King Saud University
College of Pharmacy
Department of Pharmaceutics
LAB 6
Kinetics: order of reactions
Rates and orders of reactions


Rate:
the rate of a chemical reaction of a process is the
velocity with which the reaction occurs. Consider
the following chemical reaction:
drug A → drug B
Rate constant:
the order of a reaction refers to the way in which
the concentration of drug influences the rate of a
chemical reaction or process.
Zero-Order Reactions
When the reaction rate is independent of the
concentration of the reacting substance.
A = A₀ - k₀t
Where:
A₀: amount of drug at t=0.
A: amount of drug at time t.
k₀: zero-order rate constant, (mass/time).

Zero-Order Reactions
A
A₀
slope = -k₀
Slope = ∆Y = y₂-y₁
∆X
x₂ - x₁
Time
Graph of zero-order equation A = A₀ - k₀t
First-Order Reactions
When the reaction rate depends on the
concentration of the reactant.
-kt
A = A₀ e
Or
log A = -kt/2.303 + log A₀
Where:
A₀: amount of drug at t=0.
A: amount of drug at time t.
k: first-order rate constant, (time⁻¹).

First-Order Reactions
log A
log A ₀
slope = -k/2.303
Time
Graph of first-order equation log A = -kt/2.303 + log A₀
Half-Life

Half-Life (t½):
is the time required for the amount or
concentration of a drug to decrease by one half.
 Zero-order
half-life:
t½ = 0.5 A₀/ k₀
 First-order
half-life:
t½ = 0.693/ k
Shelf life

Shelf life (t½):
is the time required for the amount or
concentration of a drug to decrease to 90% of the
initial concentration.
 Zero-order
shelf life:
t90 = 0.1 A₀/ k₀
 First-order
shelf life :
t90 = 0.105/ k
Practice Problems
1.
Find the log of 35.
1.5441
2.
Find the log of 0.028.
- 1.553
3.
Evaluate e – 1.3
0.2725
4.
Find the value of k in the following expression:
25 = 50e –4k
K= 0.173
Practice Problems
5.
Plot the following data on both semilog graph paper and standard
rectangular coordinates.
a.
b.
c.
d.
e.
Time (min)
Drug A (mg)
10
96.0
20
89.0
40
73.0
60
57.0
90
34.0
120
10.0
130
2.5
Does the decrease in the amount of drug A appear to be a zeroorder or a first-order process?
Does the amount of drug A extrapolate to zero on the x axis?
What is the equation for the line produced on the graph?
What is the rate constant k?
What is the half-life t 1/2 t90?
Home Work
6.
Plot the following data on both semilog graph paper
and standard rectangular coordinates.
Time (min) Drug A (mg)
4
70.0
10
58.0
20
42.0
30
31.0
60
12.0
90
4.5
120
1.7
Answer questions a, b, c, d, and e as stated in Q5.