Reversible Two-Way Reactions

In reversible reactions the transformation of reagent into product is complicated by simultaneous reverse conversion. Due to the principle of independence of the elementary stages passing the rate of the reversible reaction is defined by the difference between rates of direct and reverse stages. Example for reaction 

It is possible that the term reversible reactions is not quite well turned in this particular case of chemical transformations, because from the position of thermodynamics all reaction are reversible without any exclusion. Here we talk about reversibility in formal-kinetic sense, e.g., it is implied that the rate constants of both stages have commensurable values, and we cannot neglect the rate of any of those stages. 

Mathematic analysis of this kinetic scheme becomes more convenient, when we use a helper function x(t) - the quantity of reagent A in volume unit that have had reacted by the moment of time f. In this case mathematic model of the reaction could be expressed by the differential equation 

Here variables are easily separated, therefore, the function x t) could be defined by the means of MathCAD (Fig. 1.7). For initial condition x(0) = 0 we get 

Trend of kinetic curves for each participant of the reaction is modeled in Fig. 1.7. It is seen, that in some time the concentrations of the substances become time-undependable, which corresponds to the equilibrium condition. Time-dependences of the rate of each stage are also shown here, and that illustrates the dynamic character of the chemical equilibrium reaching equilibrium condition does not mean the end of the reaction. In equilibrium condition the total rate of the reaction is equal to zero because of the equality of the rates of direct and reverse reaction, which have quiet definite values. 

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