Chemical equilibrium

In a chemical process, chemical equilibrium is the state in which the chemical activities or concentrations of the reactants and products have no net change over time. In a " scientific " sense a chemical process is a method or means of somehow changing one or more Chemicals or Chemical compounds Such a chemical Activity in Chemistry is a measure of an “effective concentration” of a species In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance Usually, this would be the state that results when the forward chemical process proceeds at the same rate as their reverse reaction. In a " scientific " sense a chemical process is a method or means of somehow changing one or more Chemicals or Chemical compounds Such a chemical A reversible reaction is a Chemical reaction that results in an equilibrium mixture of Reactants and products. The reaction rates of the forward and reverse reactions are generally not zero but, being equal, there are no net changes in any of the reactant or product concentrations. The reaction rate or rate of reaction for a Reactant or product in a particular reaction is intuitively defined as how fast a reaction takes This process is called dynamic equilibrium ^[1] ^[2]

Concepts in Chemical Equilibria
Acid dissociation constant
Binding constant
Chemical equilibrium
Chemical stability
Dissociation constant
Distribution coefficient
Distribution ratio
Equilibrium constant
Equilibrium unfolding
Equilibrium stage
Liquid-liquid extraction
Phase diagram
Phase rule
Reaction quotient
Relative volatility
Solubility equilibrium
Stability constant
Thermodynamic equilibrium
Theoretical plate
Vapor-liquid equilibrium
edit

Introduction

A burette, an apparatus for carrying out e.g. acid-base titration, is an important part of equilibrium chemistry.

A burette, an apparatus for carrying out e. A dynamic equilibrium occurs when two opposing Processes proceed at the same rate The binding constant is a special case of the Equilibrium constant K Chemical stability when used in the technical sense in Chemistry, means thermodynamic stability of a chemical system In the fields of organic and Medicinal chemistry, a partition (P or distribution coefficient (D is Relative volatility is a measure comparing the Vapor pressures of the components in a liquid mixture of chemicals For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. In Biochemistry, equilibrium unfolding is the process of unfolding a protein or RNA molecule by gradually changing its solution conditions i A theoretical plate in many Separation processes is a hypothetical zone or stage in which two phases such as the Liquid and Vapor phases of a substance Liquid-liquid extraction, also known as solvent extraction and partitioning, is a method to separate compounds based on their relative solubilities in two In Physical chemistry, Mineralogy, and Materials science, a phase diagram is a type of graph used to show the equilibrium conditions Gibbs' phase rule, stated by Josiah Willard Gibbs in the 1870s is the fundamental rule on which Phase diagrams are based In Chemistry, reaction quotient is a quantitative measure of the extent of reaction the relative proportion of products and reactants present in the reaction mixture at some Relative volatility is a measure comparing the Vapor pressures of the components in a liquid mixture of chemicals Solubility equilibrium is any type Chemical equilibrium between solid and dissolved states of a compound at saturation. For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and A theoretical plate in many Separation processes is a hypothetical zone or stage in which two phases such as the Liquid and Vapor phases of a substance Vapor-liquid equilibrium, abbreviated as VLE by some is a condition where a Liquid and its Vapor (gas phase are in equilibrium with each other A burette (also buret) is a vertical cylindrical piece of Laboratory glassware with a volumetric graduation on its full length and a precision tap or Stopcock g. acid-base titration, is an important part of equilibrium chemistry. Titration is a common laboratory method of Quantitative chemical analysis that is used to determine the unknown Concentration of a known Reactant

In a chemical reaction, when reactants are mixed together in a reaction vessel (and heated if needed), the whole of reactants do not get converted into the products. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called After some time (which may be shorter than millionths of a second or longer than the age of the universe), there will come a point when a fixed amount of reactants will exist in harmony with a fixed amount of products, the amounts of neither changing anymore. This is called chemical equilibrium.

The concept of chemical equilibrium was developed after Berthollet (1803) found that some chemical reactions are reversible. Claude Louis Berthollet ( December 9, 1748 &ndash November 6, 1822) was a Savoyard Chemist who "became vice president A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called A reversible reaction is a Chemical reaction that results in an equilibrium mixture of Reactants and products. For any reaction such as

