WHAT IS CHEMICAL KINETICS?
It is branch of chemistry which deals with the rates of chemical reactions and factors that influence the rates of reaction.
The word kinetics is derived from the greek word ‘kinesis’ which means movement.
Chemecal kinetics tells us about the rate of reactions.some processes,such as initial steps in vision and photosynthesis,takes place on a time scale as short as s to s.others,like curing of cement and conversion of diamond to graphite take years or millions of years to complete.
HISTORY
In the 20th century there have been significant developments in the theory of chemical kinetics (determination of rate constants and reaction orders from "first principles"). It is not yet possible, however, to predict the kinetic parameters for realworld chemical processes, and in reactor design we must rely on carefully planned and executed experiments.
•1850: Wilhelmy (Germany) studied the rate of inversion of sucrose (hydrolysis into D(+)glucose and D()fructose in the presence of an acid) and found it to be proportional to the concentrations of both the sugar and the acid.
•1864: Guldberg and Waage (Norway) formulated their "law of mass action," according to which the reaction "forces" are proportional to the product of the concentrations of the reactants:
K=[R]^{r} [S]^{s}/([A]^{a} [B]^{b}).
•1887: Ostwald (Germany; Latvia) introduces the terms "reaction order" and "halflife" in his "Lehrbuch der allgemeinen Chemie."
USES
On practical level,a knowledge of reactions rates is useful in drug design ,in pollotion control and in food processing.
Industrial chemists place more emphasis on speeding up rate of reaction rather than on maximising its yield.
The mathematical models that describe chemical reaction kinetics provide chemists and chemical engineers with tools to better understand and describe chemical processes such as food decomposition, microorganism growth, stratospheric ozone decomposition, and the complex chemistry of biological systems. These models can also be used in the design or modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful byproducts. When performing catalytic cracking of heavy hydrocarbons into gasoline and light gas, for example, kinetic models can be used to find the temperature and pressure at which the highest yield of heavy hydrocarbons into gasoline will
occur.
REPRESENTATION
We know that any reaction can be represented by general equation,
ReactionsàProducts
This equation tells us that during course of reaction ,reactants are consumed while products are formed.
Let we have A molecules which converted to B molecules,
AàB
We can express the rate of reaction in terms of change in concentration with time .Thus,for reaction AàB ,we can express the rate as,
RATE =  or RATE =
Here, denotes the difference between the final and initial concentration and time.
Where and are changes in concentration(molarity) over a time period .Because the concentration of A decreases during the time interval , is negative quantity.The rate of reaction is positive quantity ,so minus sign is needed in rate expression to make the rate positive.
On the other hand,rate of product formation doesnot require a minus sign as is a positive quantity(as concentration of B increases with time).These rates are average rates because the are averaged over a certain time period
.
DEPENDENCE OF REACTION RATE ON CONCENTRATIONà
From above graph ,it is clear that,rate of reaction is directly proportional to concentration of the reactants that is,
RATE concentration
(where is the sign of proportionality)
àRATE=k(concentration) (where k is the proportionality constant). Here, k is the rate constant .
RATE LAW
A rate law is a mathematical equation that describes the progress of the reaction. In general, rate laws must be determined experimentally. Unless a reaction is an elementary reaction, it is not possible to predict the rate law from the overall chemical equation. There are two forms of a rate law for chemical kinetics: the differential rate law and the integrated rate law.
The differential rate law relates the rate of reaction to the concentrations of the various species in the system.
Differential rate laws can take on many different forms, especially for complicated chemical reactions. However, most chemical reactions obey one of three differential rate laws. Each rate law contains a constant, k, called the rate constant. The units for the rate constant depend upon the rate law, because the rate always has units of mole L^{1} sec^{1} and the concentration always has units of mole L^{1}.
àFirstOrder Reaction
For a firstorder reaction, the rate of reaction is directly proportional to the concentration of one of the reactants.
Differential Rate Law: r = k [A]
The rate constant, k has units of sec^{1}.
àSecondOrder Reaction
For a secondorder reaction, the rate of reaction is directly proportional to the square of the concentration of one of the reactants.
Differential Rate Law: r = k [A]^{2}
The rate constant, k, has units of L mole^{1} sec^{1}.
ORDER OF THE REACTION
It is the sum of the powers to which the concentrations terms are raised in rate law equation to express the observed rate of the reaction.
If the rate of reaction,
aA + bB + cC àproducts
is given by rate law as:
RATE=k
Then, the order of the reaction,is:
n = p + q + r.
here,p,q and r are the orders with respect to individual reactants and overall order of reaction is sum of these exponents that is p+q+r.
p,q and r are found experimentally.
àORDER OF A REACTION CAN BE IN FRACTION AND CAN BE A WHOLE NUMBER.
àEXAMPLES OF REACTIONS OF DIFFERENT ORDERSà
(a) RXN OF FIRST ORDER,
Decomposition of nitrogen pentoxide( )
(g) à 2 (g) + (g)
RATE = k (Here,n=1,order =1)
(b) RXN OF SECOND ORDER,
Decomposition of nitrogen peroxide,
à +
UNITS OF RATE CONSTANTà
RATE = k
= K
AS RATE = , HERE , N IS ORDER OF REACTION.
K = 
OR
àFOR FIRST ORDER REACTIONà N=1
K= 
K=
àFOR SECOND ORDER REACTIONà N=2
K= 
K=
à
Integrated Rate Expressions
Concentration dependence of rate is a differential equation . It is tedious to determine the instantaneous rates from the slopes of the tangents for each value of t and this in turn makes the rate law determination difficult. To avoid this difficulty, the integrated form of the rate law expression is used.
From the integrated rate equation, the extent of a reaction in terms of the concentration of the reactant can be measured, if the rate constant is known. If the extent of the reaction is known, then the rate constant can be easily calculated. The integrated rate expressions are different for reactions of different orders. The integrated rate expressions for zero order and first order are derived in the subsequent sections.
à FIRST ORDER REACTIONà
A first order reaction is a reaction whose rate depends on the reactant concentration raised to the first power. In a first power reaction of the type,
R à Products
Let [R] is concentration of the reactant R and k be the rate constant .For the first order reaction,the rate of the reaction is directly propotional to the concentration of reactant R.
Rate = k[R]
Integrated Form of the FirstOrder Rate Law
The original firstorder rate law equation is:
The integrated form of the firstorder rate law equation is:
Integration of the differential equation gives
In [A] =  kt + constant
At t = 0, [A] = [A]_{o}
ln [A]_{o} = constant
On substitution, the integrated equation is transformed to
The rate constant k_{1}, of a first order reaction can be determined from the expression,
The integrated rate equation can also be written in the form,
This equation shows that the concentration of the reactant decreases exponentially. From the equation it can be seen that if ln[A] is plotted against t, a straight line is obtained with the slope equal to (k).
 Where X is the concentration of a reactant at any moment in time, (X)_{o} is the initial concentration of this reactant, k is the constant for the reaction, and t is the time since the reaction started.
 This equation is useful in calculating how much of a substance remains after a certain amount of time has passed, or to calculate how long it takes until the concentration is at a certain point.
àGRAPHSà
FirstOrder Reaction

