Kinetics for Pharmaceutical analysis and Physical Pharmacy

1. Dr.S.Alexandar,M.Pharm,Ph.D,
Associate Professor
Vinayaka Missions College of Pharmacy,
Yercaud main road,
Kondappanaickanpatty,
Salem,Tamilnadu,
Pin:636008
Chemical KineticsChemical Kinetics

4. Chemical KineticsChemical Kinetics
A study of
(1) reaction rates
(2) the factors affecting reaction rates
(3) reaction mechanisms
(the detailed steps involved in
reactions)

5. Outline: KineticsOutline: Kinetics
Reaction Rates How we measure rates.
Rate Laws
How the rate depends on
amounts of reactants.
Integrated Rate Laws
How to calc amount left or time
to reach a given amount.
Half-life
How long it takes to react 50%
of reactants.
Arrhenius Equation
How rate constant changes with
T.
Mechanisms
Link between rate and molecular
scale processes.

6. Explosive reactions
2H2(g) + O2(g) → 2H2O(l)

7. Potassium reacts with water
vigorously
Vigorous reactions
2K(s) + 2H2O(l) → 2KOH(aq) + H2(g)

8. Very rapid reactions
Ag
+
(aq) + Cl
−
(aq)→ AgCl(s)
Formation of insoluble salts

9. Fe3+
(aq) + 3OH
−
(aq)→ Fe(OH)3(s)
Very rapid reactions
Formation of insoluble bases

10. Very rapid reactions
H+
(aq) + OH
−
(aq)→ H2O(l)
Acid-alkali neutralization reactions

11. Rapid or moderate reactions
Zn(s) + 2Ag+
(aq) → Zn2+
(aq) + 2Ag(s)
Displacement reactions of metals : -

12. Slow reactions
Fermentation of glucose
C6H12O6(aq) → 2C2H5OH(aq) + 2CO2(g)

13. Very slow reactions
Rusting of iron
4Fe(s) + 3O2(g) + 2nH2O(l) → 2Fe2O3 · nH2O(s)

14. Extremely slow reactions
CaCO3(s) + 2H
+
(aq) → Ca
2+
(aq) + CO2(g) + H2O(l)
Before corrosion After corrosion

15. Rates of Reaction
An important part of studying
chemical reactions is to monitor the
speed at which they occur. Chemists
look at how quickly, or slowly,
reactions take place and how these
rates of reaction are affected by
different factors.
The light produced by a firefly depends
on the speed of a particular chemical
reaction that occurs in its abdomen.
Chapter 6: Rates of Reaction

16. Section 6.1
Chemical Reaction Rates
Chemical kinetics is the study of the rate at which
chemical reactions occur.
Chapter 6: Rates of Reaction
The term reaction rate, or rate of reaction refers to:
• the speed that a chemical reaction occurs at, or
• the change in amount of reactants consumed or
products formed over a specific time interval

17. Chemical kinetics
Chemical kinetics is the study of the rates and the mechanism of
chemical reactions. Commonly the measure of how fast the products
are formed and the reactants consumed is given by the rate values.
The study of chemical kinetics has been highly useful in determining
the factors that influence the rate, maximum yield and conversion in
industrial processes. The mechanism or the sequence of steps by
which the reaction occurs can be known. It is also useful in selecting
the optimum conditions for maximum rate and yield of the chemical
process.

18. The rate of a reaction tells us how fast the reaction occurs. Let us consider
a simple reaction.
A + B → C + D
As the reaction proceeds, the concentration of the reactant A and B
decreases with time and the concentration of the products C + D increase
with time simultaneously. The rate of the reaction is defined as the change
in the concentration of any reactant or product in the reaction per unit
time.
For the above reaction,
Rate of the reaction
= Rate of disappearance of A
= Rate of disappearance of B
= Rate of appearance of C
= Rate of appearance of D

19. Types of RatesTypes of Rates
Initial Rates
◦ Rates measured at the beginning of the
reaction, which is dependent on the initial
concentrations of reactants.
Instantaneous Rates
◦ Rates measured at any point during the
reaction.
Average Rates
◦ An overall rate measured over a period or time
interval.

