ON THE SECOND ORDER RATE EQUATION ABDEL 5. SAID New York, N. Y.' THEeauation which determines the rate of a second order reaction is as follows:
Second Method.
but according to a theorem in mathematics where a and b represent the initial molar concentrations of the two reacting substances, x is the molar concentration of the fraction that has reacted in time t and k is the velocity constant. For the special case where b = a, the corresponding equation cannot be readily obtained from the general equation, since by substituting b = a we get kt = 0/0 which is an indeterminate value. The rate equation for the special case is therefore derived by integrating t,he initial differential equation
where f ( b ) and d ( 6 ) are functions of b which tend to eero as b tends to a and f ' ( b ) , +'(b) are the first derivatives wibh respect t o b.
=
lim
1 b
a-0
1 b - z -1
t,he solution of which is
Such derivation terest to derive tion. This has theory of limits;
is very simple yet it should be of inthis equation from the general equabeen accomplished by applying the three different methods are presented.
1 b(a - x ) kt = lim In a-.a-b a(b-s)
First Method. kt
=
Let us assume a
=
Since In ( I
as r
-
+
Third Method
1 b(a - z ) lim -In 6-oa-b a(b-z)
=
b
+c
1 In (1 lim -
.-o
L
+ a P - a,
- az
and since lim n+m
-+2 3
y ) = y - y2 tZ
a Z - a.
?I' -
- az
- -1
t % '
2 (a' - a. - a z ) ?
0 all terms except first term will approach 0 and
'Present address: 630 W. 168th Street, New York.
VOLUME 34, NO. 5, MAY, 1957
+...I
(1
= !?
%)
=
eY
