First Order & Zero Order Reaction
Rate
The rate of a chemical reaction of process
Is the velocity with which the reaction occurs.
For drug A (decreasing)
-dA/dt
For Drug B (increasing)
+dB/dt
Rate Constant
Zero order reactions
Amount of drug A is decreasing at a constant rate for
each time interval
-dA/dt=-k0
k0= is the zero order rate constant and is expressed in
units of mass/time
Equation:
At=A0-k0 t
Ct=C0-k0 t
At=A0-k0 t
zero order
Drug concentration(mg/ml)
A
120
A0
100
Slope=-k0
80
60
zero order
40
20
0
t
0
2
4
6
Time (hr)
8
10
12
Drug Concentration
(mg/ml)
100
95
90
85
80
75
70
5mg/ml
5mg/ml
5mg/ml
5mg/ml
5mg/ml
5mg/ml
Time
(hr)
0
2
4
6
8
10
12
First order Half life




The time required for the amount to decrease
by one half life
It is constant
no matter what the initial concentation of a
drug is
Drug concentration(mg/ml)
zero order
120
100
80
60
zero order
40
20
0
0
2
4
6
Time (hr)
8
10
12

C0 =100mg/ml at t=0
C =90mg/ml at t=4hr
90=-k0(4)+100
 K0 =2.5mg/ml hr

The amount of drug A is decreasing at a rate
that is proprotional to the amount of drug
remaining.
-dA/dt=K A

At=A0e-kt
Ct=C0e-kt
Half life
t1/2
The period of time required for the amount or
concentration of a drug to decrease by one
half.

Not constant
The zero order t1/2 is proportional to the initial
amount or concentration of the drug and is
inversely proportional to the zero order rate
constant k0
t1/2= 0.5A0
k0
Drug Concentration (mg/ml)
Time
(hr)
100
0
50
4
25
8
12.5
12
6.25
16
3.13
20
1.56
24
First order



The amount of drug eliminated over a certain
time period increases as the amount of drug
in the body increases.
The amount of drug eliminated per unit of
time decreases as the amount of drug in the
body decreases
But the fraction of a drug remain constant
Zero order


The amount of drug eliminated for each time
interval is constant ,regardless of the amount
in the body.
In other words the amount of drug in the body
does not change with the amount or
concentration of the drug in the body. but the
fraction removed varies
First Order Elimination
time
Amount of drug Amount of drug
in the body (mg) eliminated (mg)
Fraction of drug
eliminated over
preceding hour
0
1000
-
0.15
1
850
150
0.15
2
723
127
0.15
3
614
109
0.15
4
522
92
0.15
5
444
78
0.15
6
377
67
0.15
zero order
zero order on semilog paper
1200
1000
800
600
Series1
400
concentration
concentration
1000
100
Series1
10
200
0
1
0
1
2
3
time
4
5
6
0
1
2
3
time
4
5
6
time
Amount of drug Amount of drug
in the body (mg) eliminated (mg)
Fraction of drug
eliminated over
preceding hour
0
1000
-
-
1
850
150
0.15
2
700
150
0.18
3
550
150
0.21
4
400
150
0.27
5
250
150
0.38
6
100
150
0. 60
First order
first order on semilog paper
first order
1000
1200
conc
800
Series1
600
conc
400
concentration
1000
100
Series1
conc
10
200
1
0
0
1
2
3
time
4
5
6
0
1
2
3
time
4
5
6