20.  During the reaction, a change in the concentration is infinitesimally small
even for small changes in time when considered in seconds. Therefore
differential form of rate expression is adopted. The negative sign shows the
concentration decrease trend and the positive sign shows the concentration
increase trend.
 Units of Rate
 Reaction rate has units of concentration divided by time.
 Zero order k = Msec-1
 1st order k = sec-1
 2nd order k = M-1
sec-1
 Mole / litre sec or mol 1-1
s
 Mole / litre min or mol 1-1
min-1
 Mole / litre hour mol 1-1
h-1


21. Factors influencing reaction rates
There are number of factors which influence the rate of the
reaction.
These are :
(i) Nature of the reactants and products concentration
(ii) Concentration of the reacting species
(iii) Temperature of the system
(iv) Presence of catalyst
(v) Surface area of reactants
(vi) Exposure to radiation

22. (i) Effect of nature of the reactant and product
Each reactant reacts with its own rate. Changing the
chemical nature of any reacting species will change the rate
of the reaction.
(ii) Concentration of the reacting species
As the initial concentration of the reactants increase in the
reaction mixture, the number of reacting molecules will
increase. Since the chemical reaction occurs when the
reacting species come close together and collide, the
collisions are more frequent when the concentrations are
higher. This effect increases the reaction rate.

23. (iii) Effect of temperature
Increase in temperature of the system increases the rate of the reaction. This
is because, as the temperature increases the kinetic energy of the molecules
increases, which increases the number of collisions between the molecules.
Therefore the overall rate of the reaction increases.
(iv) Effect of presence of catalyst
A catalyst is a substance that alters the rate of a chemical reaction, while
concentration of catalyst remaining the same before and after the reaction.
The addition of catalyst generally increases the rate of the reaction at a given
temperature. Also, catalyst is specific for a given reaction.

24. (v) Effect of surface area of reactants
As the particle size decreases surface area increases for the same mass. More
number of molecules at the surface will be exposed to the reaction conditions such
that the rate of the reaction increases. Thus the reactants in the powdered form (or)
in smaller particles react rapidly than when present in larger particles.
(vi) Effect of radiation
Rates of certain reactions are increased by absorption of photons of energy. Such
reactions are known as photochemical reactions. For example, H2 and Cl2 react
only in the presence of light. With increase in the intensity of the light (or)
radiation, the product yield increases. For photosynthesis light radiation is essential
and the process does not proceed in the absence of light.

25. The Rate Law
The rate law expresses the reaction rate as a function of reactant
concentrations, product concentrations, and temperature. It is
experimentally determined.
The derived rate law for a reaction must be consistent
with the postulated chemical mechanism of the reaction!
For a general reaction: aA + bB + ..... cC + dD
rate law: rate = k[A]m
[B]n
........
k = rate constant
m and n = reaction orders (not related to a, b,...)
(for a unidirectional (one-way) reaction)!

26. Rate law : R = k [A]
α
[B]
β
...
Rate Constant
Reaction order
• The rate of reaction is often found to be proportional to the
molar concentrations of the reactants raised to a simple power.
• It cannot be overemphasized that reaction orders have no
relation to stoichiometric coefficients, and they are determined by
experiment.

27. Order of the reaction
Order of a reaction is defined as the sum of the exponential powers to which each
concentration is raised in the rate expression.
For example, if the overall rate is given by the expression
Rate = k [A]m
[B]n
Then, the overall order of the reaction is (m+n). The order with respect to A is m.
The order with respect to B is n. If m=1; n=0 and vice versa, the order of the
reaction is 1, and the reaction is called first order. If m=1, n=1, the order of the
reaction is 2 and the reaction is called second order and so on. A zero order
reaction is one where the reaction rate does not depend upon the concentration of
the reactant. In this type of reaction, the rate constant is equal to the rate of the
reaction.

29. Determining order of reaction
•Determining reaction order from rate laws
•Half life method
•Graphing kinetic data

30. Concentration-Time EquationsConcentration-Time Equations
First-Order Integrated Rate Law
– You could write the rate law in the form
]A[k
t
]A[
Rate =
∆
∆
−=

31. Concentration-Time EquationsConcentration-Time Equations
First-Order Integrated Rate Law
– Using calculus, you get the following equation.
kt-
]A[
]A[
ln
o
t
=
– Here [A]t is the concentration of reactant A at time t, and [A]o is the
initial concentration.
– The ratio [A]t/[A]o is the fraction of A remaining at time t.

32. Concentration-Time EquationsConcentration-Time Equations
Second-Order Integrated Rate Law
– You could write the rate law in the form
2
]A[k
t
]A[
Rate =
∆
∆
−=

33. Concentration-Time EquationsConcentration-Time Equations
Second-Order Integrated Rate Law
– Using calculus, you get the following equation.
ot [A]
1
kt
]A[
1
+=
– Here [A]t is the concentration of reactant A
at time t, and [A]o is the initial concentration.