$\alpha A + \beta B \rightleftharpoons \sigma S + \tau T$

to be at equilibrium the rates of the forward and backward (reverse) reactions have to be equal. The reaction rate or rate of reaction for a Reactant or product in a particular reaction is intuitively defined as how fast a reaction takes In this chemical equation with harpoon arrows pointing 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 coefficients of the respective reactants and products. A chemical equation is a symbolic representation of a Chemical reaction. A reagent or reactant is a substance or compound consumed during a Chemical reaction. Alpha (uppercase Α, lowercase α; Αλφα is the first letter of the Greek alphabet. Beta (uppercase Β, lowercase β, internal ϐ; Βήτα Vita is the second letter of the Greek alphabet. Sigma (upper case Σ, lower case σ; Greek Σιγμα lower case in word-final position ς) is the eighteenth letter of the Greek Tau (uppercase Τ, lowercase τ; Ταυ) is the 19th letter of the Greek alphabet. Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry is the Calculation of Quantitative (measurable The equilibrium position of a reaction is said to lie far to the right if, at equilibrium, nearly all the reactants are used up and far to the left if hardly any product is formed from the reactants.

Guldberg and Waage (1865), building on Berthollet’s ideas, proposed the law of mass action:

$\mbox{forward reaction rate} = k_+ {A}^\alpha{B}^\beta \,\!$

$\mbox{backward reaction rate} = k_{-} {S}^\sigma{T}^\tau \,\!$

where A, B, S and T are active masses and k₊ and k₋ are rate constants. Cato Maximilian Guldberg ( August 11 1836 in Christiania (today Oslo) – January 14 1902, Oslo) was a Norwegian Peter Waage ( June 29, 1833 &ndash January 13, 1900) was a significant Norwegian Chemist and professor at the In chemistry Law of Mass Action has two aspects 1 the equilibrium aspect concerning the composition of a reaction mixture at equilibrium and 2 the kinetic Activity in Chemistry is a measure of an “effective concentration” of a species In Chemical kinetics a reaction rate constant k or \lambda quantifies the speed of a Chemical reaction. Since forward and backward rates are equal:

$k_+ \left\{ A \right\}^\alpha \left\{B \right\}^\beta = k_{-} \left\{S \right\}^\sigma\left\{T \right\}^\tau \,$

and the ratio of the rate constants is also a constant, now known as an equilibrium constant. For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T.

$K=\frac{k_+}{k_-}=\frac{\{S\}^\sigma \{T\}^\tau } {\{A\}^\alpha \{B\}^\beta}$

By convention the products form the numerator. Numerator may refer to A numeral used to indicate a count particularly of the equal parts in a fraction For example in 3/4 3 is 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). In chemistry Law of Mass Action has two aspects 1 the equilibrium aspect concerning the composition of a reaction mixture at equilibrium and 2 the kinetic The transition state of a Chemical reaction is a particular configuration along the Reaction coordinate. The reaction rate or rate of reaction for a Reactant or product in a particular reaction is intuitively defined as how fast a reaction takes Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry is the Calculation of Quantitative (measurable In organic and Inorganic chemistry, nucleophilic substitution is a fundamental class of Substitution reaction in which an "electron rich" Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Hydrogen bromide is the diatomic molecule H[[Bromine Br]] Under standard conditions HBr is a gas but it can be liquified 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. The van 't Hoff equation (also known as the van 't Hoff isochore) in Chemical thermodynamics relates the change in temperature ( T) to the change in the 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. Catalysis is the process in which the rate of a Chemical reaction is increased by means of a Chemical substance known as a catalyst The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached. ^[3] ^[4]

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

CH₃CO₂H + H₂O ⇌ CH₃CO₂⁻ + H₃O⁺

a proton may hop from one molecule of ethanoic acid on to a water molecule and then on to an ethanoate ion to form another molecule of ethanoic acid and leaving the number of ethanoic acid molecules unchanged. Acetic acid, also known as ethanoic acid, is an organic chemical compound, giving Vinegar its sour taste An acetate, or ethanoate, is either a salt or Ester of Acetic acid. In Chemistry, hydronium is the obsolete name for the Cation H 3 O + derived from Protonation of Water This is an example of dynamic equilibrium. A dynamic equilibrium occurs when two opposing Processes proceed at the same rate Equilibriums, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior.

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

If mineral acid is added to the ethanoic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. A mineral acid is an Acid derived by Chemical reaction from inorganic Minerals as opposed to Organic acids These have Hydrogen This can also be deduced from the equilibrium constant expression for the reaction:

$K=\frac{\{CH_3CO_2^-\}\{H_3O^+\}} {\{CH_3CO_2H\}\{H_2O \}}$

if {H₃O⁺} increases {CH₃CO₂H} must increase and {CH₃CO₂⁻} must decrease.

