Equilibrium Constant

The Equilibrium Constant, Kc, relates to a chemical reaction at equilibrium. It can be calculated if the equilibrium concentration of each reactant and product in a reaction at equilibrium is known. The equilibrium expression below, formed from the general chemical equilibrium, is universally true. The chemical components happen to be gases.

aA(g) + bB(g) = cC(g) + dD(g)


The Ideal Gas Equation shows that the pressure of a gas is proprtional to its concentration.

pV = nRT

where p is pressure of a particular gas (its partial pressure) in an equilibrium mixture, V is the total volume, n is the number of moles of the particular gas, R is the general gas constant, and T is the absolute temperature.

In the above equation where the temperature is also constant,

P a n/V

The equilibrium constant can therefore also be expressed in terms of partial pressures, and is denoted as Kp:


There are several types of equilibrium constants. Each is constant at a constant temperature. For example, consider the following ionic equilibrium involving the aqueous solution of a weak acid:

CH3COOH(aq) + H2O(l) = CH3COO-(aq) + H3O+(aq)


Ka is called the 'acid dissociation constant'. Note that water is omitted from the expression because it is present in such vast excess that its concentration changes negligibly on the formation of equilibrium and is therefore effectively constant. The concentration of the water is included in the equilibrium constant, and Ka can be thought of as a modified equilibrium constant

http://www.avogadro.co.uk/definitions/kc.htm

EQUILIBRIUM CONSTANTS: Kc



This page explains what is meant by an equilibrium constant, introducing equilibrium constants expressed in terms of concentrations, Kc. It assumes that you are familiar with the concept of a dynamic equilibrium, and know what is meant by the terms "homogeneous" and "heterogeneous" as applied to chemical reactions.



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Important: If you aren't sure about dynamic equilibria it is important that you follow this link before you go on.

If you aren't sure what homogeneous and heterogeneous mean, you would find it useful to follow this link and read the beginning of the page that you will find (actually on catalysis).

Use the BACK button on your browser to return to this page.



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We need to look at two different types of equilibria (homogeneous and heterogeneous) separately, because the equilibrium constants are defined differently.

A homogeneous equilibrium has everything present in the same phase. The usual examples include reactions where everything is a gas, or everything is present in the same solution.

A heterogeneous equilibrium has things present in more than one phase. The usual examples include reactions involving solids and gases, or solids and liquids.



Kc in homogeneous equilibria

This is the more straightforward case. It applies where everything in the equilibrium mixture is present as a gas, or everything is present in the same solution.

A good example of a gaseous homogeneous equilibrium is the conversion of sulphur dioxide to sulphur trioxide at the heart of the Contact Process:



A commonly used liquid example is the esterification reaction between an organic acid and an alcohol - for example:





Writing an expression for Kc

We are going to look at a general case with the equation:



No state symbols have been given, but they will be all (g), or all (l), or all (aq) if the reaction was between substances in solution in water.

If you allow this reaction to reach equilibrium and then measure the equilibrium concentrations of everything, you can combine these concentrations into an expression known as an equilibrium constant.

The equilibrium constant always has the same value (provided you don't change the temperature), irrespective of the amounts of A, B, C and D you started with. It is also unaffected by a change in pressure or whether or not you are using a catalyst.



Compare this with the chemical equation for the equilibrium. The convention is that the substances on the right-hand side of the equation are written at the top of the Kc expression, and those on the left-hand side at the bottom.

The indices (the powers that you have to raise the concentrations to - for example, squared or cubed or whatever) are just the numbers that appear in the equation.



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Note: If you have come across orders of reaction, don't confuse this with the powers that appear in the rate equation for a reaction. Those powers (the order of the reaction with respect to each of the reactants) are experimentally determined. They don't have any direct connection with the numbers that appear in the equation

You may come across attempts to derive the expression for Kc by writing rate equations for the forward and back reactions. Except in a very limited number of very simple examples, this can't be done! These attempts make the fundamental mistake of obtaining the rate equation from the chemical equation. That's WRONG! Deriving an expression for Kc is impossible at this level of chemistry.

