Reaction Rate, Chemical

a quantity characterizing the intensity of a chemical reaction. The rate of formation of the reaction product is the amount of product formed from the reaction per unit time per unit volume (if the reaction is homogeneous) or per unit surface area (if the reaction is heterogeneous). The rate at which the reactants are consumed is determined in a similar fashion. The quantities of the substances are expressed in moles. Hence, the rates at which products are formed and reactants consumed are related by the stoichiometric coefficients of the substances in the balanced equation for the reaction. For example, in the reaction N₂ + 3H₂ + 2NH₃, the rate at which hydrogen is consumed is three times greater and the rate at which ammonia is formed is twice as great as the rate at which nitrogen is consumed.

The ratio of the rate of formation of a reaction product or rate of consumption of a reactant to the corresponding stoichiometric coefficient is called the chemical reaction rate. In the case of a homogeneous reaction occurring in a closed system of constant volume, the reaction rate

where c_i is the concentration of the reaction product, that is, the number of moles of product per unit volume, b_i is the stoichiometric coefficient of this substance, and t is the time. This equation is also applicable to the reactant if the stoichiometric coefficients of the reactants are considered negative.

For technical purposes, the rates of heterogeneous catalytic reactions are usually calculated not per unit surface of catalyst but rather per unit mass of catalyst or per unit volume of the layer of catalyst granules.

The reaction rate can vary greatly, from very low values (geological processes occurring over millions of years) to very high values (ionic reactions completed in millionths of a second).

Various methods are used in measuring reaction rates. The selection of a method is determined by the nature of the reaction and the reaction’s rate. Excluding such special types of reactions as electrode, photochemical, and radiation-chemical, the principal methods for measuring the rates of ordinary reactions resulting from the energy of thermal motion will be described. In the static method, the reaction is conducted in a closed vessel. The rate is evaluated by measuring the change in composition of the reaction mixture through either the analysis of samples or the measurement of some property of the reaction mixture dependent on composition. In the case of gaseous reactions accompanied by a change in the number of molecules, the reaction is often followed by measuring the change in pressure. The flow-rate method involves passing the reaction mixture through the reaction zone at a constant velocity. For a heterogeneous reaction, this zone is usually a volume filled with catalyst granules; for a homogeneous reaction, the zone is usually an area of elevated temperature. The degree to which reactants have been converted to products is determined by the composition of the mixture emerging from the reaction zone.

Both of the above methods are simple, but they do not give a direct reading of the reaction rates. In a static system, the composition of the reaction mixture and, consequently, the reaction rate itself vary with time. Therefore, the measured values of concentration must be differentiated with respect to time in order to determine the reaction rate, or the theoretical expression for the reaction rate must be integrated over time in order to compare the expression with experimental data. In the case of the flow-rate method, the composition of the reaction mixture is independent of time but varies in different regions of the reaction zone. Thus, any comparison of the theoretical expression for the reaction rate with the experimental results must be preceded by the integration of this expression over the volume of the reaction zone.

Direct measurement of the rate of a homogeneous reaction is achieved using a flow-mix reactor. The reactants are introduced at a constant rate into a vessel equipped with a powerful mixer, and the reaction mixture is removed in such a way that the quantity in the reaction vessel remains constant. Upon obtaining a steady-state condition, analysis of the mixture removed will indicate the composition of the reaction mixture. Knowing additionally the rate of removal of this mixture, the amount of substance formed from the reaction per unit time is determined and, hence, the reaction rate. For heterogeneous catalytic reactions with a stationary catalyst, the flow circulation method is equivalent to the method described above. Uniformity of the composition of the reaction mixture in the reaction zone is achieved by a pump’s intensive circulation of the mixture. Flow-mix reactors and flow-circulation systems belong to the class of nongradient reactors, which are thus named because of the almost complete lack of concentration and temperature gradients in the reaction zone.

Special difficulties arise in studying extremely fast reactions in solutions. If a reaction proceeds to a significant extent toward completion during the time required to mix the solutions of the reactants, then the usual methods are inapplicable. The problem of measuring the rates of such reactions is solved by the relaxation methods, which were developed by M. Eigen. A system in which a reversible reaction may occur is originally in a state of chemical equilibrium. A parameter affecting the value of the equilibrium constant (temperature, pressure, electric field) is then changed very rapidly. The system moves to a new equilibrium state over some period of time; this process is called relaxation. The reaction rate is determined by following the change in the composition by some inertia-free method, for example, by electrical conductivity. It is possible to observe relaxation times as short as 10^-6 sec. This technique has been used in measuring the rates of such reactions as H⁺ + OH- = H₂O in water.