Equilibrium chemistry is concerned with systems in
chemical equilibrium
In a chemical reaction, 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 ...
. 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
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
. Applications include
acid–base,
host–guest,
metal–complex,
solubility
In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.
The extent of the solubi ...
,
partition,
chromatography
In chemical analysis, chromatography is a laboratory technique for the separation of a mixture into its components. The mixture is dissolved in a fluid solvent (gas or liquid) called the ''mobile phase'', which carries it through a system ( ...
and
redox
Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or ...
equilibria.
Thermodynamic equilibrium
A chemical system is said to be in equilibrium when the quantities of the chemical entities involved do not and ''cannot'' change in time without the application of an external influence. In this sense a system in chemical equilibrium is in a
stable
A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many different types of stables in use today; the ...
state. The system at
chemical equilibrium
In a chemical reaction, 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 ...
will be at a constant temperature, pressure or volume and a composition. It will be insulated from exchange of heat with the surroundings, that is, it is a
closed system
A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed.
In ...
. A change of temperature, pressure (or volume) constitutes an external influence and the equilibrium quantities will change as a result of such a change. If there is a possibility that the composition might change, but the rate of change is negligibly slow, the system is said to be in a
metastable state. The equation of chemical equilibrium can be expressed symbolically as
:reactant(s) product(s)
The sign means "are in equilibrium with". This definition refers to
macroscopic properties. Changes do occur at the microscopic level of atoms and molecules, but to such a minute extent that they are not measurable and in a balanced way so that the macroscopic quantities do not change. Chemical equilibrium is a dynamic state in which forward and backward reactions proceed at such rates that the macroscopic composition of the mixture is constant. Thus, equilibrium sign symbolizes the fact that reactions occur in both forward
and backward
directions.
A
steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
, on the other hand, is not necessarily an equilibrium state in the chemical sense. For example, in a radioactive
decay chain
In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". Most radioisotopes do not decay dire ...
the concentrations of intermediate isotopes are constant because the rate of production is equal to the rate of decay. It is not a chemical equilibrium because the decay process occurs in one direction only.
Thermodynamic equilibrium
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In the ...
is characterized by the free energy for the whole (closed) system being a minimum. For systems at constant volume the
Helmholtz free energy
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz en ...
is minimum and for systems at constant pressure 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 an ...
is minimum. Thus a metastable state is one for which the free energy change between reactants and products is not minimal even though the composition does not change in time.
The existence of this minimum is due to the free energy of mixing of reactants and products being always negative. For
ideal solution
In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to ze ...
s the
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
of mixing is zero, so the minimum exists because the
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
of mixing is always positive. The slope of the reaction free energy, δ''G''
r with respect to the
reaction coordinate, ''ξ'', is zero when the free energy is at its minimum value.
:
Equilibrium constant
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 speci ...
is the partial molar free energy. The potential, ''μ
i'', of the ''i''th species in a chemical reaction is the partial derivative of the free energy with respect to the number of moles of that species, ''N
i'':
:
A general chemical equilibrium can be written as
[The general expression is not used much in chemistry. To help understand the notation consider the equilibrium
:H2SO4 + 2 OH− + 2 H2O
for this reaction , , and , Reactant1 = H2SO4, Reactant2 = OH−, Product1 = and Product2 = H2O.]
:
''n
j'' are the
stoichiometric coefficients of the reactants in the equilibrium equation, and ''m
j'' are the coefficients of the products. The value of δ''G''
r for these reactions is a function of the chemical potentials of all the species.
:
The chemical potential, ''μ
i'', of the ''i''th species can be calculated in terms of its
activity, ''a
i''.
:
''μ'' is the standard chemical potential of the species, ''R'' is the
gas constant and ''T'' is the temperature. Setting the sum for the reactants ''j'' to be equal to the sum for the products, ''k'', so that δ''G''
r(Eq) = 0:
:
Rearranging the terms,
:
:
This relates the
standard Gibbs free energy change, Δ''G''
o to an
equilibrium constant
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
, ''K'', the
reaction quotient of activity values at equilibrium.
