Engineering Chemistry S Datta

REACTION DYNAMICS/CHEMICAL KINETICS 123
Since the ‘k’ values are fairly constant by putting the data in the Ist order rate equation
i.e., the hydrolysis of methylacetate is of the Ist order.
Example 4. A Ist order reaction is 25% completed in 30 mins. Determine the time of 50%
completion of the reaction.
Sol. Time of 50% reaction, i.e., t 1/2
to be determined for Ist order reaction t 1/2
is 0.693
k
and k = 2.303 a
.log
t a–
x
Here, t = 30 min a = 100%
a = (100 – 25)% = 75%
k = 2 . 303 100
log = 0.0095 min –1
30 75
∴ t 1/2
= 0.693 = 72.9 minutes.
0.0095
Example 5. Half-life for a first order reaction is 17 mins. Calculate the rate constant
and time for 75% completion of the reaction.
Sol. We know t 1/2
= 0.693
k
Here,
t 1/2
= 17 mins.
∴ k = 0.693
17 min–1 = 0.0407 min –1
Here, a = 100%
a – x = (100 – 75)% = 25%
2.
303 100
∴ k = log
t 25
∴ t = 2.303 log 100 = 2.303 log 4 34 minutes
k 25 0.0407 = .
Example 6. The half-life for radium is 1600 years. Calculate the time for 80%
disintegration.
Sol. Radioactive disintegration is of the Ist order
∴ t 1/2
= 0.693
k
∴ 1600 = 0.693
k
∴ k = 0.693
1600 year–1 = 0.000433 year –1
k = 2.303 a
log
t a – x
Here a = 100 %
(a – x) = 100 – 80 = 20
t =
2.303 100
log = 37.17 yrs.
0.000433 20