Engineering Chemistry S Datta

REACTION DYNAMICS/CHEMICAL KINETICS 129
∴ k = 0.693
600
= 1.155 × 10 –3 sec –1
From Arrhenius equation we have,
2.303 log 10
(k/A) = – E a
/RT
or T =
E
a
2.303R log( A /K)
Here,E a
= 98,600 J. mol –1 , R = 8.316 J mol –1 K –1 , A = 4 × 10 13 sec –1
k = 1.115 × 10 –3 sec –1 .
∴ T =
98600
2.303 × 8.316 ×
F
HG
4×
10
3
1.115 × 10
–3
I
KJ K
98600
=
2.303 × 8.316 × 16.555 K
= 98600
= 373 K.
Example 17. A second order reaction, whose rate constant at 800°C was found to be
5.0 × 10 –3 l mol –1 s –1 has an activation energy of 45 kJ mol –1 . What is the value of the rate
constant at 875°C?
Sol. We have,
log K 2 E a (T 1 – T 1)
=
K 1 2.303 RT1T2
Here, K 1
= 5 × 10 –3 l mol –1 s –1 , E a
= 4.5 × 10 4 J mol –1
T 2
= (875 – 273) = 1148 K, T 1
= (800 + 273) = 1073
R = 8.314 J mol –1 K –1
∴
log K K
2
1
4
4.5 × 10 (1148 – 1073)
=
= 0.1431
2.303 × 8.314 × 1073 × 1148
∴ K 2
= Antilog 0.1431 = 1.39
K1
∴ K 2
= 1.39 × 5 × 10 –3 l mol –1 s –1
= 7.0 × 10 –3 l mol –1 s –1 .
Lasers in Chemistry
Laser means “light amplification by stimulated emission of radiation”. The use of lasers
has initiated new types of spectroscopic experiments and has improved the precision of
spectroscopic experiments.
To achieve a laser action a Population inversion should be generated in the system.
Let, the populations be n 2
and n 1
and energies of the two states be E 2
and E 1
. When
E 2
> E 1
, let us state we have a population inversion with n 2
> n 1
, then photons of frequency
1 → 2 = E 2 – E 1
are spontaneously emitted as molecules drop from the state 2 to the state 1.
h