:
:
It follows that any equilibrium of this kind can be characterized either by the standard free energy change or by the equilibrium constant. In practice concentrations are more useful than activities. Activities can be calculated from concentrations if the
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 ...
are known, but this is rarely the case. Sometimes activity coefficients can be calculated using, for example,
Pitzer equations or
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 ...
. Otherwise conditions must be adjusted so that activity coefficients do not vary much. For ionic solutions this is achieved by using a background ionic medium at a high concentration relative to the concentrations of the species in equilibrium.
If activity coefficients are unknown they may be subsumed into the equilibrium constant, which becomes a concentration quotient.
[ Chapter 2, Activity and concentration quotients] Each activity ''a
i'' is assumed to be the product of a concentration,
''i''">''i'' and an activity coefficient, ''γ
i'':
:
This expression for activity is placed in the expression defining the equilibrium constant.
:
By setting the quotient of activity coefficients, ''Γ'', equal to one,
[This is equivalent to defining a new equilibrium constant as ] the equilibrium constant is defined as a quotient of concentrations.
:
In more familiar notation, for a general equilibrium
:''α'' A + ''β'' B ... ''σ'' S + ''τ'' T ...
:
This definition is much more practical, but an equilibrium constant defined in terms of concentrations is dependent on conditions. In particular, equilibrium constants for species in aqueous solution are dependent on
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 ...
, as the quotient of activity coefficients varies with the ionic strength of the solution.
The values of the standard free energy change and of the equilibrium constant are temperature dependent. To a first approximation, the
van 't Hoff equation may be used.
:
This shows that when the reaction is exothermic (Δ''H''
o, the standard
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
change, is negative), then ''K'' decreases with increasing temperature, in accordance with
Le Châtelier's principle. The approximation involved is that the standard enthalpy change, Δ''H''
o, is independent of temperature, which is a good approximation only over a small temperature range. Thermodynamic arguments can be used to show that
:
where ''C
p'' is the
heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat cap ...
at constant pressure.
Equilibria involving gases
When dealing with gases,
fugacity
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 whic ...
, ''f'', is used rather than activity. However, whereas activity is
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
less, fugacity has the dimension of
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
. A consequence is that chemical potential has to be defined in terms of a standard pressure, ''p''
o:
:
By convention ''p''
o is usually taken to be 1
bar
Bar or BAR may refer to:
Food and drink
* Bar (establishment), selling alcoholic beverages
* Candy bar
* Chocolate bar
Science and technology
* Bar (river morphology), a deposit of sediment
* Bar (tropical cyclone), a layer of cloud
* Bar ( ...
.
Fugacity can be expressed as the product of
partial pressure
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal g ...
, ''p'', and a fugacity coefficient, ''Φ'':
:
Fugacity coefficients are dimensionless and can be obtained experimentally at specific temperature and pressure, from measurements of deviations from
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
behaviour. Equilibrium constants are defined in terms of fugacity. If the gases are at sufficiently low pressure that they behave as ideal gases, the equilibrium constant can be defined as a quotient of partial pressures.
An example of gas-phase equilibrium is provided by the
Haber–Bosch process of
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 ...
synthesis.
:N
2 + 3 H
2 2 NH
3;
This reaction is strongly
exothermic
In thermodynamics, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity ...
, so the equilibrium constant decreases with temperature. However, a temperature of around 400 °C is required in order to achieve a reasonable rate of reaction with currently available
catalyst
Catalysis () is the process of increasing the 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 catalyst recyc ...
s. Formation of ammonia is also favoured by high pressure, as the volume decreases when the reaction takes place. The same reaction,
nitrogen fixation
Nitrogen fixation is a chemical process by which molecular nitrogen (), with a strong triple covalent bond, in the air is converted into ammonia () or related nitrogenous compounds, typically in soil or aquatic systems but also in industry. Atmo ...
, occurs at ambient temperatures in nature, when the catalyst is an
enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products ...
such as
nitrogenase. Much energy is needed initially to break the nitrogen–nitrogen triple bond even though the overall reaction is exothermic.
