# Reaction Quotient

In chemical thermodynamics , the reaction quotient ( QR or just Q ) is a quantity that provides a measurement of the relative amounts of products and reactants, introduced into a reaction mixture for a reaction with well-defined overall stoichiometry. There is no specific time on particular. Mathematically, it is defined as the ratio of the activities (or molar concentrations ) of the product species to that of the reactant species involved in a chemical reaction .Taking into account the stoichiometric coefficient of the reaction as an exponent. In equilibrium, the reaction quotient is constant with time and is equal to the equilibrium constant.

is a general chemical reaction, in which α moles of a reactant A and β moles of a reactant B to give the reaction moles of a product R and moles of a product S can be written as

\alpha A~+~ \beta B~ \rightleftharpoons ~ \rho R~+~ \sigma S

The reaction is written as an equilibrium, although in many cases it may appear that all the reactants on one side are converted to the other. When a mixture of A and B is made and the reaction is allowed to take place, the reaction quotient Qr is defined as a function of time t

{\displaystyle Q_{\text{r}}(t)={\frac {\{\mathrm {R} \}_{t}^{\rho }\{\mathrm {S} \}_{t} ^{\sigma }}{\{\mathrm {A} \}_{t}^{\alpha }\{\mathrm {B} \}_{t}^{\beta }}},}

where {X} t denotes the instantaneous activity of a species X at time t . There is a compact general definition (where j is the product in all j -indexed variables, and is the same for i ):

{\displaystyle Q_{\text{r}}(t)=\prod _{j}[a_{j}(t)]^{\nu _{j}},}

where fraction reaction product is a set of activitiesThe product is j , each raised to the power of a stoichiometric coefficient j , and every reactant has a corresponding product of activities. All activities refer to a time t .

#### Relation to K (Equilibrium Constant)

As the reaction proceeds with the passage of time, assuming that the activation energy does not slow the reaction prohibitively for a given amount of time, the species’ activities, and therefore the reaction quotient, change in such a way that The free energy of the chemical system decreases. , The direction of change is governed by the Gibbs free energy of the reaction by the relation

{\displaystyle \Delta _{\mathrm {r} }G=RT\ln(Q_{\mathrm {r} }/K)},

where K is independent of the initial structure, known as the equilibrium constant . The reaction proceeds in the forward direction ( towards small values ​​of q r ) when r g < 0 or in the opposite direction (towards large values ​​of q r ) when r g > 0. Eventually, as the reaction mixture reaches chemical equilibrium, the activities of the components (and thus the reaction quotient) reach constant values. The equilibrium constant is defined as the asymptotic value obtained by the reaction quotient:

{\displaystyle Q_{\mathrm {r} }\to K}~~and~~ .{\displaystyle \Delta _{\mathrm {r} }G\to 0\quad (t\to \infty )}

In theory, it takes an infinite amount of time for the reactions to reach equilibrium; In practice, equilibrium is considered, in a practical sense, when the concentrations of the equilibrating species no longer change directly (with respect to the analytical equipment used).

If a reaction mixture is started with all the components having unity activity, i.e. in their standard states , then

{\displaystyle Q_{\mathrm {r} }=1}and .{\displaystyle \Delta _{\mathrm {r} }G=\Delta _{\mathrm {r} }G^{\circ }=-RT\ln K\quad (t=0)}

This quantity,  , is called the standard Gibbs free energy of the reaction.

All reactions, no matter how favorable, are equilibrium processes, although practically speaking, if no starting material is detected after a certain point by a particular analytical technique, the reaction is said to be complete. Is.