). Études de Dynamique Chemique [Studies of chemical dynamics] (in French). Amsterdam, Netherlands: Frederik Muller & Co. pp. 4–5. Van 't Hoff called reactions that didn't proceed to completion "limited reactions". From pp. 4–5: "Or M. Pfaundler a relié ces deux phénomênes … s'accomplit en même temps dans deux sens opposés." (Now Mr. Pfaundler has joined these two phenomena in a single concept by considering the observed limit as the result of two opposing reactions, driving the one in the example cited to the formation of sea salt [i.e., NaCl] and nitric acid, [and] the other to hydrochloric acid and sodium nitrate. This consideration, which experiment validates, justifies the expression "chemical equilibrium", which is used to characterize the final state of limited reactions. I would propose to translate this expression by the following symbol:
    HCl + NO3 Na ⇌ NO3 H + Cl Na .
    I thus replace, in this case, the = sign in the chemical equation by the sign ⇌, which in reality doesn't express just equality but shows also the direction of the reaction. This clearly expresses that a chemical action occurs simultaneously in two opposing directions.)
  6. ^ Brady, James E. Chemistry: Matter and Its Changes (4th ed.). Fred Senese. ISBN 0-471-21517-1.
  7. ^ Schultz, Mary Jane (1999). "Why Equilibrium? Understanding Entropy of Mixing". Journal of Chemical Education. 76 (10): 1391. Bibcode:1999JChEd..76.1391S. doi:10.1021/ed076p1391.
  8. ^ Clugston, Michael J. (1990). "A mathematical verification of the second law of thermodynamics from the entropy of mixing". Journal of Chemical Education. 67 (3): 203. Bibcode:1990JChEd..67Q.203C. doi:10.1021/ed067p203.
  9. ^ Davies, C. W. (1962). Ion Association. Butterworths.
  10. ^ a b Grenthe, I.; Wanner, H. "Guidelines for the extrapolation to zero ionic strength" (PDF).
  11. ^ Rossotti, F. J. C.; Rossotti, H. (1961). The Determination of Stability Constants. McGraw-Hill.
  12. ^ a b c Concise Encyclopedia Chemistry. 1994. ISBN 0-89925-457-8. Missing or empty |title= (help)
  13. ^ Beck, M. T.; Nagypál, I. (1990). Chemistry of Complex Equilibria (2nd ed.). Budapest: Akadémiai Kaidó.
  14. ^
  15. ^ a b c d Gordon, Sanford; McBride, Bonnie J. (1994). "Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications" (PDF). NASA Reference publication 1311. NASA.
  16. ^ Smith, W. R.; Missen, R. W. (1991). Chemical Reaction Equilibrium Analysis: Theory and Algorithms (Reprinted ed.). Malabar, FL: Krieger Publishing.
  17. ^ "Mathtrek Systems".
  18. ^ The diagram was created with the program HySS
  19. ^ "Chemical Equilibrium with Applications". NASA. Retrieved October 5, 2019.
  20. ^ C. Kittel, H. Kroemer (1980). "9". Thermal Physics (2 ed.). W. H. Freeman Company. ISBN 0-7167-1088-9.

Further reading

  • Van Zeggeren, F.; Storey, S. H. (1970). The Computation of Chemical Equilibria. Cambridge University Press. Mainly concerned with gas-phase equilibria.
  • Leggett, D. J., ed. (1985). Computational Methods for the Determination of Formation Constants. Plenum Press.
  • Martell, A. E.; Motekaitis, R. J. (1992). The Determination and Use of Stability Constants. Wiley-VCH.

External links

Aluminium acetate

Aluminium acetate or aluminium ethanoate (also "aluminum ~"), sometimes abbreviated AlAc in geochemistry, can refer to a number of different salts of aluminum with acetic acid.