 If the rate law of a reaction is first order 
 The equation for the halflife of a substance is derived from this equation.
 Halflife  The length of time it takes for exactly half of the nuclei of a radioactive sample to decay.
The halflife of first order reaction is indepensent of concentration of reactants.
The advantages of the integrated form of the rate law are:
· It gives the concentrations for all times
· It is helpful in determining the time in which the reaction is 10% or 60% or 99% complete
The variation of concentration with time is better understood by using the integrated form of the rate law. Half  life expressions, obtained from the integrated are used in the determination of order of a reaction.
è EXAMPLEà
A first order reaction is 40% complete in 50 minutes. What is the rate constant? In what time will the reaction be 80% complete?
Suggested answer:
It is given that the reaction is 40% complete in 50 min
Hence, A = A_{o}  0.4 A_{o} = 0.6 A_{o}
è SECOND ORDER REACTIONS à
A second order reaction is a reaction whose rate depends on the reactant concentration raised to the second power. In a second power reaction of the type,
R à Products
Let [R] is concentration of the reactant R and k be the rate constant .For the first order reaction,the rate of the reaction is directly propotional to the concentration of reactant R.
Rate = k
Integrated Form of the SecondOrder Rate Law
The original equation for a secondorder rate law with a single reactant is:
The integrated form of the secondorder rate law equation is:
· Where X is the concentration of a reactant at any moment in time, (X)_{o} is the initial concentration of this reactant, k is the constant for the reaction, and t is the time since the reaction started.
 This equation is useful in calculating how much of a substance remains after a certain amount of time has passed, or to calculate how long it takes until the concentration is at a certain point
Simple Second Order Rate Equations
A typical simple second order reaction, where B is one of the reactants, would look like,
which can be rearranged for integration as,
This equation can be integrated to give,
or
We can make a quick check to see if this result fits what we know about the system. At t = 0 we get [B] = [B]_{o} which is correct and at t = infinity we find that [B] = 0 which is also what we would expect.
Halflife
We can define the halflife of a second order reaction in the same way as in first order reactions. That is, the halflife, t_{1/2}, is the time required for [B] to fall from [B]_{o}to [B]_{o}/2. Thus we use Equation 3 to give
or
and, finally,
Note that the halflife for a simple second order reactions depends on the initial concentration and that it is proportional to 1/[B]_{o}. Contrast this to what we know about first order reactions where the halflife is independent of the initial concentration. This fact may come in useful later when we try to find experimental methods for determining rate laws..
SecondOrder Reaction

 If the rate law for a reaction is second order 
àOVERVIEWà
Reaction Order  Differential Rate Law  Integrated Rate Law  Characteristic  Slope of  Units of  Halflife  

 
First 
 [A] = [A]_{0}e^{ k t}  ln [A] vs t   k  sec^{1} 
 
Second 

 1/[A] vs t  k  L mole^{1} sec^{1} 
 
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