PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 289

Note:In view of experimental errors in the measured concentration values, the rate con-

stant is not the same at all points, but it fluctuates around the mean value. We will

consider the arithmetic mean of the calculated rate constants to be the correct value.

9.3.3 Differential method

Let us have a table giving the values of the reaction rates in dependence on concentrations. In
this case the reaction order and the rate constant are determined from the differential forms of
kinetic equations.
If there is only one reactant in the reaction,

A→products,

we use equation (9.71)
r=kcnA,

wherer=−

dcA

dτ

. In order to determinenandkit is sufficient enough to know the rate of

reaction at two concentrations:

n=

lnr 1 /r 2

lncA, 1 /cA, 2

, k=

r 1

(cA, 1 )n

. (9.82)

When there are two reactants, then

r=kcαAcβB.

In order to determine the partial orders of the reaction and its rate constants, we need at least
three values of the reaction rates. We will obtain the constantsα, βandk by solving the
following set of three equations

lnr 1 = lnk+αlncA, 1 +βlncB, 1 ,

lnr 2 = lnk+αlncA, 2 +βlncB, 2 , (9.83)

lnr 3 = lnk+αlncA, 3 +βlncB, 3.

The procedure is similar in the case of three and more reactants.