Page 85 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch07 Elementary Physical Chemistry

70 Elementary Physical Chemistry

Example 7.6. The decomposition of urea (in 0.1 M HCl)

+
NH 2 CONH 2 +2H 2 O → 2NH +CO 2−
4 3
is first order with rate constants at two different temperatures
Exp T ( C) k (min −1 )
◦
1 61.05 0.713 × 10 −5
2 71.25 2.77 × 10 −5
Calculate A and E a .

Solution
[Note: ln = 2.303 log]

Exp log k 1/T
1 −5.147 2.992 × 10 −3
2 −4.558 2.904 × 10 −3

2.303 × (8.3145 J K −1 mol −1 )(5.147 − 4.558)
E a =
(2.904 − 2.992) × 10 −3 K −1
−1
= 128,100 J mol
log A = −4.558 + 128,100 J mol −1 /(2.303 × 8.3145 × 344.4Jmol −1 )
=14.86678

A =1.722
Arrhenius’ qualitative explanation of activation energy was based on the
assumption that in every system there is an equilibrium between normal
and active molecules and only active molecules can take part in chemical
reactions. According to this theory, increasing the temperature results in

(1) an increase in the number of collisions, and
(2) an increase in the concentration of active molecules.

7.10. Reaction Rate Theories
There are two theories that purport to explain reaction rates quantitatively:

(1) Collision Theory,
(2) Activated Complex Theory.