It isn't relevant to this page, but if you want to find out more about orders of reaction, you might like to follow this link at some time in the future.



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Some specific examples

The esterification reaction equilibrium

A typical equation might be:



There is only one molecule of everything shown in the equation. That means that all the powers in the equilibrium constant expression are "1". You don't need to write those into the Kc expression.



As long as you keep the temperature the same, whatever proportions of acid and alcohol you mix together, once equilibrium is reached, Kc always has the same value. At room temperature, this value is approximately 4 for this reaction.

The equilibrium in the hydrolysis of esters

This is the reverse of the last reaction:



The Kc expression is:





If you compare this with the previous example, you will see that all that has happened is that the expression has turned upside-down. Its value at room temperature will be approximately 1/4 (0.25).

It is really important to write down the equilibrium reaction whenever you talk about an equilibrium constant. That is the only way that you can be sure that you have got the expression the right way up - with the right-hand substances on the top and the left-hand ones at the bottom.

The Contact Process equilibrium

You will remember that the equation for this is:



This time the Kc expression will include some visible powers:





Although everything is present as a gas, you still measure concentrations in mol dm-3. There is another equilibrium constant called Kp which is more frequently used for gases. You will find a link to that at the bottom of the page.

The Haber Process equilibrium

The equation for this is:



. . . and the Kc expression is:





Kc in heterogeneous equilibria

Typical examples of a heterogeneous equilibrium include:

The equilibrium established if steam is in contact with red hot carbon. Here we have gases in contact with a solid.



If you shake copper with silver nitrate solution, you get this equilibrium involving solids and aqueous ions:





Writing an expression for Kc for a heterogeneous equilibrium

The important difference this time is that you don't include any term for a solid in the equilibrium expression.

Taking another look at the two examples above, and adding a third one:

The equilibrium produced on heating carbon with steam



Everything is exactly the same as before in the equilibrium constant expression, except that you leave out the solid carbon.





The equilibrium produced between copper and silver ions



Both the copper on the left-hand side and the silver on the right are solids. Both are left out of the equilibrium constant expression.





The equilibrium produced on heating calcium carbonate

This equilibrium is only established if the calcium carbonate is heated in a closed system, preventing the carbon dioxide from escaping.



The only thing in this equilibrium which isn't a solid is the carbon dioxide. That is all that is left in the equilibrium constant expression.





Calculations involving Kc

There are all sorts of calculations you might be expected to do which are centred around equilibrium constants. You might be expected to calculate a value for Kc including its units (which vary from case to case). Alternatively you might have to calculate equilibrium concentrations from a given value of Kc and given starting concentrations.

This is simply too huge a topic to be able to deal with satisfactorily on the internet. It isn't the best medium for learning how to do chemistry calculations. It is much easier to do this from a carefully structured book giving you lots of worked examples and lots of problems to try yourself.

If you have found this site useful, you might like to have a look at my book on chemistry calculations. It covers equilibrium constant calculations starting with the most trivial cases, and gradually getting harder - up to the moderately difficult examples which may be asked in a UK A' level examination.

http://www.chemguide.co.uk/physical/equilibria/kc.html

To determine the amount of each compound that will be present at equilibrium you must know the equilibrium constant. To determine the equilibrium constant you must consider the generic equation:

aA + bB <--> cC + dD
The upper case letters are the molar concentrations of the reactants and products. The lower case letters are the coefficients that balance the equation. Use the following equation to determine the equilibrium constant (K_c).


For example, determining the equilibrium constant of the following equation can be accomplished by using the K_c equation.
Using the following equation, calculate the equilibrium constant.
N₂(g) + 3H₂(g) <--> 2NH₃(g)
A one-liter vessel contains 1.60 moles NH₃, .800 moles N₂, and 1.20 moles of H₂. What is the equilibrium constant?


