the Determination of a Rate Equation

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THE DETERMINATION OF A RATE EQUATION

Rate equation has the form rate = k [A]x[B]y which shows how the rate of a chemical reaction depends on the concentration of the reactants (A&B) and the rate constant k. The rate equation normally indicates what species are involved in the rate-determining step and how many species are involved.

        A rate equation is used to describe how the concentration of a product increases or the concentration of the reactants decreases with time, the equation also indicates how the concentration of one or more reactants directly affects the rate. Occasionally it can even be the concentration of a product that affects the rate. In general the rate equation for the reaction:

                                        A + B         C + D

Is found by experiment to follow simple kinetics with the rate equation being written as:

                                        Rate = k [A]x[B]y       

k = rate constant, x = order with respect to [A], y = order with respect with [B].

        There are three orders of reactions, zero order, first order and second order.

Zero order = the rate does not depend upon the concentration of the reactant. The rate of reaction is fixed. Doubling or tripling the concentration of the reactant makes no difference to the rate. Thus:

Rate of reaction = k or rate of reaction = k[A]0.

First order = the rate of reaction depends directly upon the concentration of the reactant. If the concentration of the reactant is doubled, the rate doubles, thus:

Rate of reaction = k[A] or rate of reaction = k[A]1

Second order = the rate of reaction depends directly upon the square of the concentration of the reactants. If its concentration is doubled, its rate of reaction quadruples. Thus:

Rate of reaction = k[A]2    

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The graph below shows zero, first and second order reactions and how changes in the concentration of a reactant affect the reaction rate.

 

                                         Second order

 Reaction Rate                                                      Zero order

(Mol dm-3 s-1)

                                    ...

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