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Reaction quotient
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{{Short description|Quantity in chemical thermodynamics}} In [[chemical thermodynamics]], the '''reaction quotient''' (''Q''<sub>r</sub> or just ''Q'')<ref>{{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}}</ref> 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 [[activity (chemistry)|activities]] (or [[Molar mass|molar]] [[concentration]]s) 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'' [[mole (chemistry)|mole]]s 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 :<chem>\it \alpha\,\rm A{} + \it \beta\,\rm B{} <=> \it \rho\,\rm R{} + \it \sigma\,\rm S{}</chem>. 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''<sub>r</sub>, as a function of time ''t'', is defined as<ref>{{cite book | last1=Zumdahl|first1= Steven|last2= Zumdahl|first2= Susan | title=Chemistry |edition=6th | publisher=Houghton Mifflin | year=2003 | isbn=0-618-22158-1}}</ref> :<math>Q_\text{r} (t)= \frac{\{\mathrm{R}\}^\rho_t\{\mathrm{S}\}^\sigma_t} {\{\mathrm{A}\}^\alpha_t \{\mathrm{B}\}^\beta_t},</math> where {X}<sub>''t''</sub> denotes the ''instantaneous'' [[activity (chemistry)|activity]]<ref>Under 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.</ref> of a species X at time ''t''. A compact general definition is :<math>Q_\text{r}(t) = \prod_j [a_j(t)]^{\nu_j},</math> where П<sub>''j''</sub> denotes the product across all ''j''-indexed variables, ''a<sub>j</sub>''(''t'') is the activity of species ''j'' at time ''t'', and ''ν<sub>j</sub>'' is the [[stoichiometric coefficient|stoichiometric number]] (the stoichiometric coefficient multiplied by +1 for products and −1 for starting materials).
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