Answer: 1.85

http://www.cartage.org.lb/en/themes/Sciences/Chemistry/Inorganicchemistry/Equilibrium/Equilibrium/Equilibrium.htm


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Definition of Chemical Equilibrium


Chemical equilibrium applies to reactions that can occur in both directions. In a reaction such as:

CH₄(g) + H₂O(g) <--> CO(g) + 3H₂(g)
The reaction can happen both ways. So after some of the products are created the products begin to react to form the reactants. At the beginning of the reaction, the rate that the reactants are changing into the products is higher than the rate that the products are changing into the reactants. Therefore, the net change is a higher number of products.
Even though the reactants are constantly forming products and vice-versa the amount of reactants and products does become steady. When the net change of the products and reactants is zero the reaction has reached equilibrium. The equilibrium is a dynamic equilibrium. The definition for a dynamic equilibrium is when the amount of products and reactants are constant. (They are not equal but constant. Also, both reactions are still occurring.)
Definition of Chemical Equilibrium | Equilibrium Constant (a.k.a. K_c) | Le Chatelier's Principle | Top of Page

Equilibrium Constant


To determine the amount of each compound that will be present at equilibrium you must know the equilibrium constant. To determine the equilibrium constant you must consider the generic equation:

aA + bB <--> cC + dD The upper case letters are the molar concentrations of the reactants and products. The lower case letters are the coefficients that balance the equation. Use the following equation to determine the equilibrium constant (K_c).

For example, determining the equilibrium constant of the following equation can be accomplished by using the K_c equation.
Using the following equation, calculate the equilibrium constant.
N₂(g) + 3H₂(g) <--> 2NH₃(g)
A one-liter vessel contains 1.60 moles NH₃, .800 moles N₂, and 1.20 moles of H₂. What is the equilibrium constant?

Answer: 1.85
Definition of Chemical Equilibrium | Equilibrium Constant (a.k.a. K_c) | Le Chatelier's Principle | Top of Page

Le Chatelier's Principle


Le Chatelier's principle states that when a system in chemical equilibrium is disturbed by a change of temperature, pressure, or a concentration, the system shifts in equilibrium composition in a way that tends to counteract this change of variable. The three ways that Le Chatelier's principle says you can affect the outcome of the equilibrium are as follows:

• Changing concentrations by adding or removing products or reactants to the reaction vessel.
  
• Changing partial pressure of gaseous reactants and products.
  
• Changing the temperature.
  

These actions change each equilibrium differently, therefore you must determine what needs to happen for the reaction to get back in equilibrium.
Example involving change of concentration:


In the equation

2NO_(g) + O_2(g) <--> 2NO_2(g)
If you add more NO_(g) the equilibrium shifts to the right producing more NO_2(g)
If you add more O_2(g) the equilibrium shifts to the right producing more NO_2(g)
If you add more NO_2(g) the equilibrium shifts to the left producing more NO_(g) and O_2(g)
Example involving pressure change:


In the equation

2SO_2(g) + O_2(g) <--> 2SO_3(g), an increase in pressure will cause the reaction to shift in the direction that reduces pressure, that is the side with the fewer number of gas molecules. Therefore an increase in pressure will cause a shift to the right, producing more product. (A decrease in volume is one way of increasing pressure.)
Example involving temperature change:


In the equation

N_2(g) + 3H_2(g) <--> 2NH₃ + 91.8 kJ, an increase in temperature will cause a shift to the left because the reverse reaction uses the excess heat. An increase in forward reaction would produce even more heat since the forward reaction is exothermic. Therefore the shift caused by a change in temperature depends upon whether the reaction is exothermic or endothermic.

http://library.thinkquest.org/10429/low/equil/equil.htm

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Equilibrium Constant, K


Introduction


The equilibrium between reactants and products is described by an equilibrium constant. For the balanced reaction:
aA + bB cC + dD
The equilibrium constant, K_eq is defined as:
[C]^c [D]^d
K_eq = ---------
[A]^{a b}
where the [] brackets indicate the concentration of the chemical species.

[b]Rules for Writing K Expressions

1. Products are always in the numerator.
   
2. Reactants are always in the denominator.
   
3. Express gas concentrations as partial pressure, P, and dissolved species in molar concentration, [].
   
4. The partial pressures or concentrations are raised to the power of the stoichiometric coefficient for the balanced reaction.
   
