Basic HTML Version
206
1
M
w
,2
=
1
M
w
,0
+
k
1
2
M
0
t
1
at T
1
(lowest T)
1
M
w
,2
=
1
M
w
,0
+
k
2
2
M
0
t
2
at T
2
(highest T)
⇓
k
1
t
1
=
k
2
t
2
⇔
t
2
t
1
=
k
1
k
2
Thus, the rate constant is simply inversely proportional to the reaction time.
And the ratio between k
1
and k
2
is given by the Arrhenius equation:
k
2
k
1
=
e
−
E
A
R
⎛
⎝⎜
⎞
⎠⎟
1
T
1
−
1
T
2
⎛
⎝⎜
⎞
⎠⎟
Insert for E
A
, T
1
and T
2
and calculate. So if k
2
/k
1
for example equals 5, then
the reaction time is reduced 5 times by increasing the temperature to T
2
.
5.2.3. Role of pH.
Reactions that are catalyzed by H
+
or OH
-
will depend strongly on pH. As a
general rule we can assume that the rate of reaction is proportional to the
concentration of the catalyst:
For acid hydrolysis:
k
∝
[H
+
] or log k = log [H
+
] + c (constant) = -pH + c.
Hence a plot of log k as a function of pH should give a straight line with slope
-1.
For alkaline degradation:
k
∝
[OH
-
] or log k = log [OH
-
] + c (constant) = -log [H+] - 14 + c = pH – 14 + c.