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Reversible reaction

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From Wikipedia, the free encyclopedia
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  1. Reversible reaction

A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously.

A and B can react to form C and D or, in the reverse reaction, C and D can react to form A and B. This is distinct from a reversible process in thermodynamics.

Weak acids and bases undergo reversible reactions. For example, carbonic acid:

H2CO3(aq) + H2O(l) ⇌ HCO−3(aq) + H3O+(aq)

The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents (A and B or C and D) and the equilibrium constant, K. The magnitude of the equilibrium constant depends on the Gibbs free energy change for the reaction.1 So, when the free energy change is large (more than about 30 kJ·mol−1), the equilibrium constant is large (log K > 3) and the concentrations of the reactants at equilibrium are very small. Such a reaction is sometimes considered to be an irreversible reaction, although small amounts of the reactants are still expected to be present in the reacting system. A truly irreversible chemical reaction is usually achieved when one of the products exits the reacting system, for example, as does carbon dioxide (volatile) in the reaction

CaCO3 + 2 HCl → CaCl2 + H2O + CO2↑

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Where Reversible reaction leads. Every connection below has a source: a link in this article, a shared Wikipedia category, or CirrusSearch text similarity. Articles already on your trail are left out.

Contents
  • (Top)
  • History
  • Reaction kinetics
  • See also
  • References
  • Recent changes
  • Rabbit hole
Contents
Contents6 sections
  • (Top)
  • History
  • Reaction kinetics
  • See also
  • References
  • Recent changes
  • Rabbit hole
Categories:
  • Equilibrium chemistry
  • Physical chemistry

516 words · 3 references · revision 1351833404 · CC BY-SA 4.0

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Key concepts

  • Reversible process (thermodynamics)1
  • Thermodynamics1
  • Acids1
  • Base (chemistry)1
  • Carbonic acid1
  • Concentration1
  • Analytical concentration1
  • Equilibrium constant1
  • Gibbs free energy1
  • Claude Louis Berthollet1

The articles this one links to most, weighted towards the introduction.

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History

The concept of a reversible reaction was introduced by Claude Louis Berthollet in 1803, after he had observed the formation of sodium carbonate crystals at the edge of a salt lake2 (one of the natron lakes in Egypt, in limestone):

2 NaCl + CaCO3 → Na2CO3 + CaCl2

He recognized this as the reverse of the familiar reaction

Na2CO3 + CaCl2 → 2 NaCl + CaCO3

Until then, chemical reactions were thought to always proceed in one direction. Berthollet reasoned that the excess of salt in the lake helped push the "reverse" reaction towards the formation of sodium carbonate.3

In 1864, Peter Waage and Cato Maximilian Guldberg formulated their law of mass action which quantified Berthollet's observation. Between 1884 and 1888, Le Chatelier and Braun formulated Le Chatelier's principle, which extended the same idea to a more general statement on the effects of factors other than concentration on the position of the equilibrium.

Reaction kinetics

For the reversible reaction A⇌B, the forward step A→B has a rate constant k1k_{1}k1​ and the backwards step B→A has a rate constant k−1k_{-1}k−1​. The concentration of A obeys the following differential equation:

d[A]dt=−k1[A]+k-1[B]{\frac {d[\mathrm {A} ]}{dt}}=-k_{\text{1}}[\mathrm {A} ]+k_{\text{-1}}[\mathrm {B} ]dtd[A]​=−k1​[A]+k-1​[B]

See also

  • Dynamic equilibrium
  • Chemical equilibrium
  • Irreversibility
  • Microscopic reversibility
  • Static equilibrium

References

  1. 1at constant pressure.
  2. 2How did Napoleon Bonaparte help discover reversible reactions?. Chem1 General Chemistry Virtual Textbook: Chemical Equilibrium Introduction: reactions that go both ways.
  3. 3Claude-Louis Berthollet,"Essai de statique chimique", Paris, 1803. (Google books)
Study aids for Reversible reaction

Equations (12)

  • {\ce {{\mathit {a}}\;A{}+{\mathit {b}}\;B<=>{\mathit {c}}\;C{}+{\mathit {d}}\;D}}
  • d[A]dt=−k1[A]+k-1[B]{\frac {d[\mathrm {A} ]}{dt}}=-k_{\text{1}}[\mathrm {A} ]+k_{\text{-1}}[\mathrm {B} ]dtd[A]​=−k1​[A]+k-1​[B]Reaction kinetics
  • [B]=[A]0−[A][\mathrm {B} ]=[\mathrm {A} ]_{\text{0}}-[\mathrm {A} ][B]=[A]0​−[A]Reaction kinetics
  • d[A]dt=−k1[A]+k-1([A]0−[A]){\frac {d[\mathrm {A} ]}{dt}}=-k_{\text{1}}[\mathrm {A} ]+k_{\text{-1}}([\mathrm {A} ]_{\text{0}}-[\mathrm {A} ])dtd[A]​=−k1​[A]+k-1​([A]0​−[A])
  • C=−ln⁡(−k1[A]0)k1+k-1C={\frac {{-\ln }(-k_{\text{1}}[\mathrm {A} ]_{\text{0}})}{k_{\text{1}}+k_{\text{-1}}}}C=k1​+k-1​−ln(−k1​[A]0​)​
  • [A]=k-1[A]0k1+k-1+k1[A]0k1+k-1exp⁡(−k1−k-1)t[\mathrm {A} ]={\frac {k_{\text{-1}}[\mathrm {A} ]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}+{\frac {k_{\text{1}}[\mathrm {A} ]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}\exp {{(-k_{\text{1}}-k_{\text{-1}}})t}[A]=k1​+k-1​k-1​[A]0​​+k1​+k-1​k1​[A]0​​exp(−k1​−k-1​)t