34. Concentration-Time EquationsConcentration-Time Equations
Zero-Order Integrated Rate Law
– The Zero-Order Integrated Rate Law equation
is:.
o]A[kt]A[ +−=

35. Half-lifeHalf-life
The half-life of a reaction is the time required
for the reactant concentration to decrease to
one-half of its initial value.
– Solving for t1/2 we obtain:
k
693.0
t2
1 =

36. Half-Life (1st order)Half-Life (1st order)
Half-life: the time
that it takes for the
reactant
concentration to drop
to half of its original
value.

37. Half-LifeHalf-Life
 The decomposition of ethane (C2H6) to methyl radicals
(⋅CH3) is a first order reaction with a rate constant of
5.36 x 10−4
s−1
at 700 0
C.
C2H6 → 2CH3
Calculate the half-life in minutes.
1/2 4 1
0.693
t 1293 s
5.36 10 s
1 min
1293 s 21.5 min
60 s
− −
= =
×
× =

38. Half-lifeHalf-life
The half-life of a reaction is the time required
for the reactant concentration to decrease to
one-half of its initial value.
– For a first-order reaction, the half-life is independent of the initial
concentration of reactant.
2
1kt)ln(2
1 −=
– In one half-life the amount of reactant decreases by one-half. Substituting
into the first-order concentration-time equation, we get:

39. Half-lifeHalf-life
For a second-order reaction, half-life
depends on the initial concentration and
becomes larger as time goes on.
– Again, assuming that [A]t = ½[A]o after one half-life, it can be shown that:
o]A[k
1
t2
1 =

40. Half-lifeHalf-life
For Zero-Order reactions, the half-lite is
dependent upon the initial concentration
of the reactant and becomes shorter as
the reaction proceeds.
k2
]A[
t o
2
1 =

41. Summary of OrdersSummary of Orders

42. Graphing Kinetic DataGraphing Kinetic Data
 In addition to the method of initial rates, rate laws can
be deduced by graphical methods.
– If we rewrite the first-order concentration-
time equation in a slightly different form, it
can be identified as the equation of a straight
line.
ot ]Aln[kt]Aln[ +−=
y = mx + b
This means if you plot ln[A] versus time, you will get a straight line for a
first-order reaction.

43. Graphing Kinetic DataGraphing Kinetic Data
– If we rewrite the second-order concentration-time equation in a slightly
different form, it can be identified as the equation of a straight line.
ot ]A[
1
kt
]A[
1
+=
y = mx + b
This means if you plot 1/[A] versus time, you will get a straight line
for a second-order reaction.

44. Graphical MethodsGraphical Methods
Given concentration and time data,
graphing can determine order

45. Collision TheoryCollision Theory
Rate constants vary with temperature.
Consequently, the actual rate of a
reaction is very temperature dependent.
• Why the rate depends on temperature
can by explained by collision theory.

46. Collision TheoryCollision Theory
Collision theory assumes that for a
reaction to occur, reactant molecules must
collide with sufficient energy and the
proper orientation.
• The minimum energy of collision required
for two molecules to react is called the
activation energy, Ea.

47. Collision TheoryCollision Theory
Particles must collide in order to react
The greater frequency of collisions, the
higher the reaction rate
Only two particles may react at one time
Many factors must be met:
◦ Orientation
◦ Energy needed to break bonds (activation
energy)

48. Collision TheoryCollision Theory

49. Collision TheoryCollision Theory
Though it seems simple, not all collisions
are effective collisions
Effective collisions: a collision that does
result in a reaction
An activated complex (transition state)
forms in an effective collision

50. Activation EnergyActivation Energy
 In other words, there is a minimum amount of energy
required for reaction: the activation energy, Ea.
 Just as a ball cannot get over a hill if it does not roll up
the hill with enough energy, a reaction cannot occur
unless the molecules possess sufficient energy to get over
the activation energy barrier.

51. Activation EnergyActivation Energy

52. Molecularity of the reaction
 Molecularity is defined as the number of atoms or molecules taking part in
an elementary step leading to a chemical reaction. The overall chemical
reaction may consist of many elementary steps. Each elementary reaction
has its own molecularity which is equal to number of atoms or molecules
participating in it. If the reaction takes place in more than one step there is
no molecularity for the overall reaction. However molecularity and order
are identical for elementary reaction (one step). There are many differences
between the concepts of order and molecularity.