Gas-phase equilibria occur during
combustion
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. Combus ...
and were studied as early as 1943 in connection with the development of the
V2 rocket engine
A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accorda ...
.
The calculation of composition for a gaseous equilibrium at constant pressure is often carried out using ΔG values, rather than equilibrium constants.
Multiple equilibria
Two or more equilibria can exist at the same time. When this is so, equilibrium constants can be ascribed to individual equilibria, but they are not always unique. For example, three equilibrium constants can be defined for a
dibasic acid
In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a se ...
, H
2A.
[The definitions given are association constants. A dissociation constant is the reciprocal of an association constant.]
:A
2− + H
+ HA
−;
:HA
− + H
+ H
2A;
:A
2− + 2 H
+ H
2A;
The three constants are not independent of each other and it is easy to see that . The constants ''K''
1 and ''K''
2 are stepwise constants and ''β'' is an example of an overall constant.
Speciation
The concentrations of species in equilibrium are usually calculated under the assumption that activity coefficients are either known or can be ignored. In this case, each equilibrium constant for the formation of a complex in a set of multiple equilibria can be defined as follows
:''α'' A + ''β'' B ... A
''α''B
''β''...;
The concentrations of species containing reagent A are constrained by a condition of
mass-balance, that is, the total (or analytical) concentration, which is the sum of all species' concentrations, must be constant. There is one mass-balance equation for each reagent of the type
:
There are as many mass-balance equations as there are reagents, A, B..., so if the equilibrium constant values are known, there are ''n'' mass-balance equations in ''n'' unknowns,
.., the so-called free reagent concentrations. Solution of these equations gives all the information needed to calculate the concentrations of all the species.
[
Thus, the importance of equilibrium constants lies in the fact that, once their values have been determined by experiment, they can be used to calculate the concentrations, known as the ]speciation
Speciation is the evolutionary process by which populations evolve to become distinct species. The biologist Orator F. Cook coined the term in 1906 for cladogenesis, the splitting of lineages, as opposed to anagenesis, phyletic evolution withi ...
, of mixtures that contain the relevant species.
Determination
There are five main types of experimental data that are used for the determination of solution equilibrium constants. Potentiometric data obtained with a glass electrode
A glass electrode is a type of ion-selective electrode made of a doped glass membrane that is sensitive to a specific ion. The most common application of ion-selective glass electrodes is for the measurement of pH. The pH electrode is an exampl ...
are the most widely used with aqueous solutions. The others are Spectrophotometric, Fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
(luminescence) measurements and NMR chemical shift measurements;[ simultaneous measurement of ''K'' and Δ''H'' for 1:1 adducts in biological systems is routinely carried out using ]Isothermal Titration Calorimetry
Isothermal titration calorimetry (ITC) is a physical technique used to determine the thermodynamic parameters of interactions in solution. It is most often used to study the binding of small molecules (such as medicinal compounds) to larger macro ...
.
The experimental data will comprise a set of data points. At the i'th data point, the analytical concentrations of the reactants, ''T''A(''i''), ''T''B(''i'') etc. will be experimentally known quantities and there will be one or more measured quantities, ''yi'', that depend in some way on the analytical concentrations and equilibrium constants. A general computational procedure has three main components.
# Definition of a chemical model of the equilibria. The model consists of a list of reagents, A, B, etc. and the complexes formed from them, with stoichiometries A''p''B''q''... Known or estimated values of the equilibrium constants for the formation of all complexes must be supplied.
# Calculation of the concentrations of all the chemical species in each solution. The free concentrations are calculated by solving the equations of mass-balance, and the concentrations of the complexes are calculated using the equilibrium constant definitions. A quantity corresponding to the observed quantity can then be calculated using physical principles such as the Nernst potential In a biological membrane, the reversal potential is the membrane potential at which the direction of ionic current reverses. At the reversal potential, there is no net flow of ions from one side of the membrane to the other. For channels that are pe ...
or Beer-Lambert law which relate the calculated quantity to the concentrations of the species.
# Refinement of the equilibrium constants. Usually a Non-linear least squares procedure is used. A weighted sum of squares, ''U'', is minimized. The weights, ''wi'' and quantities ''y'' may be vectors. Values of the equilibrium constants are refined in an iterative procedure.