1

If we consider that the concentration of product B at anytime is equal to the concentration of reactants at time zero minus the concentration of reactants at time ttt, we can set up the following equation:

[B]=[A]0−[A][\mathrm {B} ]=[\mathrm {A} ]_{\text{0}}-[\mathrm {A} ][B]=[A]0​−[A]

2

Combining 1 and 2, we can write

d[A]dt=−k1[A]+k-1([A]0−[A]){\frac {d[\mathrm {A} ]}{dt}}=-k_{\text{1}}[\mathrm {A} ]+k_{\text{-1}}([\mathrm {A} ]_{\text{0}}-[\mathrm {A} ])dtd[A]​=−k1​[A]+k-1​([A]0​−[A])

Separation of variables is possible and using an initial value [A](t=0)=[A]0[\mathrm {A} ](t=0)=[\mathrm {A} ]_{0}[A](t=0)=[A]0​, we obtain:

C=−ln⁡(−k1[A]0)k1+k-1C={\frac {{-\ln }(-k_{\text{1}}[\mathrm {A} ]_{\text{0}})}{k_{\text{1}}+k_{\text{-1}}}}C=k1​+k-1​−ln(−k1​[A]0​)​

and after some algebra we arrive at the final kinetic expression:

[A]=k-1[A]0k1+k-1+k1[A]0k1+k-1exp⁡(−k1−k-1)t[\mathrm {A} ]={\frac {k_{\text{-1}}[\mathrm {A} ]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}+{\frac {k_{\text{1}}[\mathrm {A} ]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}\exp {{(-k_{\text{1}}-k_{\text{-1}}})t}[A]=k1​+k-1​k-1​[A]0​​+k1​+k-1​k1​[A]0​​exp(−k1​−k-1​)t

The concentration of A and B at infinite time has a behavior as follows:

[A]∞=k-1[A]0k1+k-1[\mathrm {A} ]_{\infty }={\frac {k_{\text{-1}}[\mathrm {A} ]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}[A]∞​=k1​+k-1​k-1​[A]0​​
[B]∞=[A]0−[A]∞=[A]0−k-1[A]0k1+k-1[\mathrm {B} ]_{\infty }=[\mathrm {A} ]_{\text{0}}-[\mathrm {A} ]_{\infty }=[\mathrm {A} ]_{\text{0}}-{\frac {k_{\text{-1}}[\mathrm {A} ]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}[B]∞​=[A]0​−[A]∞​=[A]0​−k1​+k-1​k-1​[A]0​​
[B]∞[A]∞=k1k-1=Keq{\frac {[\mathrm {B} ]_{\infty }}{[\mathrm {A} ]_{\infty }}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}=K_{\text{eq}}[A]∞​[B]∞​​=k-1​k1​​=Keq​
[A]=[A]∞+([A]0−[A]∞)exp⁡(−k1+k-1)t[\mathrm {A} ]=[\mathrm {A} ]_{\infty }+([\mathrm {A} ]_{\text{0}}-[\mathrm {A} ]_{\infty })\exp(-k_{\text{1}}+k_{\text{-1}})t[A]=[A]∞​+([A]0​−[A]∞​)exp(−k1​+k-1​)t

Thus, the formula can be linearized in order to determine k1+k−1k_{1}+k_{-1}k1​+k−1​:

ln⁡([A]−[A]∞)=ln⁡([A]0−[A]∞)−(k1+k-1)t\ln([\mathrm {A} ]-[\mathrm {A} ]_{\infty })=\ln([\mathrm {A} ]_{\text{0}}-[\mathrm {A} ]_{\infty })-(k_{\text{1}}+k_{\text{-1}})tln([A]−[A]∞​)=ln([A]0​−[A]∞​)−(k1​+k-1​)t

To find the individual constants k1k_{1}k1​ and k−1k_{-1}k−1​, the following formula is required:

Keq=k1k-1=[B]∞[A]∞K_{\text{eq}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}={\frac {[\mathrm {B} ]_{\infty }}{[\mathrm {A} ]_{\infty }}}Keq​=k-1​k1​​=[A]∞​[B]∞​​
Reaction kinetics
Reaction kinetics
Reaction kinetics
Created
29 Apr 2004
History
255 edits
174 contributors
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Last edited
30 Apr 2026

255 revisions in total · 174 contributors

  1. 30 Apr 2026, 12:24 UTCTemporary accountPut minus infront of k_1 and k_(-1)+1diff
  2. 30 Apr 2026, 12:21 UTCTemporary accountChanged the minus sign in front of k1−1diff
  3. 10 Mar 2026, 14:27 UTCTioseafjThis is a circular citation-- lumenlearning is largely a clone of Wikipedia, it cannot be used as a source−178diff
  4. 21 Oct 2025, 15:51 UTCRedAndCyanmCarbonic acid dissolves in water and should be (aq) not (l).+1diff
  5. 4 Sept 2025, 14:01 UTCJulen ArtanoChanged to chem2, spaces, italics, "A, B, C, D" changed to roman, as they are names for hypothetical substances rather than variables.+140diff
  6. 5 Jun 2025, 17:18 UTCOzzie10aaaamCleaned up using AutoEd−5diff
  7. 15 Sept 2024, 07:59 UTCMaidenhairThe previous edit includes wiki errors, but had no edit summary, so the intent is unclear. Revert.+22diff
  8. 10 Sept 2024, 08:43 UTCAnonymous contributorrevertedNo edit summary−22diff

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Created
29 Apr 2004
History
255 edits
174 contributors
No edits in the last 30 days
Last edited
30 Apr 2026

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