Engineering Chemistry S Datta

REACTION DYNAMICS/CHEMICAL KINETICS 115
(ii) Half-life method
The half-lives (t 1/2
) for reactions of different orders are as follows:
First order = 0.693/k (fixed)
Second order = 1/(ak)
Third order = 1/(a 2 k′)
In separate sets of experiments if different concentrations are taken and t 1/2
are measured
the order can easily be determined. If t 1/2
remains constant the reaction is of the first order, if
t 1/2
varies inversely as the initial concentration the reaction is of the second order, i.e., plot of
t 1/2
vs. 1/a will give a straight line. If the plot t 1/2
vs. 1/a 2 gives a straight line, the reaction is of
third order.
(iii) Van’t Hoff’s differential method
Let, the order of a reaction be = n.
For, the first experiment the initial concentration = c 1
.
For the second experiment the initial concentration = c 2
.
So, the rate equations for the two experiments will be
R 1
= – dc1
= kc n
dt 1
;
R 2
= – dc2
= kc n
dt 2
.
Taking ‘log’ on both the sides
log R 1
= log k + n log c 1
log R 2
= log k + n log c 2
log R 1 − log R2
or n =
log c1 − log c2
If the rates of reaction determined initially R 1
and R 2
are known, so the order can be
determined.
(iv) Graphical method
If we plot ‘time’ vs ‘a function of concentration’, we can get the order of a reaction. By
plotting log c vs t if a straight line is obtained the reaction is of first order. If a plot of 1/c vs ‘t’
gives a straight line the reaction is of second order and if the plot of 1/c 2 vs ‘t’ gives a straight
line the reaction is of third order (Fig. 5.1 (a) and (b)).
A
Amount decomposed (x)
C
dx
B
Slop = tan
=
dx
dt
Rate of reaction (dx/dt)
Time (t)
(a–x)
( a )
( b)
Fig. 5.1