Reaction quotient

In chemical thermodynamics, the reaction quotient (Q_r or just Q){{Cite book|url=http://ebook.rsc.org/?DOI=10.1039/9781847557889|title=Quantities, Units and Symbols in Physical Chemistry|date=2007|publisher=Royal Society of Chemistry|isbn=978-0-85404-433-7|editor-last=Cohen|editor-first=E Richard|edition=3|location=Cambridge|language=en|doi=10.1039/9781847557889|editor-last2=Cvitas|editor-first2=Tom|editor-last3=Frey|editor-first3=Jeremy G|editor-last4=Holström|editor-first4=Bertil|editor-last5=Kuchitsu|editor-first5=Kozo|editor-last6=Marquardt|editor-first6=Roberto|editor-last7=Mills|editor-first7=Ian|editor-last8=Pavese|editor-first8=Franco|editor-last9=Quack|editor-first9=Martin}} is a dimensionless quantity that provides a measurement of the relative amounts of products and reactants present in a reaction mixture for a reaction with well-defined overall stoichiometry at a particular point in time. Mathematically, it is defined as the ratio of the activities (or molar concentrations) of the product species over those of the reactant species involved in the chemical reaction, taking stoichiometric coefficients of the reaction into account as exponents of the concentrations. In equilibrium, the reaction quotient is constant over time and is equal to the equilibrium constant.

A general chemical reaction in which α moles of a reactant A and β moles of a reactant B react to give ρ moles of a product R and σ moles of a product S can be written as

:\it \alpha\,\rm A{} + \it \beta\,\rm B{} <=> \it \rho\,\rm R{} + \it \sigma\,\rm S{}.

The reaction is written as an equilibrium even though, in many cases, it may appear that all of the reactants on one side have been converted to the other side. When any initial mixture of A, B, R, and S is made, and the reaction is allowed to proceed (either in the forward or reverse direction), the reaction quotient Q_r, as a function of time t, is defined as{{cite book | last1=Zumdahl|first1= Steven|last2= Zumdahl|first2= Susan | title=Chemistry |edition=6th | publisher=Houghton Mifflin | year=2003 | isbn=0-618-22158-1}}

: $Q_\text{r} (t)= \frac{\{\mathrm{R}\}^\rho_t\{\mathrm{S}\}^\sigma_t} {\{\mathrm{A}\}^\alpha_t \{\mathrm{B}\}^\beta_t},$

where {X}_t denotes the instantaneous activityUnder certain circumstances (see chemical equilibrium) each activity term such as {A} may be replaced by a concentration term, [A]. Both the reaction quotient and the equilibrium constant are then concentration quotients. of a species X at time t.

A compact general definition is

: $Q_\text{r}(t) = \prod_j [a_j(t)]^{\nu_j},$

where П_j denotes the product across all j-indexed variables, a_j(t) is the activity of species j at time t, and ν_j is the stoichiometric number (the stoichiometric coefficient multiplied by +1 for products and −1 for starting materials).

Relationship to ''K'' (the equilibrium constant)

As the reaction proceeds with the passage of time, the species' activities, and hence the reaction quotient, change in a way that reduces the free energy of the chemical system. The direction of the change is governed by the Gibbs free energy of reaction by the relation

: $\Delta_{\mathrm{r}}G=RT\ln(Q_{\mathrm{r}}/K)$ ,

where K is a constant independent of initial composition, known as the equilibrium constant. The reaction proceeds in the forward direction (towards larger values of Q_r) when Δ_rG < 0 or in the reverse direction (towards smaller values of Q_r) when Δ_rG > 0. Eventually, as the reaction mixture reaches chemical equilibrium, the activities of the components (and thus the reaction quotient) approach constant values. The equilibrium constant is defined to be the asymptotic value approached by the reaction quotient:

: $Q_{\mathrm{r}}\to K$ and $\Delta_{\mathrm{r}}G\to 0\quad (t\to\infty)$ .

The timescale of this process depends on the rate constants of the forward and reverse reactions. In principle, equilibrium is approached asymptotically at t → ∞; in practice, equilibrium is considered to be reached, in a practical sense, when concentrations of the equilibrating species no longer change perceptibly with respect to the analytical instruments and methods used.

If a reaction mixture is initialized with all components having an activity of unity, that is, in their standard states, then

: $Q_{\mathrm{r}}=1$ and $\Delta_{\mathrm{r}}G= \Delta_{\mathrm{r}}G^\circ=-RT\ln K\quad (t=0)$ .

This quantity, Δ_rG°, is called the standard Gibbs free energy of reaction.The standard free energy of reaction can be determined using the difference between the sum of the standard free energies of formation of products and the sum of the standard free energies of formation of reactants, accounting for stoichiometries: $\Delta_{\mathrm{r}} G^\circ=\sum_{\mathrm{prod.}}^i \nu_i\Delta_{\mathrm{f}}G^\circ
-\sum_{\mathrm{react.}}^j\nu_j\Delta_{\mathrm{f}}G^\circ$ .

All reactions, regardless of how favorable, are equilibrium processes, though practically speaking, if no starting material is detected after a certain point by a particular analytical technique in question, the reaction is said to go to completion.

In biochemistry

In biochemistry, the reaction quotient is often referred to as the mass-action ratio with the symbol $\Gamma$ .

Applications

The reaction quotient can be used to predict the direction and extent of an equilibrium chemical reaction. At equilibrium, the reaction quotient (Q) is equal to the equilibrium constant (K) for the reaction, where Q = K. If Q > K, the formation of reactants is favored. This is because the ratio of the numerator to the denominator in Q is greater than that of K, indicating there are more products than at equilibrium. As Le Chatelier's Principle states systems tend towards equilibrium, the equilibrium shifts in the reverse direction favoring the formation of the products. Similarly, when Q < K, the formation of products is favored and the reaction is progressing in the forwards direction. {{Cite web |date=2013-10-02 |title=The Reaction Quotient |url=https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Equilibria/Chemical_Equilibria/The_Reaction_Quotient |access-date=2025-05-15 |website=Chemistry LibreTexts |language=en}}

References

External links

Reaction quotient tutorials

[http://elchem.kaist.ac.kr/vt/chem-ed/courses/equil/intro/reactquo.htm tutorial I]{{cite web|url=http://elchem.kaist.ac.kr|title=elchem website tutorial 1|access-date=28 April 2021|archive-date=23 January 2020|archive-url=https://web.archive.org/web/20200123034508/http://elchem.kaist.ac.kr/|url-status=dead}} No longer accessible as of November 2023
[http://www.chem.purdue.edu/gchelp/howtosolveit/Equilibrium/Reaction_Quotient.htm tutorial II]{{cite web|url=http://elchem.kaist.ac.kr|title=elchem website tutorial 2|access-date=28 April 2021|archive-date=23 January 2020|archive-url=https://web.archive.org/web/20200123034508/http://elchem.kaist.ac.kr/|url-status=dead}}
[https://web.archive.org/web/20070702190749/http://www.cartage.org.lb/en/themes/sciences/Chemistry/Miscellenous/Helpfile/Equilibrium/ReactionQuotient.htm tutorial III]{{cite web|url=http://elchem.kaist.ac.kr|title=elchem website tutorial 3|access-date=28 April 2021|archive-date=23 January 2020|archive-url=https://web.archive.org/web/20200123034508/http://elchem.kaist.ac.kr/|url-status=dead}}

Category:Equilibrium chemistry

Category:Physical chemistry