A quantitative version is given by the reaction quotient. In Chemistry, reaction quotient is a quantitative measure of the extent of reaction the relative proportion of products and reactants present in the reaction mixture at some

J.W. Gibbs suggested in 1873 that equilibrium is attained when the Gibbs energy of the system is at its minimum value (assuming the reaction is carried out under constant pressure). Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical 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, signalling a stationary point. In Chemistry, a reaction coordinate is an abstract one-dimensional Coordinate which represents progress along a Reaction pathway. Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry is the Calculation of Quantitative (measurable In Mathematics, particularly in Calculus, a stationary point is an input to a function where the Derivative is zero (equivalently the This derivative is usually called, for certain technical reasons, the Gibbs energy change. ^[5] 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. In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic The equilibrium constant can be related to the standard Gibbs energy change for the reaction by the equation

$\Delta G^\ominus = -RT \ln K_{eq}$

where R is the universal gas constant and T the temperature. In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater 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 Chemistry, a solution is a Homogeneous Mixture composed of two or more substances The ionic strength, I, of a solution is a function of the Concentration of all Ions present in a Solution. An activity coefficient is a factor used in Thermodynamics to account for deviations from ideal behaviour in a Mixture of Chemical substances In an In that case the concentration quotient, K_c,

$K_c=\frac{[S]^\sigma [T]^\tau } {[A]^\alpha [B]^\beta}$

where [A] is the concentration of A, etc. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance , is independent of the analytical concentration of the reactants. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance For this reason, equilibrium constants for solutions are usually determined in media of high ionic strength. In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances Equilibrium constants are determined in order to quantify Chemical equilibria. K_c varies with ionic strength, temperature and pressure (or volume). Likewise K_p for gases depends on partial pressure. In a mixture of Ideal gases each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume These constants are easier to measure and encountered in high-school chemistry courses.

Thermodynamics

The relationship between the Gibbs energy and the equilibrium constant can be found by considering chemical potentials. The thermodynamic condition for chemical equilibrium is^[6]

At constant pressure ΔG=0 (ΔG is the change Gibbs free energy for the reaction)
At constant volume ΔA=0 (ΔA is the change in Helmholtz free energy for the reaction)

In this article only the constant pressure case is considered. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic The constant volume case is important in geochemistry and atmospheric chemistry where pressure variations are significant. The field of geochemistry involves study of the chemical composition of the Earth and other Planets chemical processes and reactions that govern the composition Atmospheric chemistry is a branch of Atmospheric science in which the Chemistry of the Earth's atmosphere and that of other planets is studied Note that, if reactants and products were in standard state (completely pure), then there would be no reversibility and no equilibrium. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing) to states containing equal mixture of products and reactants. The entropy of mixing is the change in the Configuration entropy, an extensive thermodynamic quantity when two different Chemical substances The combination of the standard Gibbs energy change and the Gibbs energy of mixing determines the equilibrium state. ^[7]

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

$\alpha A + \beta B \rightleftharpoons \sigma S + \tau T$

In order to meet the thermodynamic condition for equilibrium, the Gibbs energy must be stationary, meaning that the derivative of G with respect to reaction coordinate (ΔG) must be zero. In Chemistry, a reaction coordinate is an abstract one-dimensional Coordinate which represents progress along a Reaction pathway. It can be shown that ΔG is, in fact, equal to the difference between the chemical potentials of the products and those of the reactants. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products.

$\alpha \mu_A + \beta \mu_B = \sigma \mu_S + \tau \mu_T \,$

where μ is in this case a partial molar Gibbs energy, a chemical potential. Mu (uppercase Μ, lowercase μ; Μι or el Μυ) is the 12th letter of the Greek alphabet. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical The chemical potential of a reagent A is a function of the activity, {A} of that reagent. Activity in Chemistry is a measure of an “effective concentration” of a species

$\mu_A = \mu_{A}^{\ominus} + RT \ln\{A\} \,$

Substituting expressions like this into the Gibbs energy equation:

$\Delta G = Vdp-SdT+\sum_{i=1}^k \mu_i dN_i + \sum_{i=1}^n X_i da_i + \cdots \,$

which at constant pressure and temperature becomes:

$\Delta G =\sum_{i=1}^k \mu_i N_i$

results in:

$\Delta G = \sigma \mu_{S} + \tau \mu_{T} - \alpha \mu_{A} - \beta \mu_{B} \,$

By substituting the chemical potentials:

$\Delta G = ( \sigma \mu_{S}^{\ominus} + \tau \mu_{T}^{\ominus} ) - ( \alpha \mu_{A}^{\ominus} - \beta \mu_{B}^{\ominus} ) + ( \sigma RT \ln\{S\} + \tau RT \ln\{T\} ) - ( \alpha RT \ln\{A\} + \beta RT \ln \{B\} )$

the relationship becomes:

$\Delta G =\sum_{i=1}^k \mu_i^\ominus v_i + RT \ln \frac{\{S\}^\sigma \{T\}^\tau} {\{A\}^\alpha \{B\}^\beta}$

At equilibrium $\Delta G = 0 \,$ and therefore

$\sum_{i=1}^k \mu_i^\ominus v_i + RT \ln \frac{\{S\}^\sigma \{T\}^\tau} {\{A\}^\alpha \{B\}^\beta} = 0$

leading to:

$\Delta G_m^{\ominus} = -RT \ln K$

ΔG_m^O is the standard molar Gibbs energy change for the reaction and K is the equilibrium constant. In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. Note that activities and equilibrium constants are dimensionless numbers.

Treatment of activity

The expression for the equilibrium constant can be re-written as the product of a concentration quotient, K_c and an activity coefficient quotient, Γ. An activity coefficient is a factor used in Thermodynamics to account for deviations from ideal behaviour in a Mixture of Chemical substances In an

$K=\frac{{[S]} ^\sigma {[T]}^\tau ... } {{[A]}^\alpha {[B]}^\beta ...} \times \frac{{\gamma_S} ^\sigma {\gamma_T}^\tau ... } {{\gamma_A}^\alpha {\gamma_B}^\beta ...} = K_c \Gamma$

[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^[8] or Pitzer equations^[9] may be used. The Debye-Hückel limiting law, named for its developers Peter Debye and Erich Hückel, provides one way to obtain Activity coefficients. ^{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 a mixture of Ideal gases each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume Fugacity is a measure of a Chemical potential in the form of 'adjusted pressure In the real world, for example, when making ammonia in industry, fugacity coefficients must be taken into account. The Haber process, also called the Haber–Bosch process, is the Nitrogen fixation reaction of Nitrogen and Hydrogen, over an iron substrate Fugacity, f, is the product of partial pressure and fugacity coefficient. The chemical potential of a species in the gas phase is given by

$\mu = \mu^{\Theta} + RT \ln \left( \frac{f}{bar} \right) + RT \ln \gamma$

so the general expression defining an equilibrium constant is valid for both solution and gas phases.

Justification for the use of concentration quotients

In aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as sodium nitrate NaNO₃ or Potassium perchlorate KClO₄. Sodium nitrate is the Chemical compound with the formula NaNO3 Potassium perchlorate, a Perchlorate salt with the chemical formula K[[chlorine Cl]] O4, is a strong oxidizer. The ionic strength, I, of a solution containing a dissolved salt, X⁺Y^-, is given by

$I = \frac{1}{2}\left(c_X z_X^2 + c_Y z_Y^2 + \sum_{i=1}^n c_i z_i^2\right)$

where c stands for concentration, z stands for ionic charge and the sum is taken over all the species in equilibrium. The ionic strength, I, of a solution is a function of the Concentration of all Ions present in a Solution. When the concentration of dissolved salt is much higher than the analytical concentrations of the reagents, the ionic strength is effectively constant. Since activity coefficients depend on ionic strength the activity coefficients of the species are effectively independent of concentration. Thus, the assumption that Γ is constant is justified. Gamma (uppercase &Gamma, lowercase γ Γάμμα is the third letter of the Greek alphabet. The concentration quotient is a simple multiple of the equilibrium constant. ^[10]

$K_c = \frac{K}{\Gamma}$

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. ^[9] The concentration quotient obtained in this manner is known, paradoxically, as a thermodynamic equilibrium constant.

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

Metastable mixtures

A mixture may be appear to have no tendency to change, though it is not at equilibrium. For example, a mixture of SO₂ and O₂ is metastable as there is a kinetic barrier to formation of the product, SO₃. Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Metastability is a general scientific concept which describes states of delicate equilibrium In Chemistry, activation energy, also called midnight energy, is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined Sulfur trioxide (also spelled sulphur trioxide) is the chemical compound with the formula SO3

2SO₂ + O₂ $\rightleftharpoons$ 2SO₃

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. Catalysis is the process in which the rate of a Chemical reaction is increased by means of a Chemical substance known as a catalyst The contact process is the current method of producing Sulfuric acid in the high concentrations needed for industrial processes