In the solid state, three salts exist under this name:

Neutral aluminium triacetate, Al(CH3CO2)3, which is formally called aluminium acetate under IUPAC rules, with CAS RN 139-12-8

Basic aluminium diacetate, HOAl(CH3CO2)2, also known as basic aluminium acetate, and formally named hydroxyaluminium diacetate, with CAS RN 142-03-0

Basic aluminium monoacetate, (HO)2AlCH3CO2, also known as dibasic aluminium acetate, and formally named dihydroxyaluminium acetate, with CAS RN 7360-44-3In aqueous solution, aluminium triacetate hydrolyses to form a mixture of the other two, and all solutions of all three can be referred to as "aluminium acetate" as the species formed co-exist and inter-convert in chemical equilibrium.


A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction. Such a reaction is called an autocatalytic reaction.

A set of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set).

Carbonic acid

Not to be confused with carbolic acid, an antiquated name for phenol.Carbonic acid is a chemical compound with the chemical formula H2CO3 (equivalently: OC(OH)2). It is also a name sometimes given to solutions of carbon dioxide in water (carbonated water), because such solutions contain small amounts of H2CO3. In physiology, carbonic acid is described as volatile acid or respiratory acid, because it is the only acid excreted as a gas by the lungs. It plays an important role in the bicarbonate buffer system to maintain acid–base homeostasis.

Carbonic acid, which is a weak acid, forms two kinds of salts: the carbonates and the bicarbonates. In geology, carbonic acid causes limestone to dissolve, producing calcium bicarbonate, which leads to many limestone features such as stalactites and stalagmites.

It was long believed that carbonic acid could not exist as a pure compound. However, in 1991 it was reported that NASA scientists had succeeded in making solid H2CO3 samples.

Chemical potential

In thermodynamics, chemical potential of a species is 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 in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. The molar chemical potential is also known as partial molar free energy. When both temperature and pressure are held constant, chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum.In semiconductor physics, the chemical potential of a system of electrons at a temperature of zero Kelvin is known as the Fermi energy.

Chemical stability

Chemical stability when used in the technical sense in chemistry, means thermodynamic stability of a chemical system.Thermodynamic stability occurs when a system is in its lowest energy state, or chemical equilibrium with its environment. This may be a dynamic equilibrium, where individual atoms or molecules change form, but their overall number in a particular form is conserved. This type of chemical thermodynamic equilibrium will persist indefinitely unless the system is changed. Chemical systems might include changes in the phase of matter or a set of chemical reactions.

State A is said to be more thermodynamically stable than state B if the Gibbs energy of the change from A to B is positive.


Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion in a fire produces a flame, and the heat produced can make combustion self-sustaining. Combustion is often a complicated sequence of elementary radical reactions. Solid fuels, such as wood and coal, first undergo endothermic pyrolysis to produce gaseous fuels whose combustion then supplies the heat required to produce more of them. Combustion is often hot enough that incandescent light in the form of either glowing or a flame is produced. A simple example can be seen in the combustion of hydrogen and oxygen into water vapor, a reaction commonly used to fuel rocket engines. This reaction releases 242 kJ/mol of heat and reduces the enthalpy accordingly (at constant temperature and pressure):

2H2(g) + O2(g) → 2H2O(g)Combustion of an organic fuel in air is always exothermic because the double bond in O2 is much weaker than other double bonds or pairs of single bonds, and therefore the formation of the stronger bonds in the combustion products CO2 and H2O results in the release of energy. The bond energies in the fuel play only a minor role, since they are similar to those in the combustion products; e.g., the sum of the bond energies of CH4 is nearly the same as that of CO2. The heat of combustion is approximately -418 kJ per mole of O2 used up in the combustion reaction, and can be estimated from the elemental composition of the fuel.Uncatalyzed combustion in air requires fairly high temperatures. Complete combustion is stoichiometric with respect to the fuel, where there is no remaining fuel, and ideally, no remaining oxidant. Thermodynamically, the chemical equilibrium of combustion in air is overwhelmingly on the side of the products. However, complete combustion is almost impossible to achieve, since the chemical equilibrium is not necessarily reached, or may contain unburnt products such as carbon monoxide, hydrogen and even carbon (soot or ash). Thus, the produced smoke is usually toxic and contains unburned or partially oxidized products. Any combustion at high temperatures in atmospheric air, which is 78 percent nitrogen, will also create small amounts of several nitrogen oxides, commonly referred to as NO x , since the combustion of nitrogen is thermodynamically favored at high, but not low temperatures. Since combustion is rarely clean, flue gas cleaning or catalytic converters may be required by law.