Acid–base equilibria
Brønsted and Lowry characterized an acid–base equilibrium as involving a proton exchange reaction:[
Chapter 5: Acids and Bases]
:acid + base conjugate base + conjugate acid.
An acid is a proton donor; the proton is transferred to the base, a proton acceptor, creating a conjugate acid. For aqueous solutions of an acid HA, the base is water; the conjugate base is A− and the conjugate acid is the solvated hydrogen ion. In solution chemistry, it is usual to use H+ as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution H+ denotes a solvated hydronium ion.[The bare proton does not exist in aqueous solution. It is a very strong acid and combines the base, water, to form the hydronium ion
:H+ + H2O → H3O+
The hydronium ion forms various weak complexes by hydrogen bonding with more water molecules.]
The Brønsted–Lowry definition applies to other solvents, such as dimethyl sulfoxide
Dimethyl sulfoxide (DMSO) is an organosulfur compound with the formula ( CH3)2. This colorless liquid is the sulfoxide most widely used commercially. It is an important polar aprotic solvent that dissolves both polar and nonpolar compounds a ...
: the solvent S acts as a base, accepting a proton and forming the conjugate acid SH+. A broader definition of acid dissociation includes hydrolysis
Hydrolysis (; ) is any chemical reaction in which a molecule of water breaks one or more chemical bonds. The term is used broadly for substitution, elimination, and solvation reactions in which water is the nucleophile.
Biological hydrolysi ...
, in which protons are produced by the splitting of water molecules. For example, boric acid
Boric acid, more specifically orthoboric acid, is a compound of boron, oxygen, and hydrogen with formula . It may also be called hydrogen borate or boracic acid. It is usually encountered as colorless crystals or a white powder, that dissolve ...
, , acts as a weak acid, even though it is not a proton donor, because of the hydrolysis equilibrium
: + + H+.
Similarly, metal ion hydrolysis causes ions such as to behave as weak acids:[ Section 9.1 "Acidity of Solvated Cations" lists many p''K''a values.]
: + .
Acid–base equilibria are important in a very wide range of applications, such as acid–base homeostasis, ocean acidification
Ocean acidification is the reduction in the pH value of the Earth’s ocean. Between 1751 and 2021, the average pH value of the ocean surface has decreased from approximately 8.25 to 8.14. The root cause of ocean acidification is carbon dioxid ...
, pharmacology
Pharmacology is a branch of medicine, biology and pharmaceutical sciences concerned with drug or medication action, where a drug may be defined as any artificial, natural, or endogenous (from within the body) molecule which exerts a biochemica ...
and analytical chemistry
Analytical chemistry studies and uses instruments and methods to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separati ...
.
Host–guest equilibria
A host–guest complex, also known as a donor–acceptor complex, may be formed from a Lewis base
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 ...
, B, and a 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 ...
, A. The host may be either a donor or an acceptor. In biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
host–guest complexes are known as receptor
Receptor may refer to:
*Sensory receptor, in physiology, any structure which, on receiving environmental stimuli, produces an informative nerve impulse
*Receptor (biochemistry), in biochemistry, a protein molecule that receives and responds to a n ...
-ligand complexes; they are formed primarily by non-covalent bond
In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The ...
ing. Many host–guest complexes has 1:1 stoichiometry, but many others have more complex structures. The general equilibrium can be written as
:''p'' A + ''q'' B A''p''B''q''
The study of these complexes is important for supramolecular chemistry and 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 ...
. The objective of these studies is often to find systems with a high binding selectivity
Binding selectivity is defined with respect to the binding of ligands to a substrate forming a complex. Binding selectivity describes how a ligand may bind more preferentially to one receptor than another. A selectivity coefficient is the equi ...
of a host (receptor) for a particular target molecule or ion, the guest or ligand. An application is the development of chemical sensor
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
s. Finding a drug which either blocks a receptor, an antagonist
An antagonist is a character in a story who is presented as the chief foe of the protagonist.
