digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Business

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

For the economic concept, see Dynamic equilibrium (economics)

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.

Examples[edit]

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 CO2 may leave the liquid phase, but within a very short time another molecule of CO2 will pass from the gas to the liquid, and vice-versa. At equilibrium the rate of transfer of CO2 from the gas to the liquid phase is equal to the rate from liquid to gas. In this case, the equilibrium concentration of CO2 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.[1] This relationship is written as

 c = kp \,

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 CO2 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.

Henry's law may be derived by setting the chemical potentials 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.

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.

CH3CO2H is in equilibrium with CH3CO2- + H+

At equilibrium the concentration quotient, K, the acid dissociation constant, is constant (subject to some conditions)

K_c=\mathrm{\frac{[CH_3CO_2^-][H^+]}{[CH_3CO_2H]}}

In this case, the forward reaction involves the liberation of some protons 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 complexes are also dynamic equilibria and concentrations are governed by the stability constants of complexes.

Dynamic equilibria can also occur in the gas phase as, for example, when nitrogen dioxide dimerizes.

2NO2 is in equilibrium with N2O4; K_P=\mathrm{ \frac{P(N_2O_4)}{P(NO_2)^2}   }

In the gas phase, square brackets are not used as these indicate a concentration, instead a capitalised P is used to indicate partial pressure.[2]

Relationship between equilibrium and rate constants[edit]

In a simple reaction such as the isomerization:

 A \rightleftharpoons B

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 reactions, then the rate of reaction is given by[3]

\frac{d[A]}{dt}=-k_f[A]_t+k_b[B]_t

where kf is the rate constant for the forward reaction and kb 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]0, the sum of the two concentrations, [A]t and [B]t, at time t, will be equal to [A]0.

\frac{d[A]}{dt}= -k_f[A]_t+k_b\left([A]_0-[A]_t\right)
% concentrations of species in isomerization reaction. kf = 2 s-1, kr = 1 s-1

The solution to this differential equation is

[A]_t=\frac{k_b+k_fe^{-\left(k_f+k_b\right)t}}{k_f+k_b}[A]_0

and is illustrated at the right. As time tends towards infinity, the concentrations [A]t and [B]t tend towards constant values. Let t approach infinity, that is, t→∞, in the expression above:

[A]_\infty =\frac{k_b}{k_f+k_b}[A]_0;[B]_\infty =\frac{k_f}{k_f+k_b}[A]_0

In practice, concentration changes will not be measurable after t \gtrapprox \frac{10}{k_f+k_b}. Since the concentrations do not change thereafter, they are, by definition, equilibrium concentrations. Now, the equilibrium constant for the reaction is defined as

K=\frac{[B]_{eq}}{[A]_{eq}}

It follows that the equilibrium constant is numerically equal to the quotient of the rate constants.

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}}

In general they may be more than one forward reaction and more than one backward reaction. Atkins states[4] that, for a general reaction, the overall equilibrium constant is related to the rate constants of the elementary reactions by

K=\left(\frac{k_f}{k_b}\right)_1\times \left(\frac{k_f}{k_b}\right)_2\dots .

See also[edit]

References[edit]

Atkins, P.W.; de Paula, J. (2006). Physical Chemistry (8th. ed.). Oxford University Press. ISBN 0-19-870072-5. 

  1. ^ Atkins, Section 5.3
  2. ^ Denbeigh, K (1981). The principles of chemical equilibrium (4th. ed.). Cambridge, U.K.: Cambridge University Press. ISBN 0-521-28150-4. 
  3. ^ Atkins, Section 22.4
  4. ^ Atkins, Section 22.4

External Links[edit]

http://demonstrations.wolfram.com/DynamicEquilibriumExample/


Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Dynamic_equilibrium — Please support Wikipedia.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
228015 videos foundNext > 

What is Dynamic Equilibrium? | The Chemistry Journey | The Fuse School

Learn about dynamic equilibrium, the conditions required for dynamic equilibrium to be reached and examples of systems at equilibrium. At Fuse School, teache...

Dynamic Equilibrium - PANGEA (Official Video)

Post Crack Era on iTunes: https://itunes.apple.com/us/album/post-crack-era/id848355392 Directed by: Genmotion Contact info: contact@genmotion.com DynamicEqui...

Dynamic Equilibrium

Dynamic Equilibrium. A-Level Chemistry teaching/revision resource.