Fires occur naturally, ignited by lightning strikes or by volcanic products. Combustion (fire) was the first controlled chemical reaction discovered by humans, in the form of campfires and bonfires, and continues to be the main method to produce energy for humanity. Usually, the fuel is carbon, hydrocarbons or more complicated mixtures such as wood that contains partially oxidized hydrocarbons. The thermal energy produced from combustion of either fossil fuels such as coal or oil, or from renewable fuels such as firewood, is harvested for diverse uses such as cooking, production of electricity or industrial or domestic heating. Combustion is also currently the only reaction used to power rockets. Combustion is also used to destroy (incinerate) waste, both nonhazardous and hazardous.

Oxidants for combustion have high oxidation potential and include atmospheric or pure oxygen, chlorine, fluorine, chlorine trifluoride, nitrous oxide and nitric acid. For instance, hydrogen burns in chlorine to form hydrogen chloride with the liberation of heat and light characteristic of combustion. Although usually not catalyzed, combustion can be catalyzed by platinum or vanadium, as in the contact process.

Dynamic equilibrium

In chemistry, and in physics, a dynamic equilibrium exists once a reversible reaction occurs. The ratio of reactants/products changes, but substances move between the chemicals at an equal rate, meaning there is no net change. Reactants and products are formed at such a rate that the concentration of neither changes. It is a particular example of a system in a steady state. In thermodynamics, a closed system is in thermodynamic equilibrium when reactions occur at such rates that the composition of the mixture does not change with time. Reactions do in fact occur, sometimes vigorously, but to such an extent that changes in composition cannot be observed. Equilibrium constants can be expressed in terms of the rate constants for elementary reactions.

Equilibrium chemistry

Equilibrium chemistry is concerned with systems in chemical equilibrium. The unifying principle is that the free energy of a system at equilibrium is the minimum possible, so that the slope of the free energy with respect to the reaction coordinate is zero. This principle, applied to mixtures at equilibrium provides a definition of an equilibrium constant. Applications include acid–base, host–guest, metal–complex, solubility, partition, chromatography and redox equilibria.

Fischer–Speier esterification

Fischer esterification or Fischer–Speier esterification is a special type of esterification by refluxing a carboxylic acid and an alcohol in the presence of an acid catalyst. The reaction was first described by Emil Fischer and Arthur Speier in 1895. Most carboxylic acids are suitable for the reaction, but the alcohol should generally be primary or secondary. Tertiary alcohols are prone to elimination. Contrary to common misconception found in organic chemistry textbooks, phenols can also be esterified to give good to near quantitative yield of products. Commonly used catalysts for a Fischer esterification include sulfuric acid, tosylic acid, and Lewis acids such as scandium(III) triflate. For more valuable or sensitive substrates (for example, biomaterials), dicyclohexylcarbodiimide is often used. The reaction is often carried out without a solvent (particularly when a large reagent excess of alcohol is used) or in a non-polar solvent (e.g. toluene) to facilitate the Dean-Stark method. Typical reaction times vary from 1–10 hours at temperatures of 60-110 °C.

Direct acylations of alcohols with carboxylic acids is preferred over acylations with anhydrides (poor atom economy) or acid chlorides (moisture sensitive). The main disadvantage of direct acylation is the unfavorable chemical equilibrium that must be remedied (e.g. by a large excess of one of the reagents), or by the removal of water (e.g. by using Dean-Stark distillation, anhydrous salts, molecular sieves, or by using a stoichiometric quantity of acid catalyst).


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 which has the same temperature and molar Gibbs free energy as the real gas.

Fugacities are determined experimentally or estimated from various models such as a Van der Waals gas that are closer to reality than an ideal gas. The real gas pressure and fugacity are related through the dimensionless fugacity coefficient φ.