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

CO₂ + 2H₂O $\rightleftharpoons$ HCO₃^- +H₃O⁺

but almost instantaneous in the presence of the catalytic enzyme carbonic anhydrase. In Inorganic chemistry, bicarbonate ( IUPAC -recommended nomenclature hydrogencarbonate) is an intermediate form in the Deprotonation Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Water is a common Chemical substance that is essential for the survival of all known forms of Life. Enzymes are Biomolecules that catalyze ( ie increase the rates of Chemical reactions Almost all enzymes are Proteins The carbonic anhydrases (or carbonate dehydratases) form a family of Enzymes that catalyze the rapid conversion of Carbon dioxide to Bicarbonate

Pure compounds in equilibria

When pure substances (liquids or solids) are involved in equilibria they do not appear in the equilibrium equation ^[11]

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

$CH_3CO_2H + H_2O \rightleftharpoons CH_3CO_2^- + H_3O^+$

$K_c=\frac{[{CH_3CO_2}^-][{H_3O}^+]} {[{CH_3CO_2H}][{H_2O}]}$

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

$K=\frac{[{CH_3CO_2}^-][{H_3O}^+]} {[{CH_3CO_2H}]}$

where now

$K=K_c*[H_2O]\,$

a constant factor is incorporated into the equilibrium constant.

A particular case is the self-ionization of water itself

$H_2O + H_2O \rightleftharpoons H_3O^+ + OH^-$

The self-ionization constant of water is defined as

$K_w = [H^+][OH^-]\,$

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. The self-ionization of water (also autoionization of water, and autodissociation of water) is the chemical reaction in which two water molecules react to produce a In Chemistry, hydronium is the obsolete name for the Cation H 3 O + derived from Protonation of Water Solvation, commonly called dissolution, is the process of attraction and association of Molecules of a Solvent with molecules or Ions of a K_w varies with variation in ionic strength and/or temperature.

The concentrations of H⁺ and OH^- are not independent quantities. Most commonly [OH^-] is replaced by K_w[H⁺]^-1 in equilibrium constant expressions which would otherwise hydroxide. In Chemistry, hydroxide is the most common name for the diatomic Anion OH− consisting of Oxygen and Hydrogen

Solids also do not appear in the equilibrium equation. An example is the Boudouard reaction ^[11]:

$2CO \rightleftharpoons CO_2 + C$

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

$K_c=\frac{[CO_2]} {[CO]^2}$

Multiple equilibria

Consider the case of a dibasic acid H₂A. The Boudouard reaction is the Redox reaction of a Chemical equilibrium mixture of carbon monoxide and carbon dioxide at a given temperature When dissolved in water, the mixture will contain H₂A, HA^- and A^2-. This equilibrium can be split into two steps in each of which one proton is liberated.

$H_2A \rightleftharpoons HA^- + H^+ :K_1=\frac{[HA^-][H^+]} {[H_2A]}$

$HA^- \rightleftharpoons A^{2-} + H^+ :K_2=\frac{[A^{2-}][H^+]} {[HA^-]}$

K₁ and K₂ are examples of stepwise equilibrium constants. The overall equilibrium constant, $β D$ , is product of the stepwise constants.

$H_2A \rightleftharpoons A^{2-} + 2H^+ :\beta_D = \frac{[A^{2-}][H^+]^2} {[H_2A]}=K_1K_2$

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.

$A^{2-} + H^+ \rightleftharpoons HA^- :\beta_1=\frac {[HA^-]} {[A^{2-}][H^+]}$

$A^{2-} + 2H^+ \rightleftharpoons H_2A :\beta_2=\frac {[H_2A]} {[A^{2-}][H^+]^2}$

β₁ and β₂ are examples of association constants. Clearly β₁ = 1/K₂ and β₂ = 1/β_D; lg β₁ = pK₂ and lg β₂ = pK₂ + pK₁^[12]

Effect of temperature change on an equilibrium constant

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

$\frac {d\ln K} {dT} = \frac{{\Delta H_m}^{\Theta}} {RT^2}$

Thus, for exothermic reactions, (ΔH is negative) K decreases with temperature, but, for endothermic reactions, (ΔH is positive) K increases with temperature. The van 't Hoff equation (also known as the van 't Hoff isochore) in Chemical thermodynamics relates the change in temperature ( T) to the change in the In Thermodynamics, the word exothermic "outside heating" describes a process or reaction that releases Energy usually in the form of Heat, but In Thermodynamics, the word endothermic "within-heating" describes a process or reaction that absorbs Energy in the form of Heat. An alternative formulation is

$\frac {d\ln K} {d(1/T)} = -\frac{{\Delta H_m}^{\Theta}} {R}$

At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of K with temperature. In practice, however, the method is unreliable because error propagation almost always gives very large errors on the values calculated in this way.

