# Reaction quotient

In chemistry, a reaction quotient: Qr is a function of the activities or concentrations of the chemical species involved in a chemical reaction. In the special case that the reaction is at equilibrium the reaction quotient is constant and equal to the equilibrium constant which appears in the expression of the law of mass action.

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

αA + βB σS + τT

The reaction is written as an equilibrium even though in many cases it may appear to have gone to completion. When a mixture of A and B is made up and the reaction is allowed to occur, the reaction quotient, Qr, is defined as:[1]

$Q_r = \frac{\left\{S_t\right\}^\sigma \left\{T_t\right\}^\tau }{\left\{A_t\right\}^\alpha \left\{B_t\right\}^\beta }$

where {Xt} denotes the instantaneous activity[2] of a species X at time, t. A compact general definition is (where Пj is the product across all j-indexed variables, and idem for Пi):

$Q_r=\frac{\prod_j a_{j(t)}^{\nu_j}}{\prod_i a_{i(t)}^{\nu_i}}$

where the numerator is a product of reaction product activities, a j, each raised to the power of a stoichiometric coefficient, ν j, and the denominator is a similar product of reactant activities. All activities refer to a time t.

As the reaction proceeds (assuming that there is no energy barrier to the reaction) with the passage of time the species' activities and hence the reaction quotient change. Eventually the activities become constant and the mixture is then said to be at equilibrium. An equilibrium constant, K, can be expressed symbolically as

K = Qr (t=∞)

though equilibrium will be effectively reached in a finite time in most reactions.