For an ideal gas, fugacity and pressure are equal and so φ = 1. Taken at the same temperature and pressure, the difference between the molar Gibbs free energies of a real gas and the corresponding ideal gas is equal to RT ln φ.

The fugacity is closely related to the thermodynamic activity. For a gas, the activity is simply the fugacity divided by a reference pressure to give a dimensionless quantity. This reference pressure is called the standard state and normally chosen as 1 atmosphere or 1 bar.

Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. The thermodynamic condition for chemical equilibrium is that the total chemical potential of reactants is equal to that of products. If the chemical potential of each gas is expressed as a function of fugacity, the equilibrium condition may be transformed into the familiar reaction quotient form (or law of mass action) except that the pressures are replaced by fugacities.

For a condensed phase (liquid or solid) in equilibrium with its vapor phase, the chemical potential is equal to that of the vapor, and therefore the fugacity is equal to the fugacity of the vapor. This fugacity is approximately equal to the vapor pressure when the vapor pressure is not too high.

Henry Louis Le Chatelier

Henry Louis Le Chatelier (French pronunciation: ​[ɑ̃ʁi lwi lə ʃɑtlje]; 8 October 1850 – 17 September 1936) was a French chemist of the late 19th and early 20th centuries. He devised Le Chatelier's principle, used by chemists to predict the effect a changing condition has on a system in chemical equilibrium.

Keto–enol tautomerism

In organic chemistry, keto–enol tautomerism refers to a chemical equilibrium between a keto form (a ketone or an aldehyde) and an enol (an alcohol). The keto and enol forms are said to be tautomers of each other. The interconversion of the two forms involves the movement of an alpha hydrogen atom and the reorganisation of bonding electrons; hence, the isomerism qualifies as tautomerism.

A compound containing a carbonyl group (C=O) is normally in rapid equilibrium with an enol tautomer, which contains a pair of doubly bonded carbon atoms adjacent to a hydroxyl (−OH) group, C=C-OH. The keto form predominates at equilibrium for most ketones. Nonetheless, the enol form is important for some reactions. The deprotonated intermediate in the interconversion of the two forms, referred to as an enolate anion, is important in carbonyl chemistry, in large part because it is a strong nucleophile.

Normally, the keto–enol tautomerization chemical equilibrium is highly thermodynamically driven, and at room temperature the equilibrium heavily favors the formation of the keto form. A classic example for favoring the keto form can be seen in the equilibrium between vinyl alcohol and acetaldehyde (K = [enol]/[keto] ≈ 3 × 10−7). However, it is reported that in the case of vinyl alcohol, formation of a stabilized enol form can be accomplished by controlling the water concentration in the system and utilizing the kinetic favorability of the deuterium-produced kinetic isotope effect (kH+/kD+ = 4.75, kH2O/kD2O = 12). Deuterium stabilization can be accomplished through hydrolysis of a ketene precursor in the presence of a slight stoichiometric excess of heavy water (D2O). Studies show that the tautomerization process is significantly inhibited at ambient temperatures ( kt ≈ 10−6 M/s), and the half-life of the enol form can easily be increased to t1/2 = 42 minutes for first-order hydrolysis kinetics.

Another exception is the 1,3-diketones, such as acetylacetone (2,4-pentanedione), which favor the enol form.

Law of mass action

In chemistry, the law of mass action is the proposition that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dynamic equilibrium. Specifically, it implies that for a chemical reaction mixture that is in equilibrium, the ratio between the concentration of reactants and products is constant.Two aspects are involved in the initial formulation of the law: 1) the equilibrium aspect, concerning the composition of a reaction mixture at equilibrium and 2) the kinetic aspect concerning the rate equations for elementary reactions. Both aspects stem from the research performed by Cato M. Guldberg and Peter Waage between 1864 and 1879 in which equilibrium constants were derived by using kinetic data and the rate equation which they had proposed. Guldberg and Waage also recognized that chemical equilibrium is a dynamic process in which rates of reaction for the forward and backward reactions must be equal at chemical equilibrium. In order to derive the expression of the equilibrium constant appealing to kinetics, the expression of the rate equation must be used. The expression of the rate equations was rediscovered later independently by Jacobus Henricus van 't Hoff.

