Editing Reversible reaction

{{Short description|Chemical reaction whose products can react together to produce the reactants again}}
A '''reversible reaction''' is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously.<ref>{{Cite web|url=https://courses.lumenlearning.com/cheminter/chapter/reversible-reaction/ |title=Reversible Reaction |website=lumenlearning.com |access-date=2021-01-08}}</ref>

:<chem> \mathit aA{} + \mathit bB <=> \mathit cC{} + \mathit dD</chem>

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 (thermodynamics)|reversible process]] in [[thermodynamics]].

Weak [[acids]] and [[Base (chemistry)|bases]] undergo reversible reactions. For example, [[carbonic acid]]: 

: H<sub>2</sub>CO<sub>3 (l)</sub> + H<sub>2</sub>O<sub>(l)</sub> ⇌ HCO<sub>3</sub><sup>−</sup><sub>(aq)</sub> + H<sub>3</sub>O<sup>+</sup><sub>(aq)</sub>.

The [[concentration]]s of reactants and products in an equilibrium mixture are determined by the [[analytical concentration]]s 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.<ref>at constant pressure.</ref> So, when the free energy change is large (more than about 30 kJ mol<sup>&minus;1</sup>), 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
: CaCO<sub>3</sub> + 2HCl → CaCl<sub>2</sub> + H<sub>2</sub>O + CO<sub>2</sub>↑
== 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 lake]]<ref>[http://www.chem1.com/acad/webtext/chemeq/Eq-01.html#NAP How did Napoleon Bonaparte help discover reversible reactions?]. Chem<sub>1</sub> General Chemistry Virtual Textbook: Chemical Equilibrium Introduction: reactions that go both ways.</ref> (one of the [[natron]] lakes in Egypt, in [[limestone]]):

:2NaCl + CaCO<sub>3</sub> → Na<sub>2</sub>CO<sub>3</sub> + CaCl<sub>2</sub>

He recognized this as the reverse of the familiar reaction
: Na<sub>2</sub>CO<sub>3</sub> + CaCl<sub>2</sub>→ 2NaCl + CaCO<sub>3</sub>

Until then, [[chemical reaction]]s 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.<ref>Claude-Louis Berthollet,"Essai de statique chimique", Paris, 1803. [https://books.google.com/books?id=cKU5AAAAcAAJ&q=berthollet+essai (Google books)]</ref>

In 1864, [[Peter Waage]] and [[Cato Maximilian Guldberg]] formulated their [[law of mass action]] which quantified Berthollet's observation. Between 1884 and 1888, [[Henry Louis Le Chatelier|Le Chatelier]] and [[Karl Ferdinand Braun|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 <math>k_1</math> and the backwards step B→A has a rate constant <math>k_{-1}</math>. The concentration of A obeys the following differential equation:

{{NumBlk|:|<math>\frac{d[A]}{dt}=-k_\text{1}[A]+k_\text{-1}[B]</math>.|{{EquationRef|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 <math>t</math>, we can set up the following equation:

{{NumBlk|:|<math>[B]=[A]_\text{0}-[A]</math>.|{{EquationRef|2}}}}

Combining {{EquationNote|1}} and {{EquationNote|2}}, we can write

:<math>\frac{d[A]}{dt}=-k_\text{1}[A]+k_\text{-1}([A]_\text{0}-[A])</math>.

Separation of variables is possible and using an initial value <math>[A](t=0) = [A]_0</math>, we obtain:

:<math>C=\frac{{-\ln}(-k_\text{1}[A]_\text{0})}{k_\text{1}+k_\text{-1}}</math>

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

:<math>[A]=\frac{k_\text{-1}[A]_\text{0}}{k_\text{1}+k_\text{-1}}+\frac{k_\text{1}[A]_\text{0}}{k_\text{1}+k_\text{-1}}\exp{{(-k_\text{1}+k_\text{-1}})t}</math>.

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

:<math>[A]_\infty=\frac{k_\text{-1}[A]_\text{0}}{k_\text{1}+k_\text{-1}}</math>

:<math>[B]_\infty=[A]_\text{0}-[A]_\infty=[A]_\text{0}-\frac{k_\text{-1}[A]_\text{0}}{k_\text{1} +k_\text{-1}}</math>

:<math>\frac{[B]_\infty}{[A]_\infty}=\frac{k_\text{1}}{k_\text{-1}}=K_\text{eq}</math>

:<math>[A]=[A]_\infty+([A]_\text{0}-[A]_\infty)\exp(-k_\text{1}+k_\text{-1})t</math>

Thus, the formula can be linearized in order to determine <math>k_1+k_{-1}</math>:

:<math>\ln([A]-[A]_\infty)=\ln([A]_\text{0}-[A]_\infty)-(k_\text{1}+k_\text{-1})t</math>

To find the individual constants <math>k_1</math> and <math>k_{-1}</math>, the following formula is required:

:<math>K_\text{eq}=\frac{k_\text{1}}{k_\text{-1}}=\frac{[B]_\infty}{[A]_\infty}</math>

==See also==
* [[Dynamic equilibrium]]
* [[Chemical equilibrium]]
* [[Irreversibility]]
* [[Microscopic reversibility]]
* [[Static equilibrium]]

== References ==
{{reflist}}

[[Category:Equilibrium chemistry]]
[[Category:Physical chemistry]]