Types of equilibrium and some applications

In the gas phase. Rocket engines ^[13]
The industrial synthesis such as ammonia in the Haber-Bosch process (depicted right) takes place through a succession of equilibrium steps including adsorbtion processes. A rocket engine is a Jet engine that uses only Propellant mass for forming its high speed propulsive jet. Ammonia is a compound with the formula N[[hydrogen H3]] It is normally encountered as a Gas with a characteristic pungent Odor The Haber process, also called the Haber–Bosch process, is the Nitrogen fixation reaction of Nitrogen and Hydrogen, over an iron substrate Adsorption is a process that occurs when a gas or liquid Solute accumulates on the surface of a solid or a liquid (adsorbent forming a film of molecules or atoms (the

atmospheric chemistry
Seawater and other natural waters: Chemical oceanography
Distribution between two phases
1. LogD-Distribution coefficient: Important for pharmaceuticals where lipophilicity is a significant property of a drug
2. Liquid-liquid extraction, Ion exchange, Chromatography
3. Solubility product
4. Uptake and release of oxygen by haemoglobin in blood
Acid/base equilibria: Acid dissociation constant, hydrolysis, buffer solutions, indicators, acid-base homeostasis
Metal-ligand complexation: sequestering agents, chelation therapy, MRI contrast reagents, Schlenk equilibrium
Adduct formation: Host-guest chemistry, supramolecular chemistry, molecular recognition, dinitrogen tetroxide
In certain oscillating reactions, the approach to equilibrium is not asymptotically but in the form of a damped oscillation ^[11]. Atmospheric chemistry is a branch of Atmospheric science in which the Chemistry of the Earth's atmosphere and that of other planets is studied Chemical oceanography is the study of the behavior of the Chemical elements within the Earth 's Oceans The ocean is unique in that it contains - in greater In the fields of organic and Medicinal chemistry, a partition (P or distribution coefficient (D is Liquid-liquid extraction, also known as solvent extraction and partitioning, is a method to separate compounds based on their relative solubilities in two Ion exchange is an exchange of Ions between two Electrolytes or between an electrolyte Solution and a complex. Chromatography (from Greek χρώμα chroma, color and γραφειν"graphein" to write is the collective term for a family of Laboratory Solubility equilibrium is any type Chemical equilibrium between solid and dissolved states of a compound at saturation. Hemoglobin ( also spelled haemoglobin and abbreviated Hb or Hgb) is the Iron -containing Oxygen -transport Metalloprotein Hydrolysis is a Chemical reaction during which one or more water molecules are split into hydrogen and hydroxide ions which may go on to participate in further reactions For an individual weak acid or weak base component see Buffering agent. A pH indicator is a halochromic chemical compound that is added in small amounts to a Solution so that the PH ( Acidity or Acid-base homeostasis is the part of Human homeostasis concerning the proper balance between Acids and bases, in other words the PH. Chelation is the binding or complexation of a bi- or multidentate Ligand. Chelation therapy is the administration of chelating agents to remove Heavy metals from the body The Schlenk equilibrium is a Chemical equilibrium named after its discoverer Wilhelm Schlenk taking place in solutions of Grignard reagents The In Supramolecular chemistry, host-guest chemistry describes complexes that are composed of two or more Molecules or Ions held together in unique Supramolecular chemistry refers to the area of Chemistry that focuses on the Noncovalent bonding interactions of molecules The term molecular recognition refers to the specific interaction between two or more Molecules through Noncovalent bonding such as including hydrogen bonding Nitrogen tetroxide ( dinitrogen tetroxide or nitrogen peroxide) is the Chemical compound N2O4 A chemical clock is a complex mixture of reacting chemical compounds in which the Concentration of one component shows an abrupt change accompanied by a
The related Nernst equation in electrochemistry gives the difference in electrode potential as a function of redox concentrations. In Electrochemistry, the Nernst equation is an equation which can be used (in conjunction with other information to determine the equilibrium Reduction potential
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/dissociation constant are used. In biochemistry, it is common to give units for binding constants, which serve to define the concentration units used when the constant’s value was determined.

Composition of an equilibrium mixture

When the only equilibrium is that of the formation of a 1:1 adduct as the composition of a mixture, there are any number of ways that the composition of a mixture can be calculated. For example, see ICE table for a traditional method of calculating the pH of a solution of a weak acid. An ICE table or ICE chart is a tabular system of keeping track of changing concentrations in an Equilibrium reaction.