The law is a statement about equilibrium and gives an expression for the equilibrium constant, a quantity characterizing chemical equilibrium. In modern chemistry this is derived using equilibrium thermodynamics. It can also be derived with the concept of chemical potential.

List of types of equilibrium

This is a list of various types of equilibrium, the condition of a system in which all competing influences are balanced.

Partition equilibrium

Partition equilibrium is a special case of chemical equilibrium. The most common chemical equilibrium systems involve reactants and products in the same phase - either all gases or all solutions. However, it is also possible to get equilibria between substances in different phases, such as two liquids that do not mix (are immiscible). Partition equilibria are described by Nernst's distribution law.

Physical chemistry

Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mechanics, analytical dynamics and chemical equilibrium.

Physical chemistry, in contrast to chemical physics, is predominantly (but not always) a macroscopic or supra-molecular science, as the majority of the principles on which it was founded relate to the bulk rather than the molecular/atomic structure alone (for example, chemical equilibrium and colloids).

Some of the relationships that physical chemistry strives to resolve include the effects of:

Intermolecular forces that act upon the physical properties of materials (plasticity, tensile strength, surface tension in liquids).

Reaction kinetics on the rate of a reaction.

The identity of ions and the electrical conductivity of materials.

Surface science and electrochemistry of cell membranes.

Interaction of one body with another in terms of quantities of heat and work called thermodynamics.

Transfer of heat between a chemical system and its surroundings during change of phase or chemical reaction taking place called thermochemistry

Study of colligative properties of number of species present in solution.

Number of phases, number of components and degree of freedom (or variance) can be correlated with one another with help of phase rule.

Reactions of electrochemical cells.

Selenium monochloride

Selenium monochloride is an inorganic compound with the formula Se2Cl2. Although it is called selenium monochloride, a more descriptive name might be diselenium dichloride. It is a reddish-brown, oily liquid that hydrolyses slowly. It exists in chemical equilibrium with SeCl2, SeCl4, chlorine, and elemental selenium. Selenium monochloride is mainly used as a reagent for the synthesis of Se-containing compounds.

Solubility equilibrium

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 reaction with another constituent of the solvent, such as acid or alkali. Each type of equilibrium is characterized by a temperature-dependent equilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.

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, there must be a flow through the system (compare mass balance). A simple example of such a system is the case of a bathtub with the tap running but with the drain unplugged: after a certain time, the water flows in and out at the same rate, so the water level (the state variable Volume) stabilizes and the system is in a steady state.

The steady state concept is different from chemical equilibrium. Although both may create a situation where a concentration does not change, in a system at chemical equilibrium, the net reaction rate is zero (products transform into reactants at the same rate as reactants transform into products), while no such limitation exists in the steady state concept. Indeed, there does not have to be a reaction at all for a steady state to develop.

The term steady state is also used to describe a situation where some, but not all, of the state variables of a system are constant. For such a steady state to develop, the system does not have to be a flow system. Therefore, such a steady state can develop in a closed system where a series of chemical reactions take place. Literature in chemical kinetics usually refers to this case, calling it steady state approximation.

In simple systems the steady state is approached by state variables gradually decreasing or increasing until they reach their steady state value. In more complex systems state variable might fluctuate around the theoretical steady state either forever (a limit cycle) or gradually coming closer and closer. It theoretically takes an infinite time to reach steady state, just as it takes an infinite time to reach chemical equilibrium.

Both concepts are, however, frequently used approximations because of the substantial mathematical simplifications these concepts offer. Whether or not these concepts can be used depends on the error the underlying assumptions introduce. So, even though a steady state, from a theoretical point of view, requires constant drivers (e.g. constant inflow rate and constant concentrations in the inflow), the error introduced by assuming steady state for a system with non-constant drivers may be negligible if the steady state is approached fast enough (relatively speaking).

Chemical equilibria


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