Engineering Chemistry S Datta

110 ENGINEERING CHEMISTRY
or
or
Taking
dx
dt
= k(a – x)2
dx
( a – x) 2 = k dt
1
= kt + z (integration constant)
a – x
when t = 0, x = 0, z = 1 a
∴ kt =
1 1
– or k = 1 x
.
a – x a t aa ( − x)
if we put a – x = c
then, kt = 1 – 1 ∴ 1 c a c = kt + 1 a .
Characteristic of a Second Order Reaction
i.e.,
(i) Time of half reaction
t 1/2
= 1 x 1 a/
2 1
. = =
k aa ( – x)
kaa ( – a/ 2)
ak
half decomposition time of a second order reaction is inversely proportional to the first
power of initial concentration and is equal to 1 k when a = 1
i.e.,
(ii) Unit of rate constant k
dx
dt = k(a – x)2 = kc 2 when (a – x) = c
∴ k = dx . 1 conc 1
= ×
dt c time conc
(iii) Physical significance
2 2
k = dx
dt = When c = 1
= conc –1 . time –1 = l . mol –1 sec –1 [l = litre]
k is the rate of decomposition at unit concentration of the reactants.
Examples of a Second Order Reaction
(i) Decomposition (gas phase):
(a) 2HI ⎯⎯→ H 2
+ I 2
(b) 2NO 2
⎯⎯→ 2NO + O 2
(c) 2NOCl ⎯⎯→ 2NO + Cl 2
(ii) Displacement reaction (gas phase):
(a)
(b)
H + D 2
⎯⎯→ HD + D
Cl + H 2
⎯⎯→ HCl + H