APPENDIXG
Summary of Useful Formulas
1. Half Lives and Shelf Lives
Integrated Rate Half Life
Order Equation Units ofk
t1l2
(linear form)
Zero C
=
Co - kot cone time-10.5C
a
ka
k
ttime-I 0.693
First 10gC
=
10gCa___
I - -
2.303 k,
Shelf Life
t90
O.lC
a
ko
0.105
k,
2. Temperature Effects
Typical Values (approx.)
Quantity Relationship to K Minimum Maximum
Activation energy
Ea
QIO
Ea
log k==Iog
A> 2.303RT
k, _
Ea(T2 -T,)
logk - 2.303RT,T
2
1
k(T+IO)
QIO
=
-k-
T
10 kcal/mol 25 kcal/mol
24
3.pH Effects
Type of Profile Usual Interpretation Useful Relationships
(may be aEErox.)
V-Graph
Sigmoid curve
Specific acid and base
catalysis
One ionizable group
affecting rate
Two ionizable groups
affecting rate
1 11 kH
PH . =-pK
+-
og-
nun
2
w
2 kOH
pHinfl
=
pKa (for k vs. pH plot)
Bell-shaped curve 1
pHmax
=
"2
(pK, +pK
2)
