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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
Chemical KineticsChemical Kinetics
A study of
(1) reaction rates
(2) the factors affecting reaction rates
(3) reaction mechanisms
(the detailed steps involved in
reactions)
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.
Explosive reactions
2H2(g) + O2(g) → 2H2O(l)
Potassium reacts with water
vigorously
Vigorous reactions
2K(s) + 2H2O(l) → 2KOH(aq) + H2(g)
Very rapid reactions
Ag
+
(aq) + Cl
−
(aq)→ AgCl(s)
Formation of insoluble salts
Fe3+
(aq) + 3OH
−
(aq)→ Fe(OH)3(s)
Very rapid reactions
Formation of insoluble bases
Very rapid reactions
H+
(aq) + OH
−
(aq)→ H2O(l)
Acid-alkali neutralization reactions
Rapid or moderate reactions
Zn(s) + 2Ag+
(aq) → Zn2+
(aq) + 2Ag(s)
Displacement reactions of metals : -
Slow reactions
Fermentation of glucose
C6H12O6(aq) → 2C2H5OH(aq) + 2CO2(g)
Very slow reactions
Rusting of iron
4Fe(s) + 3O2(g) + 2nH2O(l) → 2Fe2O3 · nH2O(s)
Extremely slow reactions
CaCO3(s) + 2H
+
(aq) → Ca
2+
(aq) + CO2(g) + H2O(l)
Before corrosion After corrosion
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
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
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.
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
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.
 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

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
(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.
(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.
(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.
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)!
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.
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.
Determining order of reaction
•Determining reaction order from rate laws
•Half life method
•Graphing kinetic data
Concentration-Time EquationsConcentration-Time Equations
First-Order Integrated Rate Law
– You could write the rate law in the form
]A[k
t
]A[
Rate =
∆
∆
−=
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.
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 =
∆
∆
−=
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.
Concentration-Time EquationsConcentration-Time Equations
Zero-Order Integrated Rate Law
– The Zero-Order Integrated Rate Law equation
is:.
o]A[kt]A[ +−=
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 =
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.
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
− −
= =
×
× =
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:
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 =
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 =
Summary of OrdersSummary of Orders
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.
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.
Graphical MethodsGraphical Methods
Given concentration and time data,
graphing can determine order
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.
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.
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)
Collision TheoryCollision Theory
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
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.
Activation EnergyActivation Energy
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.
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.
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)
 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
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
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
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)
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.
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
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
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
Phase Diagram for H2
O

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Kinetic 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
  • 2.
  • 3.
  • 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.
  • 28.
  • 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 =
  • 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)
  • 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.
  • 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.
  • 60.
  • 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

Editor's Notes

  1. Image source: MHR, Chemistry 12 © 2011. ISBN 07-106010-3; page 276