Rate of a Reaction . . Dependence of Rate on Concentration Consider a general reaction aA + bB ® cC + dD where a, b, c and d are the stoichiometric coefficients of reactants and products. The rate expression for this reaction is Rate µ [A] x [B] y ( .
) where exponents x and y may or may not be equal to the stoichiometric coefficients (a and b) of the reactants. Above equation can also be written as Rate = k [A] x [B] y ( .4a) ] [ ] x y d R A B d ( .4b) This form of equation ( . b) is known as differential rate equation, where k is a proportionality constant called rate constant . The equation like ( .
), which relates the rate of a reaction to concentration of reactants is called rate law or rate expression. Thus, rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation . For example: 2NO(g) + O (g) ® 2NO (g) We can measure the rate of this reaction as a function of initial concentrations either by keeping the concentration of one of the reactants constant and changing the concentration of the other reactant or by changing the concentration of both the reactants. The following results are obtained (Table .
). Table . : Initial rate of formation of NO Experiment Initial [NO]/ mol L - Initial [O ]/ mol L - Initial rate of formation of NO / mol L - s - . .
. . It is obvious, after looking at the results, that when the concentration of NO is doubled and that of O is kept constant then the initial rate increases by a factor of four from . to .
mol L – s – . This indicates that the rate depends upon the square of the concentration of NO. When concentration of NO is kept constant and concentration of O is doubled the rate also gets doubled indicating that rate depends on concentration of O to the first power. Hence, the rate equation for this reaction will be Rate = k [NO] [O ] The differential form of this rate expression is given as