Etymology
The English word antagonist comes from the Greek ἀνταγωνιστής – ''antagonistēs'', "opponent, competitor, villain, enemy, ri ...
which forms a strong complex the receptor, or activate it, an agonist
An agonist is a chemical that activates a receptor to produce a biological response. Receptors are cellular proteins whose activation causes the cell to modify what it is currently doing. In contrast, an antagonist blocks the action of the ag ...
, is an important pathway to drug discovery
In the fields of medicine, biotechnology and pharmacology, drug discovery is the process by which new candidate medications are discovered.
Historically, drugs were discovered by identifying the active ingredient from traditional remedies or b ...
.
Complexes of metals
The formation of a complex between a metal ion, M, and a ligand, L, is in fact usually a substitution reaction. For example, In aqueous solution
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be r ...
s, metal ions will be present as aquo ions, so the reaction for the formation of the first complex could be written as[Electrical charges are omitted from such expressions because the ligand, L, may or may not carry an electrical charge.]
: 2O)''n''">(H2O)''n''+ L 2O)''n''−1L">(H2O)''n''−1L+ H2O
However, since water is in vast excess, the concentration of water is usually assumed to be constant and is omitted from equilibrium constant expressions. Often, the metal and the ligand are in competition for protons.[ For the equilibrium
:''p'' M + ''q'' L + ''r'' H M''p''L''q''H''r''
a stability constant can be defined as follows:
:
The definition can easily be extended to include any number of reagents. It includes ]hydroxide
Hydroxide is a diatomic anion with chemical formula OH−. It consists of an oxygen and hydrogen atom held together by a single covalent bond, and carries a negative electric charge. It is an important but usually minor constituent of water. ...
complexes because the concentration of the hydroxide ions is related to the concentration of hydrogen ions by the self-ionization of water
:
Stability constants defined in this way, are ''association'' constants. This can lead to some confusion as p''K''a values are ''dissociation'' constants. In general purpose computer programs it is customary to define all constants as association constants. The relationship between the two types of constant is given in association and dissociation constants.
In biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
, an oxygen molecule can bind to an iron(II) atom in a heme
Heme, or haem (pronounced / hi:m/ ), is a precursor to hemoglobin, which is necessary to bind oxygen in the bloodstream. Heme is biosynthesized in both the bone marrow and the liver.
In biochemical terms, heme is a coordination complex "consis ...
prosthetic group
A prosthetic group is the non-amino acid component that is part of the structure of the heteroproteins or conjugated proteins, being tightly linked to the apoprotein.
Not to be confused with the cofactor that binds to the enzyme apoenzyme (eith ...
in hemoglobin
Hemoglobin (haemoglobin BrE) (from the Greek word αἷμα, ''haîma'' 'blood' + Latin ''globus'' 'ball, sphere' + ''-in'') (), abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein present in red blood cells (erythroc ...
. The equilibrium is usually written, denoting hemoglobin by Hb, as
: Hb + O2 HbO2
but this representation is incomplete as the Bohr effect
The Bohr effect is a phenomenon first described in 1904 by the Danish physiologist Christian Bohr. Hemoglobin's oxygen binding affinity (see oxygen–haemoglobin dissociation curve) is inversely related both to acidity and to the concentration o ...
shows that the equilibrium concentrations are pH-dependent. A better representation would be
: bHsup>+ + O2 HbO2 + H+
as this shows that when hydrogen ion concentration increases the equilibrium is shifted to the left in accordance with Le Châtelier's principle. Hydrogen ion concentration can be increased by the presence of carbon dioxide, which behaves as a weak acid.
:H2O + CO2 + H+
The iron atom can also bind to other molecules such as carbon monoxide
Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simpl ...
. Cigarette smoke contains some carbon monoxide so the equilibrium
:HbO2 + CO + O2
is established in the blood of cigarette smokers.
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 me ...
is based on the principle of using chelating ligands with a high binding selectivity
Binding selectivity is defined with respect to the binding of ligands to a substrate forming a complex. Binding selectivity describes how a ligand may bind more preferentially to one receptor than another. A selectivity coefficient is the equi ...
for a particular metal to remove that metal from the human body.
