Reaction Quotient
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In
chemical thermodynamics Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurement ...
, the reaction quotient (''Q''r or just ''Q'') 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 Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
, at a particular point in time. Mathematically, it is defined as the ratio of the activities (or molar
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
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 The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
. 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 :Q_\text (t)= \frac , where ''t'' denotes the ''instantaneous'' activity of a species X at time ''t''. A compact general definition is :Q_\text(t) = \prod_j _j(t), where П''j'' denotes the product across all ''j''-indexed variables, ''aj''(''t'') is the activity of species ''j'' at time ''t'', and ''νj'' 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 In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pr ...
of reaction by the relation :\Delta_G=RT\ln(Q_/K), where ''K'' is a constant independent of initial composition, known as the
equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
. The reaction proceeds in the forward direction (towards larger values of ''Q''r) when Δr''G'' < 0 or in the reverse direction (towards smaller values of ''Q''r) when Δr''G'' > 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_\to K and \Delta_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_=1 and \Delta_G= \Delta_G^\circ=-RT\ln K\quad (t=0). This quantity, Δr''G°'', is called the ''standard Gibbs free energy of reaction''. 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.


Examples

The burning of octane, C8H18 + 25/2 O2 → 8CO2 + 9H2O has a Δr''G° ~ –''240 kcal/mol, corresponding to an equilibrium constant of 10175, a number so large that it is of no practical significance, since there are only ~5 × 1024 molecules in a kilogram of octane.


References


External links

Reaction quotient tutorials
tutorial I




ref> {{Chemical equilibria Equilibrium chemistry Physical chemistry