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. ^[14]
Satisfy the equation of mass balance. A mass balance (also called a material balance is an application of Conservation of mass to the analysis of physical systems 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. The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of

Solving the equations of mass-balance

In general, the calculations are rather complicated. For instance, in the case of a dibasic acid, H₂A dissolved in water the two reactants can be specified as the conjugate base, A^2-, and the proton, H⁺. Within the Brønsted - Lowry ( protonic) theory of acids and bases, a conjugate acid is the acid member HX of a pair of two compounds that transform In Chemistry, hydronium is the obsolete name for the Cation H 3 O + derived from Protonation of Water 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:

$T_A = [A] + [HA] +[H_2A] \,$

$T_H = [H] + [HA] + 2[H_2A] - [OH] \,$

With T_A the total concentration of species A. Ethylenediamine (abbreviated as en when a Ligand) is the Organic compound with the formula C2H4(NH22 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] = K_w[H]^-1

$T_A = [A] + \beta_1[A][H] + \beta_2[A][H]^2 \,$

$T_H = [H] + \beta_1[A][H] + 2\beta_2[A][H]^2 - K_w[H]^{-1} \,$

so the concentrations of the "complexes" are calculated from the free concentrations and the equilibrium constants. General expressions applicable to all systems with two reagents, A and B would be

$T_A=[A]+\sum_i{p_i \beta_i[A]^{p_i}[B]^{q_i}}$

$T_B=[B]+\sum_i{q_i \beta_i[A]^{p_i}[B]^{q_i}}$

It is easy to see how this can be extended to three or more reagents.

Composition for polybasic acids as a function of pH

The composition of solutions containing reactants A and H is easy to calculate as a function of p[H]. pH is the measure of the acidity or alkalinity of a Solution. When [H] is known, the free concentration [A] is calculated from the mass-balance equation in A. Here is an example of the results that can be obtained.

Image:AL hydrolysis.png

This diagram, for the hydrolysis of the aluminium Lewis acid Al³⁺_aq ^[15] shows the species concentrations for a 5×10^-6M solution of an aluminium salt as a function of pH. WikipediaNaming Each concentration is shown as a percentage of the total aluminium.

Solution equilibria with 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. Precipitation is the formation of a Solid in a Solution during a Chemical reaction. At pH just below 5. 5 the main species present in a 5μM solution of Al³⁺ are aluminium hydroxides Al(OH)²⁺, Al(OH)₂⁺ and Al₁₃(OH)₃₂⁷⁺, but on raising the pH Al(OH)₃ precipitates from the solution. Aluminium hydroxide, Al(OH3 is the most stable form of Aluminium in normal conditions Aluminium hydroxide, Al(OH3 is the most stable form of Aluminium in normal conditions This occurs because Al(OH)₃ has a very large lattice energy. The lattice energy of an ionic solid is a measure of the strength of bonds in that ionic compound As the pH rises more and more Al(OH)₃ comes out of solution. This is an example of Le Chatelier's principle in action: Increasing the concentration of the hydroxide ion causes more aluminium hydroxide to precipitate, which removes hydroxide from the solution. In Chemistry, Le Chatelier's Principle, also called the Le Chatelier-Braun principle, can be used to predict the effect of a change in conditions on a Chemical When the hydroxide concentration becomes sufficiently high the soluble aluminate, Al(OH)₄^-, is formed.

Another common instance where precipitation occurs is when a metal cation interacts with an anionic ligand to form an electrically-neutral complex. If the complex is hydrophopbic, it will precipitate out of water. In Chemistry, hydrophobicity (from the combining form of water in Attic Greek hydro- and for fear phobos) refers to the physical property of 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. Nickel (ˈnɪkəl is a metallic Chemical element with the symbol Ni and Atomic number 28 Dimethylglyoxime is a Chemical compound described by the formula CH3C(NOHC(NOHCH3 Solvation, commonly called dissolution, is the process of attraction and association of Molecules of a Solvent with molecules or Ions of a

Minimization of Gibbs energy

At equilibrium, G is at a minimum:

$dG= \sum_{j=1}^m \mu_j\,dN_j = 0$

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:

$\sum_{j=1}^m a_{ij}N_j=b_i^0$

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

This is a standard problem in optimisation, known as constrained minimisation. In Mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function The most common method of solving it is using the method of Lagrange multipliers, also known as undetermined multipliers (though other methods may be used). In mathematical optimization problems the method of Lagrange multipliers, named after Joseph Louis Lagrange, is a method for finding the extrema of

Define:

$\mathcal{G}= G + \sum_{i=1}^k\lambda_i\left(\sum_{j=1}^m a_{ij}N_j-b_i^0\right)=0$

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

$\frac{\partial \mathcal{G}}{\partial N_j}=0$ and $\frac{\partial \mathcal{G}}{\partial \lambda_i}=0$

(For proof see Lagrange multipliers)

This is a set of (m+k) equations in (m+k) unknowns (the $N j$ and the $λ i$ ) and may, therefore, be solved for the equilibrium concentrations $N j$ as long as the chemical potentials are known as functions of the concentrations at the given temperature and pressure. Multivariable calculus is the extension of Calculus in one Variable to calculus in several variables the functions which are differentiated and integrated involve In mathematical optimization problems the method of Lagrange multipliers, named after Joseph Louis Lagrange, is a method for finding the extrema of (See Thermodynamic databases for pure substances). Thermodynamic databases contain information about thermodynamic properties for substances the most important being Enthalpy, Entropy, and

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. ^[13]

References

^ Atkins & Jones, 2001
^ Gold Book definition Link
^ Chemistry: Matter and Its Changes James E. For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. Equilibrium constants are determined in order to quantify Chemical equilibria. In Electrochemistry, the standard electrode potential, abbreviated Eo E0 or EO (with a superscript Plimsoll character pronounced Thermodynamic databases contain information about thermodynamic properties for substances the most important being Enthalpy, Entropy, and Autocatalytic reactions are Chemical reactions in which at least one of the products is also a Reactant. Compendium of Chemical Terminology (ISBN 0-86542-684-8 is a book published by IUPAC containing internationally accepted definitions for terms in Chemistry. Brady , Fred Senese 4th Ed. ISBN 0471215171
^ Chemical Principles: The Quest for Insight Peter Atkins, Loretta Jones 2nd Ed. ISBN 0716757010
^ Physical Chemistry by Atkins, De Paula
^ P. W. Atkins, Physical Chemistry, Oxford University Press, date
^ a) Mary Jane Schultz. Why Equilibrium? Understanding the Role of Entropy of Mixing. Journal of Chemical Education 1999, 76, 1391. b) Clugston, Michael J. A mathematical verification of the second law of thermodynamics from the entropy of mixing. Journal of Chemical Education 1990, 67, 203.
^ C. W. Davies, Ion Association,Butterworths, 1962
^ ^a ^b I. Grenthe and H. Wanner, Guidelines for the extrapolation to zero ionic strength, http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf
^ F. J,C. Rossotti and H. Rossotti, The Determination of Stability Constants, McGraw-Hill, 1961
^ ^a ^b ^c Concise Encyclopedia Chemistry 1994 ISBN 0899254578
^ M. T. Beck, Chemistry of Complex Equilibria, Van Nostrand, 1970. 2nd. Edition by M. T. Beck and I Nagypál, Akadémiai Kaidó, Budapest, 1990.
^ ^a ^b NASA Reference publication 1311, Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications
^ This approach is described in detail in W. R. Smith and R. W. Missen, Chemical Reaction Equilibrium Analysis: Theory and Algorithms, , Krieger Publishing, Malabar, Fla, 1991 (a reprint, with corrections, of the same title by Wiley-Interscience, 1982). A comprehensive treatment of the theory of chemical reaction equilibria and its computation. Details at http://www.mathtrek.com/
^ The diagram was created with the program HySS

External links

Computer programs for calculating species concentrations

There are n mass-balance equations in n unknown free concentrations. This constitutes a set of non-linear equations that must be solved by a method of successive approximations. The most commonly-used method is the Newton-Raphson method, which has been the subject of numerous publications. In Numerical analysis, Newton's method (also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson) is perhaps the Some general computer programs are listed here.

HySS Titration simulation and speciation calculations.
EQS4WIN A powerful computer program originally developed for gas-phase equilibria but subsequently extended to general applications. Uses the Gibbs energy minimization approach.
CHEMEQLA comprehensive computer program for the calculation of thermodynamic equilibrium concentrations of species in homogeneous and heterogeneous systems. Many geochemical applications.
WinSGW A Windows version of the SOLGASWATER computer program.
Visual MINTEQ A Windows version of MINTEQA2 (ver 4. 0). MINTEQA2 is a chemical equilibrium model for the calculation of metal speciation, solubility equilibria etc. for natural waters.
MINEQL+ A chemical equilibrium modeling system for aqueous systems. Handles a wide range of pH, redox, solubility and sorption scenarios.

Software for chemical equilibria

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

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |

Contents