53. Order of a reaction Molecularity of a reaction
1. It is the sum of powers raised
on concentration terms in the
rate expression.
It is the number of molecules of
reactants taking part in elementary
step of a reaction.
2. Order of a reaction is an
experimental value, derived
from rate expression.
It is a theoretical concept.
3. Order of a reaction can be zero,
fractional or integer.
Molecularity can neither be zero
nor fractional.
4. Order of a reaction may have
negative value.
Molecularity can never be negative
5. It is assigned for overall
reaction.
It is assigned for each elementary
step of mechanism.
6. It depends upon pressure,
temperature and concentration
(for pseudo order)
It is independent of pressure and
Temperature.

54. Hess’s LawHess’s Law
The overall enthalpy change in converting
reactants to products is the same regardless of
the route taken.
If a chemical change can be made to take
place in two or more different ways whether
in one step or two or more steps, the amount
of total heat change is same no matter by
which method the change is brought about.
Example
A —>B (ROUTE 1)
or
A —>C —>B (ROUTE 2)
or
A —>D —>E —>B ( ROUTE 3)

55.  HΔ 1 = route 1
 HΔ 2 + HΔ 3 = route 2
 HΔ 4 + HΔ 5 = route 3
Hess’s Law states the overall enthalpy
change will be the same – therefore:
 HΔ 1 = HΔ 2 + HΔ 3
or
= HΔ 4 + HΔ 5

56. Uses of Hess’s LawUses of Hess’s Law
We can use Hess’s Law to calculate enthalpy
changes which are very difficult or impossible to
do by experiment.
Example
The neutralisation of KOH using HCl.
We can do this by adding KOH(s) directly to
HCl(aq) – HΔ 1
or
Dissolving KOH(s) in water – HΔ 2
then
Adding KOH(aq) to HCl(aq) – HΔ 3

57. PathwayPathway
1. KOH(s) + HCl (aq) —> KCl (aq) +
H2O(l) HΔ 1
2. KOH(s) + H2O (aq) —> KOH (aq)
HΔ 2
3. KOH(aq) + HCl(aq) —>KCl (aq) +
H2O H3Δ
According to Hess’s Law
 HΔ 1 = HΔ 2 + HΔ 3

58. Carnot’s Principle
The net heat absorbed by the system, during the cyclic process is equivalent to
the total external work done. A device which transforms heat into work is
called a heat engine. This happens in a cyclic process.
Three types of cycles
Otto Cycle
Diesel Cycle
Carnot Cycle
Isothermal Process: the temperature of the system and the surroundings remain
constant at all times. (q=-w)
Adiabatic: a process in which no energy as heat flows into or out of the
system. (∆U=w)

59. Four stage reversible sequence consisting of
 1. Isothermal expansion at high temperature T2
 2. Adiabatic expansion
 3. Isothermal compression at low temperature T1
 4. Adiabatic compression
The most efficient heat engine cycle is the Carnot cycle, consisting of two
isothermal processes and two adiabatic processes. The Carnot cycle can be thought of
as the most efficient heat engine cycle allowed by physical laws. When the
second law of thermodynamics states that not all the supplied heat in a heat engine can
be used to do work, the Carnot efficiency sets the limiting value on the fraction of the
heat which can be so used.

61. Phase Rule
The phase rule is an important generalization dealing with the
behavior of heterogenous systems. In general it may be studied with
the application of phase rule is it is possible to predict qualitatively
by means of diagram the effect of changing pressure, temperature
and concentration on a heterogenous system in equilibrium. For a
closed, homogeneous system of constant composition (e.g., an ideal
gas), we require two parameters of state (for example, T and p) in
order to describe it. For a heterogeneous system in equilibrium,
consisting of one component (e.g., water substance) and two phases
(e.g., liquid and vapour), we require only one parameter of state
(for example, T). The phase rule allows one to determine the
number of degrees of freedom (F) or variance of a chemical system.
This is useful for interpreting phase diagrams

62. The least number required to define the state of the system.
Degrees of Freedom
Intensive variables that must be known to describe the system
completely. Ex. temperature, concentration, pressure, density, etc.
The degrees of freedom of a system is expressed as follows
2+−= PCF

63. This example may be expressed more generally in terms of Gibb’s phase rule:
F = C – P + 2
Where
F is the number of degrees of freedom,
c is number of components
P is the number of phases in the system.
The number two is specified because this formulation assumes that both T and P can be
varied.
For one component system,
F = C – P + 2 = 1 – P + 2 = 3-P
When only one phase is present
F = 3 – 1 = 2
For one component system, When only one phase is present
F = 3 – 2 = 1

64. Phase Diagram for H2
O