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The reaction quotient (Qr or simply Q) is a quantity in chemical thermodynamics that provides a measurement of the relative amounts of products and reactants present in a reaction mixture at a given point in time for a reaction with well-defined overall stoichiometry. It is defined mathematically as the ratio of the activities (or molar concentrations) of the product species to those of the reactant species involved in the chemical reaction, with the stoichiometric coefficients of the reaction taken into account as exponents of the concentrations. The reaction quotient is constant over time and equal to the equilibrium constant when the system is in equilibrium. A general chemical reaction in which α moles of a reactant A and β moles of a reactant B react to produce moles of a product R and moles of a product S is written as
Even though it may appear that all of the reactants on one side have been converted to the other side, the reaction is written as an equilibrium. When any initial mixture of A, B, R, and S is prepared and the reaction is allowed to proceed (either forward or backward), the reaction quotient Qr as a function of time t is defined as
where Xt denotes a species X’s instantaneous activity at time t.
Calculating Reaction Quotient & Equilibrium Constant
Consider the following chemical reaction:
a A + b B ⇌ c C + d D
The reaction quotient can be calculated in terms of partial pressure (Qp) and molar concentration (Qc), just as the equilibrium constant can be calculated in terms of partial pressure (Kp) and molar concentration (Kc), as shown below.
The equilibrium constant expresses the relationship between the products and the reactants in an equilibrium reaction (denoted by K). When the reaction is at equilibrium, the Kc in terms of the molar concentration of the components can be given as,
And the reaction’s Kp in terms of the partial pressures of the components is given as,
Calculating Reaction Quotient
The reaction quotient, abbreviated Q, measures the amount of reactant and product present at a given point in a chemical reaction. When the reaction is not in equilibrium, we express the reaction quotient in terms of molar concentration as,
And the reaction quotient in terms of the components’ partial pressures as,
Q. What is the formula for calculating the reaction quotient?
Ans: To calculate the reaction quotient Q, multiply the activities of the products by the activities of the reagents, then raise each of these values to the power of the corresponding stoichiometric coefficient.
Q. What is the distinction between Q and K?
Ans: Q is a quantity that varies as a reaction system nears equilibrium. The numerical value of Q at the “end” of the reaction, when equilibrium is reached, is denoted by K.
Q. Why are Q and K values unitless?
Ans: The reaction quotient (Q) is the specific ratio of concentration terms that we write for a given reaction. It is essentially the same as K, except that Q is not at equilibrium; instead, it is simply product concentrations over reactant concentrations from the chemical formula. K has no units.