CHAP. 9: CHEMICAL KINETICS [CONTENTS] 287
9.3 Methods to determine reaction orders and rate constants
9.3.1 Problem formulation
In order to be able to use kinetic equations, we need to know the reaction order, the partial
orders with respect to individual components, and the rate constant. Theoretical methods to
determine these quantities are not yet sufficiently elaborated, and consequently we have to
resort to the measurement of the reaction kinetics.
When we have at our disposal a table giving the values of:
a) concentrations of reactants in dependence on time, or
b) reaction half-life in dependence on the initial concentrations, or
c) rates of reaction in dependence on concentrations,
the further procedure consists in the choice of an appropriate numerical method.
9.3.2 Integral method.
Let us have a table giving the values of the concentrations of reactants in dependence on time^1.
We choose a kinetic equation and from its integral form calculate the rate constant for all
items in the table. If the calculated values of the rate constant do not dependsystematically
on time, the chosen kinetic equation is correct. This determines both the rate constant and the
reaction order. The method is suitable particularly for reactions of integer orders, but it may
be used for non-integer orders as well, as is shown in the following example.
Example
Kinetic data have been measured for the thermal decomposition of dioxan: dioxan→products
at a temperature of 777 K. The results are shown in the following table:
τ[s] 0 240 660 1200 1800 2400
c· 103 [mol dm−^3 ] 8.46 7.20 5.55 4.04 3.05 2.41
Determine the reaction order and the rate constant.(^1) It is sufficient enough to know the concentration of one reactant. The concentrations of other reacting
components are then given by initial conditions and the material balance.