5. Leave out pure solids or liquids and any solvent. Only variables will be in a K expression: partial pressure of gases and concentrations of solutes in solution.
   

Example:
Zn _(s) + 2 H⁺_(aq) Zn²⁺_(aq) + H_{2 (g)} P_H[sub]2[/sub] [Zn²⁺]
K = -----------
[H⁺]²

Specific Equilibrium Constants


The equilbrium constant has specific names for several classes of reactions:

1. Gas-phase reactions that use units of partial pressure: K_p
   
2. Dissociation of water: dissociation constant of water, K_w
   
3. Dissociation of acids: acid dissociation constant, K_a
   
4. Reaction of bases with water: base hydrolysis constant, K_b
   
5. Solubility of precipitates: solubility product, K_sp
   
6. Formation of complexes: formation constant, K_f
   

For a general chemical reaction Chemical reaction

A chemical reaction is a process that results in the interconversion of chemical substances . The substance or substances initially involved in a chemical reaction are called reactants....
the equilibrium constant can be defined by where is the activity Activity (chemistry)

Activity in chemistry is a measure of how different molecules in a non-ideal gas or solution interact with each other....
of the chemical species A etc (activity is a dimensionless quantity). It is conventional to put the activities of the products in the numerator and those of the reactants in the denominator. See Chemical equilibrium Chemical equilibrium

Chemical equilibrium is the state in which the concentrations of the reactants and products have no net change over time....
for a derivation of this expression.

For equilibria in a gas phase, the activity of a gaseous component is the product of the component's partial pressure Partial pressure

In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume....
and the fugacity Fugacity

What is Fugacity?Fugacity is initially a hard concept to grasp since it was completely invented....
coefficient for this component. In this case activity is dimensionless as fugacity has the dimension Dimension

In common usage, a dimension is a parameter or measurement required to define the characteristics of an object—i.e. length, width, and height or size and shape....
1/pressure.

For equilibria in solution activity is the product of concentration Concentration

In chemistry, concentration is the measure of how much of a given chemical substance there is mixed with another substance....
and activity coefficient Activity (chemistry)

Activity in chemistry is a measure of how different molecules in a non-ideal gas or solution interact with each other....
. It is common practice to determine equilibrium constants in a medium of high ionic strength Ionic strength

The ionic strength of a solution is a function of the concentration of ions in a solution.where is the molarity concentration of ion , is the charge of that ion, and the sum is taken over all ions in the solution....
. In those circumstances the quotient of activity coefficients is effectively constant and the equilibrium constant is taken to be a concentration quotient. However, the value of K_c will depend on the ionic strength. All equilibrium constants depend on temperature and pressure (or volume).

A knowledge of equilibrium constants is essential for the understanding of many natural processes such as oxygen transport by haemoglobin in blood and acid-base homeostasis Acid-base homeostasis

Acid-base homeostasis is the part of human homeostasis concerning the proper balance between acids and Chemical base, in other words the pH....
in the human body.

Stability constants, formation constants, binding constants, association constants and dissociation constants are all types of equilibrium constant. See also Determination of equilibrium constants Determination of equilibrium constants

Equilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant is expressed as a concentration quotient,...
for experimental and computational methods.


Types of equilibrium constants


Cumulative and stepwise formation constants

A cumulative or overall constant, given the symbol , is the constant for the formation of a complex from reagents. For example, the cumulative constant for the formation of ML₂ is given by The stepwise constant, K, for the formation of the same complex from ML and L is given by It follows that A cumulative constant can always be expressed as the product of stepwise constants. There is no agreed notation for stepwise constants, though a symbol such as is sometimes found in the literature. It is best always to define each stability constant by reference to an equilibrium expression.


Competition method

A particular use of a stepwise constant is in the determination of stability constant values outside the normal range for a given method. For example, EDTAEDTA

EDTA is the chemical compound ethylenediaminetetraacetic acid. EDTA is a chelating agent, forming complexs with most monovalent, divalent, trivalent and tetravalent metal ions, such as silver, calcium, manganese, copper, iron and zirconiu...
complexes of many metals are outside the range for the potentiometric method. The stability constants for those complexes were determined by competition with a weaker ligand.


Association and dissociation constants

In organic chemistry and biochemistry it is customary to use pK_a values for acid dissociation equilibria. where K_diss is a stepwise acid dissociation constantAcid dissociation constant

In chemistry and biochemistry, the acid dissociation constant, the acidity constant, or the acid-ionization constant is a specific type of equilibrium constant that indicates the extent of dissociation of hydrogen ions from an ac...
(lg stands for log₁₀). For bases, the base association constant, pK_b is used. For any given acid or base the two constants are related by pK_a + pK_b = pK_w, so pK_a can always be used in calculations.

On the other hand stability constants for metal complexes, and binding constants for host-guestHost-guest chemistry

In supramolecular chemistry, host-guest chemistry describes complex that are composed of two or more molecules or ions held together in unique structural relationships by hydrogen bonding or by ion pairing or by Van der Waals force other than ...
complexes are generally expressed as association constants. When considering equilibria such as it is customary to use association constants for both ML and HL. Also, in generalised computer programs dealing with equilibrium constants it is general practice to use cumulative constants rather than stepwise constants and to omit ionic charges from equilibrium expressions. For example, if NTA, nitrilotriacetic acidNitrilotriacetic acid

Nitrilotriacetic acid is a chemical compound used as a chelating agent which forms coordination compounds with metal ions such as Ca2+, Cu2+ or Fe3+....
, HC(CH₂CO₂H)₃ is designated as H₃L and forms complexes ML and MHL with a metal ion M, the following expressions would apply for the dissociation constants. The cumulative association constants can be expressed as Note how the subscripts define the stoichiometry of the equilibrium product.


Micro-constants

When two or more sites in an asymmetrical molecule may be involved in an equilibrium reaction there are more than one possible equilibrium constants. For example, the molecule L-dopaLevodopa

Levodopa or L-DOPA is an intermediate in dopamine biosynthesis. Clinically, levodopa is used in the management of Parkinson's disease....
has two non-equivalent hydroxyl groups which may be deprotonated. Denoting L-Dopa as LH₂, the following diagram shows all the species that may be formed (X=CH₂CH(NH₂)CO₂H)

The first protonation constants are

[L¹H] = k₁₁[L][H], [L²H] = k₁₂[L][H] The concentration of LH^- is the sum of the concentrations of the two micro-species. Therefore, the equilibrium constant for the reaction, the macro-constant, is the sum of the micro-constants.

K₁ = k₁₁ + k₁₂ In the same way,

K₂ = k₂₁ + k₂₂ Lastly, the cumulative constant is

&szlig;₂=K₁K₂=k₁₁k₂₁=k₁₂k₂₂ Thus, although there are six micro-and macro-constants, only three of them are mutually independent. Moreover, the isomerization constant, K_i, is equal to the ratio of the microconstants.

K_i=k₁₁/k₁₂ In L-Dopa the isomerization constant is 0.9, so the micro-species L¹H and L²H have almost equal concentrations at all pH values.

In general a macro-constant is equal to the sum of all the micro-constants and the occupancy of each site is proportional to the micro-constant. The site of protonation can be very important, for example, for biological activity.

Micro-constants cannot be determined individually by the usual methods Determination of equilibrium constants

Equilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant is expressed as a concentration quotient,...
, which give macro-constants. Methods which have been used to determine micro-constants include:

• blocking one of the sites, for example by methylation of a hydroxyl group, to determine one of the micro-constants
  
• using a spectroscopic technique, such as infrared spectroscopy Infrared spectroscopy
  
  Infrared spectroscopy is the subset of spectroscopy that deals with the Infrared part of the electromagnetic spectrum....
  , where the different micro-species give different signals.
  