Dynamic Equilibrium | Age of Enlightenment feat. ScienZe

Download: https://soundcloud.com/dynamicequilibriumnyc/age-of-enlightenment-ft Post Crack Era on iTunes: https://itunes.apple.com/us/album/post-crack-era/id848355392 Directed by: Genmotion...

Dynamic Equilibrium - Lucidity ( Presented by GENMOTION)

http://hiphoppush.com New video just dropped by Dynamic called "Equilibrium" We do not own copyright to this video. No copyright infringement intended.

Chemistry: The Concept of Equilibrium

http://www.mindbites.com/lesson/1292 for full video. http://www.mindbites.com/series/501 for a bundle of videos on Principles of Chemical Equilibrium. For an...

Equilibrium Simplified (dynamic chemical equilibrium)

This is really simplified, I am not joking. This short video explains one of the toughest concepts in chemistry down to just 3 words. Dynamic chemical equili...

Static and Dynamic Equilibrium

http://www.aklectures.com/lecture/static-and-dynamic-equilibrium The website organizes the videos into clear and structured chapters that you can use to watc...

7.1: Dynamic Equilibrium

Dynamic Equilibrium.

dynamic equilibrium

CLHS Honors Chem: Chemical Equilibrium.

228015 videos foundNext > 

13 news items

 
Flathead Publishing Group
Wed, 27 Aug 2014 01:15:00 -0700

Before installing the demonstration buffer, the landowners wanted to replace their crumbling seawall with a dynamic equilibrium beach. Dynamic equilibrium beaches are a natural looking alternative to seawalls that disburse wave energy better than ...
 
Daily Herald
Thu, 14 Aug 2014 00:16:17 -0700

They thus have formed an integrated set of species, including predators and parasites and their hosts, which have come to a sort of dynamic equilibrium. When a new invasive species arrives, it may sometimes not be able to survive, or survive only to a ...
 
Jakarta Post
Fri, 15 Aug 2014 23:37:45 -0700

He said that the country had established strategic cooperation with world powers and emerging countries alike in order to strike a dynamic equilibrium that could withstand geopolitical shifts and ensure they did not breed additional conflicts. “We are ...

Lawfare (blog)

Lawfare (blog)
Fri, 01 Aug 2014 11:00:00 -0700

Some might see it as a dynamic equilibrium, behavioral move and technological countermove (or technological move and behavioral countermove, if you prefer). It is unlikely to remain in equilibrium forever, however. Over time, I believe, a side can ...

BeritaSatu

BeritaSatu
Fri, 22 Aug 2014 06:18:45 -0700

Pada kesempatan itu, Yuli menyampaikan capaian-capaian yang diraih pemerintah di bidang politik luar negeri. Disebutkan, selama ini Indonesia tetap konsisten menerapkan kebijakan “Thousand Friends, Zero Enemy” serta menjaga “dynamic equilibrium. ”.

SINDOnews.com

Okezone
Thu, 14 Aug 2014 20:56:15 -0700

Pemerintah terus mengupayakan keseimbangan dinamis atau dynamic equilibrium agar tidak menimbulkan konflik. Konflik seperti yang terjadi di Ukraina, telah menimbulkan ketidakseimbangan dan bahkan ada warga negara Indonesia (WNI) yang turut ...
 
Harian Medan Bisnis - Membangun Indonesia yang Lebih Baik
Thu, 14 Aug 2014 23:22:00 -0700

"Kita juga terus mengupayakan keseimbangan yang dinamis, dynamic equilibrium, di kawasan, sehingga pergeseran geopolitik yang kini sedang terjadi tidak mengakibatkan ketegangan atau konflik baru," imbuh Presiden SBY.(dtc). Iklan Baris Gratis Dilihat ...
 
Pikiran Rakyat
Thu, 14 Aug 2014 21:18:45 -0700

Kita juga terus mengupayakan keseimbangan yang dinamis – dynamic equilibrium -- di kawasan, sehingga pergeseran geopolitik yang kini sedang terjadi tidak mengakibatkan ketegangan atau konflik baru. Yang jelas, situasi internasional yang kita hadapi ...
Loading

Oops, we seem to be having trouble contacting Twitter

Talk About Dynamic equilibrium

You can talk about Dynamic equilibrium with people all over the world in our discussions.

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!