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| :''For the economic concept, see [[Dynamic equilibrium (economics)]]
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| A '''dynamic equilibrium''' exists once a [[reversible reaction]] ceases to change its ratio of reactants/products, but substances move between the chemicals at an equal rate, meaning there is no net change. It is a particular example of a system in a [[steady state]]. In [[thermodynamics]] a [[closed system]] is in [[thermodynamic equilibrium]] when reactions occur at such rates that the composition of the mixture does not change with time. Reactions do in fact occur, sometimes vigorously, but to such an extent that changes in composition cannot be observed. Equilibrium constants can be expressed in terms of the rate constants for elementary reactions.
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| == Examples ==
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| In a new bottle of cola the concentration of [[carbon dioxide]] in the liquid phase has a particular value. If half of the liquid is poured out and the bottle is sealed, carbon dioxide will leave the liquid phase at an ever decreasing rate and the [[partial pressure]] of carbon dioxide in the gas phase will increase until equilibrium is reached. At that point, due to thermal motion, a molecule of CO<sub>2</sub> may leave the liquid phase, but within a very short time another molecule of CO<sub>2</sub> will pass from the gas to the liquid, and vice-versa. At equilibrium the rate of transfer of CO<sub>2</sub> from the gas to the liquid phase is equal to the rate from liquid to gas. In this case, the equilibrium concentration of CO<sub>2</sub> in the liquid is given by [[Henry's law]], which states that the solubility of a gas in a liquid is directly proportional to the [[partial pressure]] of that gas above the liquid.<ref>Atkins, Section 5.3</ref> This relationship is written as
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| :<math> c = kp \,</math>
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| where ''k'' is a temperature-dependent constant, ''p'' is the partial pressure and ''c'' is the concentration of the dissolved gas in the liquid. Thus, the partial pressure of CO<sub>2</sub> in the gas has increased until Henry's law is obeyed. The concentration of carbon dioxide in the liquid has decreased and the drink has lost some of its fizz.
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| Henry's law may be derived by setting the [[chemical potential]]s of carbon dioxide in the two phases to be equal to each other. Equality of chemical potential defines [[chemical equilibrium]]. Other constants for dynamic equilibrium involving phase changes include [[partition coefficient]] and [[solubility product]]. [[Raoult's law]] defines the equilibrium [[vapor pressure]] of an [[ideal solution]].
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| Dynamic equilibria can also exist in a single-phase system. A simple example occurs with [[acid-base]] equilibria such as the "dissociation" of [[acetic acid]], in aqueous solution.
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| : CH<sub>3</sub>CO<sub>2</sub>H {{Eqm}} CH<sub>3</sub>CO<sub>2</sub><sup>-</sup> + H<sup>+</sup>
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| At equilibrium the [[concentration (chemistry)|concentration]] quotient, ''K'', the [[acid dissociation constant]], is constant (subject to some conditions)
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| :<math>K_c=\mathrm{\frac{[CH_3CO_2^-][H^+]}{[CH_3CO_2H]}}</math>
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| In this case, the forward reaction involves the liberation of some [[proton]]s from acetic acid molecules and the backward reaction involves the formation of acetic acid molecules when an acetate ion accepts a proton. Equilibrium is attained when the sum of chemical potentials of the species on the left-hand side of the equilibrium expression is equal to the sum of chemical potentials of the species on the right-hand side. At the same time the rates of forward and backward reactions are equal to each other. Equilibria involving the formation of [[chemical complex]]es are also dynamic equilibria and concentrations are governed by the [[stability constants of complexes]].
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| Dynamic equilibria can also occur in the gas phase as, for example, when [[nitrogen dioxide]] dimerizes.