Complexes with polyamino carboxylic acid left, 120px, a metal complex with the EDTA anion
120px, Aspartic acid is an aminodicarboxylic acid and precursor to other ligands.
An aminopolycarboxylic acid (sometimes abbreviated APCA) is a chemical compound containing one or more nitrogen at ...
s find a wide range of applications. EDTA
Ethylenediaminetetraacetic acid (EDTA) is an aminopolycarboxylic acid with the formula H2N(CH2CO2H)2sub>2. This white, water-soluble solid is widely used to bind to iron (Fe2+/Fe3+) and calcium ions (Ca2+), forming water-soluble complexes ev ...
in particular is used extensively.
Redox equilibria
A reduction–oxidation (redox
Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or ...
) equilibrium can be handled in exactly the same way as any other chemical equilibrium. For example,
:Fe2+ + Ce4+ Fe3+ + Ce3+;
However, in the case of redox reactions it is convenient to split the overall reaction into two half-reactions. In this example
:Fe3+ + e− Fe2+
:Ce4+ + e− Ce3+
The standard free energy change, which is related to the equilibrium constant by
:
can be split into two components,
:
The concentration of free electrons is effectively zero as the electrons are transferred directly from the reductant to the oxidant. The standard electrode potential, ''E''0 for the each half-reaction is related to the standard free energy change by
:
where ''n'' is the number of electrons transferred and ''F'' is the Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of ...
. Now, the free energy for an actual reaction is given by
:
where ''R'' is the gas constant and ''Q'' a reaction quotient. Strictly speaking ''Q'' is a quotient of activities, but it is common practice to use concentrations instead of activities. Therefore:
:
For any half-reaction, the redox potential of an actual mixture is given by the generalized expression[The alternative expression is sometimes used, as in the ]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 tempe ...
.
:
This is an example of the 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 tempe ...
. The potential is known as a reduction potential. Standard electrode potentials are available in a table of values. Using these values, the actual electrode potential for a redox couple can be calculated as a function of the ratio of concentrations.
The equilibrium potential for a general redox half-reaction (See #Equilibrium constant above for an explanation of the symbols)
:''α'' A + ''β'' B... + ''n'' e− ''σ'' S + ''τ'' T...
is given by
:
Use of this expression allows the effect of a species not involved in the redox reaction, such as the hydrogen ion in a half-reaction such as
: + 8 H+ + 5 e− Mn2+ + 4 H2O
to be taken into account.
The equilibrium constant for a full redox reaction can be obtained from the standard redox potentials of the constituent half-reactions. At equilibrium the potential for the two half-reactions must be equal to each other and, of course, the number of electrons exchanged must be the same in the two half reactions.
Redox equilibria play an important role in the electron transport chain
An electron transport chain (ETC) is a series of protein complexes and other molecules that transfer electrons from electron donors to electron acceptors via redox reactions (both reduction and oxidation occurring simultaneously) and couples ...
. The various cytochrome
Cytochromes are redox-active proteins containing a heme, with a central Fe atom at its core, as a cofactor. They are involved in electron transport chain and redox catalysis. They are classified according to the type of heme and its mode of ...
s in the chain have different standard redox potentials, each one adapted for a specific redox reaction. This allows, for example, atmospheric oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
to be reduced in photosynthesis
Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemical energy is stored in ...
. A distinct family of cytochromes, the cytochrome P450 oxidases, are involved in steroidogenesis and detoxification
Detoxification or detoxication (detox for short) is the physiological or medicinal removal of toxic substances from a living organism, including the human body, which is mainly carried out by the liver. Additionally, it can refer to the period of ...
.
Solubility
When a solute forms a saturated solution
In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.
The extent of the solubi ...
in a solvent
A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
, the concentration of the solute, at a given temperature, is determined by the equilibrium constant at that temperature.
:
The activity of a pure substance in the solid state is one, by definition, so the expression simplifies to
:
If the solute does not dissociate the summation is replaced by a single term, but if dissociation occurs, as with ionic substances
:
For example, with Na2SO4, and so the solubility product is written as
: