CHAP. 9: CHEMICAL KINETICS [CONTENTS] 290
Note:The drawback of this method is the difficult determination of reaction rates from ex-
perimental data. The rate can be estimated by substituting the derivative of concentration
with respect to time with the ratio of differences, see relation (9.7)dc
dτ
≈∆c
∆τ
When ∆τis small, ∆cis subject to considerable error; if ∆τis large, the substitution of
the derivative with the ratio of differences may be rather inaccurate.
It is possible determine the rate of reaction more accurately based on measurements in a
stirred flow reactor [see9.7.3].Example
The rate of the reaction
A→products
is 0.01 mol dm−^3 min−^1 atcA= 1 mol dm−^3 , and 0.005 mol dm−^3 min−^1 atcA= 0.5 mol dm−^3.
Determine the reaction order and the rate constant.Solution
We substitute into equations (9.82)n=ln 0. 01 / 0. 005
ln 1/ 0. 5=
ln 2
ln 2= 1, k=0. 01
11
= 0.01 min−^1.9.3.4 Method of half-lives.
This method is usually applied in the case of reactions with one reactant. The initial data are
the reaction half-lives for at least two different initial concentrations of the reactant.
If the reaction half-life does not depend on the initial concentration, the reaction is first
order [see equations (9.26)]. If it does depend on the initial concentration, we use relation (9.74)
which we write for two initial concentrations (cA0) 1 and (cA0) 2. This set of two equations for