• applying mathematical procedures to ¹³C NMR data.
  

pH considerations (Br&oslash;nsted constants)

pH PH

pH is a measure of the acid of a solution, in terms of Activity of hydrogen ions . For dilute solutions, however, it is convenient to substitute the activity of the hydrogen ions with the molarity of the hydrogen ions ....
is defined in terms of the activity Activity (chemistry)

Activity in chemistry is a measure of how different molecules in a non-ideal gas or solution interact with each other....
of the hydrogen ion If, when determining an equilibrium constant, pH is measured by means of a glass electrode, a mixed equilibrium constant, also known as a Br&oslash;nsted constant, may result. It all depends on whether the electrode is calibrated by reference to solutions of known activity or known concentration. In the latter case the equilibrium constant would be a concentration quotient. If the electrode is calibrated in terms of known hydrogen ion concentrations it would be better to write p[H] rather than pH, but this suggestion is not generally adopted.

Hydrolysis constants

In aqueous solution the concentration of the hydroxide ion is related to the concentration of the hydrogen ion by The first step in metal ion hydrolysis Hydrolysis

Hydrolysis is a chemical reaction or process in which a molecule is split into two parts by reacting with a molecule of Water , which has the chemical formula Hydrogen2Oxygen....
can be expressed in two different ways

1. 
   
2. 
   

It follows that . Hydrolysis constants are usually reported in the form and this leads to them appearing to have strange values. For example, if lgK=4 and lg K_W=-14, lg = 4 -14 = -10. In general when the hydrolysis product contains n hydroxide groups lg = lg K + n lg K_W

Conditional constants

Conditional constants, also known as apparent constants, are concentration quotients which are not true equilibrium constants but can be derived from them. A very common instance is where pH is fixed at a particular value. For example, in the case of iron(III) interacting with EDTA, a conditional constant could be defined by This conditional constant will vary with pH. It has a maximum at a certain pH. That is the pH where the ligand sequesters the metal most effectively.

In biochemistry equilibrium constants are often measured at a pH fixed by means of a buffer solution Buffer solution

Buffer solutions are solutions which resist change in hydronium ion and the hydroxide ion concentration upon addition of small amounts of acid or base , or upon dilution....
. Such constants are, by definition, conditional and different values may be obtained when using different buffers.

Temperature dependence


The van 't Hoff equation. shows that when the reaction is exothermic (?H^o is negative), then K decreases with increasing temperature, in accordance with Le Chatelier's principle Le Châtelier's principle

In chemistry, Le Chtelier's principle can be used to predict the effect of a change in conditions on a chemical equilibrium....
. It permits calculation of the reaction equilibrium constant at temperature T₂ if the reaction constant at T₁ is known and the standard reaction enthalpy can be assumed to be independent of temperature even though each standard enthalpy change is defined at a different temperature.However, this assumption is valid only for small temperature differences T₂ - T₁. In fact standard thermodynamic arguments can be used to show that where C_p is the heat capacity Specific heat capacity

Specific heat capacity, also known simply as specific heat is the measure of the energy required to raise the temperature of a specific quantity of a substance by certain amount, usually one kelvin....
at constant pressure The equilibrium constant is related to the standard Gibbs energy change of reaction as where ?G^o is the standard Gibbs energy change of reaction, R is the gas constant Gas constant

The gas constant is a physical constant used in equations of state to relate various groups of state functions to one another....
, and T the absolute temperature.

If the equilibrium constant has been determined and the standard reaction enthalpy has also been determined, by calorimetry, for example, this equation allows the standard entropy change for the reaction to be derived.

A more complex formulation

The calculation of K_T2 from known K_T1 can be approached as follows if standard thermodynamic properties are available. The effect of temperature on equilibrium constant is equivalent to the effect of temperature on Gibbs energy because:

where is the reaction standard Gibbs energy, which is the sum of the standard Gibbs energies of the reaction products minus the sum of standard Gibbs energies of reactants.

Here, the term "standard" denotes the ideal behaviour (i.e., an infinite dilution) and a hypothetical standard concentration (typically 1 mol/kg). It does not imply any particular temperature or pressure because, although contrary to IUPAC recommendation, it is more convenient when describing aqueous systems over a wide temperature and pressure ranges.