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| :2NO<sub>2</sub> {{Eqm}} N<sub>2</sub>O<sub>4</sub>; <math>K_P=\mathrm{ \frac{P(N_2O_4)}{P(NO_2)^2} }</math>
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| In the gas phase, square brackets are not used as these indicate a concentration, instead a capitalised P is used to indicate partial pressure.<ref>{{cite book|last=Denbeigh|first=K|title=The principles of chemical equilibrium|publisher=Cambridge University Press |location=Cambridge, U.K.|year=1981|edition=4th.|isbn=0-521-28150-4}}</ref>
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| ==Relationship between equilibrium and rate constants==
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| In a simple reaction such as the [[isomerization]]:
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| :<math> A \rightleftharpoons B </math>
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| there are two reactions to consider, the forward reaction in which the species A is converted into B and the backward reaction in which B is converted into A. If both reactions are [[elementary reaction]]s, then the [[rate of reaction]] is given by<ref>Atkins, Section 22.4</ref>
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| :<math>\frac{d[A]}{dt}=-k_f[A]_t+k_b[B]_t</math>
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| where ''k<sub>f</sub>'' is the [[rate constant]] for the forward reaction and ''k<sub>b</sub>'' is the rate constant for the backward reaction and the square brackets, [..] denote [[concentration]] . If only A is present at the beginning, time ''t''=0, with a concentration [A]<sub>0</sub>, the sum of the two concentrations, [A]<sub>''t''</sub> and [B]<sub>''t''</sub>, at time ''t'', will be equal to [A]<sub>0</sub>.
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| :<math>\frac{d[A]}{dt}= -k_f[A]_t+k_b\left([A]_0-[A]_t\right) </math>
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| [[Image:Dynamic equilibrium.png|thumb|% concentrations of species in isomerization reaction. k<sub>f</sub> = 2 s<sup>-1</sup>, k<sub>r</sub> = 1 s<sup>-1</sup>]]
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| The solution to this differential equation is
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| :<math>[A]_t=\frac{k_b+k_fe^{-\left(k_f+k_b\right)t}}{k_f+k_b}[A]_0</math>
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| and is illustrated at the right. As time tends towards infinity, the concentrations [A]<sub>t</sub> and [B]<sub>t</sub> tend towards constant values. Let ''t'' approach infinity, that is, ''t''→∞, in the expression above:
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| :<math>[A]_\infty =\frac{k_b}{k_f+k_b}[A]_0;[B]_\infty =\frac{k_f}{k_f+k_b}[A]_0 </math>
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| In practice, concentration changes will not be measurable after <math>t \gtrapprox \frac{10}{k_f+k_b}</math>. Since the concentrations do not change thereafter, they are, by [[equilibrium chemistry|definition]], equilibrium concentrations. Now, the [[equilibrium constant]] for the reaction is defined as
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| :<math>K=\frac{[B]_{eq}}{[A]_{eq}}</math> | |
| It follows that the equilibrium constant is numerically equal to the quotient of the rate constants.
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| :<math>K=\frac{\frac{k_f}{k_f+k_b}[A]_0 }{\frac{k_b}{k_f+k_b}[A]_0}=\frac{k_{f}}{k_{b}}</math>
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| In general they may be more than one forward reaction and more than one backward reaction. Atkins states<ref>Atkins, Section 22.4</ref> that, for a general reaction, the overall equilibrium constant is related to the rate constants of the elementary reactions by
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| :<math>K=\left(\frac{k_f}{k_b}\right)_1\times \left(\frac{k_f}{k_b}\right)_2\dots </math> .
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| ==See also==
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| *[[Equilibrium chemistry]]
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| * [[Static equilibrium]]
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| *[[Chemical equilibrium]]
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| *[[Radiative equilibrium]]
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| == References ==
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| {{cite book |title=Physical Chemistry |last=Atkins |first=P.W. |coauthors=de Paula, J. |year=2006 | publisher=Oxford University Press |edition=8th.|isbn=0-19-870072-5}}
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| {{reflist}}
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| == External Links ==
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| http://demonstrations.wolfram.com/DynamicEquilibriumExample/
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| {{chemical equilibria}}
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| {{DEFAULTSORT:Dynamic Equilibrium}}
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| [[Category:Equilibrium chemistry]]
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| [[Category:Thermodynamics]]
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Book or Script Editor Alonso Salminen from St. Albert, has hobbies including studying an instrument, deer hunter 2014 hack and cooking. Preceding year just completed a trip Stone Town of Zanzibar.
My homepage; deer hunter 2014 hack ios