PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 273

9.2.2 First-order reactions

9.2.2.1 Type of reaction

A→products. (9.22)

9.2.2.2 Kinetic equation

−

dcA

dτ

=kcA. (9.23)

9.2.2.3 Integrated form of the kinetic equation.

For time as a function of the reactant concentration we have

τ=

1

k

ln

cA0

cA

. (9.24)

For the concentration of substance A as a function of time we have

cA=cA0exp(−kτ). (9.25)

9.2.2.4 Reaction half-life

τ 1 / 2 =

ln 2

k

. (9.26)

Figure9.2shows the time dependence of the concentration of the reactant A and product B.

Example

The half-life of a certain first-order reaction at a certain temperature isτ 1 / 2 = 693s. The initial

concentration of the reactantAiscA0= 0.1 mol dm−^3. Calculate the rate constant of the

reaction and the concentration of substanceAfive minutes after the start of the reaction.