The standard Gibbs energy (for each species or for the entire reaction) can be represented (from the basic definitions) as:

In the above equation, the effect of temperature on Gibbs energy (and thus on the equilibrium constant) is ascribed entirely to heat capacity. To evaluate the integrals in this equation, the form of the dependence of heat capacity on temperature needs to be known.

Now, if one expresses the standard heat capacity , as a function of absolute temperature using correlations in on of the following forms:

• For pure substances (solids, gas, liquid):
  
• For ionic species at T < 200 deg C:
  

then the integrals can evaluated and the following final form is obtained:

The constants A,B,C,a,b and the absolute entropy, , required for evaluation of , as well as the values of G_{298 K} and S_{298 K} for many species are tabularized in the literature.

Pressure dependence

The pressure dependence of the equilibrium constant is usually weak in the range of pressures normally encountered in industry, and therefore, it is usually neglected in practice. This is true for condensed Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter....
reactant/products (i.e., when reactants and products are solids or liquid) as well as gaseous ones.

For a gaseous-reaction example, one may consider the well-studied reaction of hydrogen with nitrogen to produce ammonia:

If the pressure is increased by an addition of an inert gas, then neither the composition at equilibrium nor the equilibrium constant are appreciably affected (because the partial pressures remain constant, assuming an ideal-gas behaviour of all gases involved). However, the composition at equilibrium will depend appreciably on pressure when:

• the pressure is changed by compression of the gaseous reacting system, and
  
• the reaction results in the change of the number of moles of gas in the system.
  

In the example reaction above, the number of moles changes from 4 to 2, and an increase of pressure by system compression will result in appreciably more ammonia in the equilibrium mixture. In the general case of a gaseous reaction:

the change of mixture composition with pressure can be quantified using:

where p denote the partial pressures of the components, P is the total system pressure, X denote the number of moles, K_p is the equilibrium constant expressed in terms of partial pressures and K_X is the equilibrium constant expressed in terms of mol fractions.

The above change in composition is in accordance with Le Chatelier's principle Le Châtelier's principle

In chemistry, Le Chtelier's principle can be used to predict the effect of a change in conditions on a chemical equilibrium....
and does not involve any change of the equilibrium constant with the total system pressure. Indeed, for ideal-gas reactions K_p is independent of pressure.

In a condensed phase, the pressure dependence of the equilibrium constant is associated with the reaction molar volume. For reaction:

the reaction molar volume is:

where denotes a partial molar volume Partial molar volume

Partial molar volumes are applicable to real mixtures, including solutions, in which the volumes of the separate, initial components do not sum to the total....
of a reactant or a product.

For the above reaction, one can expect the change of the reaction equilibrium constant (based either on mole-fraction or molal-concentration scale) with pressure at constant temperature to be:

The matter is complicated as partial molar volume is itself dependent on pressure.

The Equilibrium Constant

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A chemical reaction will occur if the total free energy of the products is less than the total free energy of the reactants. (ie. The free energy change for the reaction is negative.) If the system containing the reactants and products is closed (if there is no input of reactants, for example), the concentration of reactants will decrease and the concentration of products will increase as the reaction proceeds. This will alter the state of the system and therefore alter the free energy change for the reaction (see equation 14, above).
The reaction will continue if the free energy change remains negative. Hence, the system proceeds down a free energy gradient with respect to composition and this gradient provides the driving force for the reaction to proceed. The system alters the quantities of reactants and products in response to the driving force until a minimum in free energy is reached and the gradient is zero. This is a point of equilibrium.
At equilibrium the free energy change for the reaction is equal to zero:


Therefore
(15)

For the composition at equilibrium, the quotient is equal to K_P - the equilibrium constant for the reaction at constant pressure. We see that the equilibrium composition of the system is defined by the standard free energy change, ΔG°. Equation 15 provides a link between the thermodynamics of a reaction and its chemistry. ΔG° for a reaction is hence a very useful value to know.

http://www.yteach.com/page.php/resources/view_all?id=reaction_reversible_irreversible_state_equilibrium_constant_page_3&from=search

http://nvl.nist.gov/pub/nistpubs/jres/041/1/V41.N01.A02.pdf

Acid-Base Equilibrium Constant

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