Chemical Kinetics Ipe

Chemical kinetics

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CHEMICAL KINETICS Chemical kinetics deals with 1) Study of rates of reactions 2) Factors affecting rate of reaction 3) Study of mechanisms of reactions Rate of reaction : The rate of reaction is defined as the change in molar concentration of either reactants or products in unit time. change in concentration time interval Let ‘dc’ is the decrease in concentration of reactants in a small interval of time ‘dt’ then rate  r  =

dc ( negative sign indicates decrease in concentration ) dt If ‘dx’ is the increase in concentration of products in a small interval of time ‘dt’ then dx ( positive sign indicates increase in concentration ) dt

E.g., For a reaction, A  B

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r=

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r=-

d  A  d  B  dt dt In general for a reaction, pP + qQ  rR + sS the relations between rates of reaction with respect to P,Q,R and S can be written as

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1 d  P  1 d Q 1 d R  1 d S ==+ =+ p dt q dt r dt s dt

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-

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rate  r  

 2NH3 g  , the relations can be expressed as Eg., for the reaction, N 2 g  +3H 2 g  

-

d  N2  1 d H2  1 d  NH 3   dt 3 dt 2 dt

Factors affecting the rate of reaction 1) Nature of reactants: Rate of a reaction depends on the nature of bonding in the reactants. Ionic compounds react faster than covalent compounds. The reactions between ionic compounds in water occur very fast as they involve only exchange of ions. Eg., AgCl is precipitated out immediately when AgNO3 solution is added to NaCl solution. AgNO 3 +NaCl  AgCl   NaNO 3 This reaction involves only exchange of ions as shown below and hence occurs very fast. Ag + +NO -3 +Na + +Cl-  AgCl   Na + NO -3 Reactions between covalent compounds take place slowly because they require energy for the cleavage of existing bonds. Eg., Following esterification of acetic acid occurs slowly as the breaking of bonds require energy. O H3C

C

+ OH

H

O C2H5

H2SO4

O H3C

+

C OC2H5

H2O

Chemical kinetics

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VA RD HA N

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concentration of reactants

2) Concentration: Rate of a reaction is directly proportional to the concentration of reactants. rate (r)  cn where c = concentration n = order of the reaction or r = kcn where k = specific rate The number of collisions increases with increase in concentration and hence the rate of the reaction also increases. The rate of a reaction decreases with time as the concentration of reactants is decreasing. This can be shown graphically as follows.

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Time

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k  t +10o C

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3) Temperature : The average kinetic energy and hence the number of collisions increase with absolute temperature. Hence rate of reaction increases with increase in temperature. Usually the rate of a reaction is doubled when the temperature is increased by 10oC. Temperature Coefficient : The ratio of rate constants of a reaction at two different temperatures which differ by 10oC is called temperature coefficient.

Temperature coefficient =

k t oC

 2 to3

The relation between rate constant and temperature can be shown by Arrhenius equation. k = A.e-Ea/RT Where k = specific rate constant A = Frequency factor Ea = Activation energy R = Universal Gas constant T = Absolute Temperature Multiplying by 'ln' (natural logarithm) on both sides, ln k = ln A-

Ea RT

or 2.303 log k = 2.303 log A-

Ea RT

Ea 2.303 RT When a graph is plotted by taking log k on y - axis and 1/T on x-axis, a straight line with negative slope is obtained.

or log k = log A-

slope = -

Ea E =- a 2.303 R 4.576

where R = 1.987 cal / K / mole

Chemical kinetics

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log A slope = -

Ea 2.303 R

log k

1 T

k2 Ea  1 1  =  -  k1 2.303R  T1 T2 

log

E a  T2 -T1  k2 = k1 2.303R T1T2

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or

log

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Relation between two rate constants at two different temperatures can be given as

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without catalyst

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Potential energy

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4) Catalyst: Catalyst is a substance which alters the rate of reaction without being consumed or without undergoing any chemical change during the reaction. A catalyst increases the rate of reaction by providing a new path with lower activation energy for the reaction. In case of reversible reactions, catalyst lowers the activation energies of both forward and backward reaction to the same extent and helps in attaining the equilibrium quickly.

in presence of catalyst

Reaction coordinate

Problems : 1) Write the relations between the rates with respect to reactants & products in the following reaction. 2N2O 2N2 + O2 Rate Equation or Rate Expression or Rate Law: Equation that describes mathematical dependance of rate of reaction on the concentration terms of the reactants is called Rate Equation. For a general reaction, x

y

r = k  A   B C 

where

xA+yB+zC  products. z

k= rate constant or specific rate x,y and z are orders with respects to A,B and C respectively.

Order of reaction :Sum of the powers of the concentration terms in the rate equation is called order of reaction. For a general reaction, xA + yB + zC  products.

Chemical kinetics

if the rate expression is

4 x

y

r = k  A   B  C 

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z

Then the order of this reaction is equal to x + y + z Note: Order of a reaction is to be determined experimentally. It may have positive or negative or zero or a fractional values. In case of simple reactions, the order of reaction and hence the rate equation can be written according to stoichiometric equation. But the actual rate law should be written by conducting experiments. Depending on the order of reaction, chemical reactions can be divided into zero, first, second & third order reactions as follows. Zero order reaction: Total order of the reaction is zero. Example: 1) Decomposition of NH3 on metal surfaces such as gold and molybdenum.

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Au N 2 g  +3H 2 g    2NH 3g 

r = k[N2]0[H2]0

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First order reaction: Total order of the reaction is one. Examples: 1) Thermal decomposition of N2O5 N2O5  N2O4 + 1/2 O2 r = k[N2O5] 2) Thermal decomposition of SO2Cl2 SO2Cl2  SO2+Cl2 r = k [ SO2Cl2] 3) Thermal decomposition of H2O2 H2O2  H2O + 1/2 O2 r = k[H2O2] 4) All radioactive disintegrations

Second order reaction : Total order of the reaction is two. Examples: 1) Thermal decomposition of N2O 2N2O  2N2 + O2 r= k [N2O]2 2) Decomposition of Cl2O 2Cl2O  2Cl2 + O2 r= k [Cl2O]2 Third order reaction : Total order of the reaction is three. Examples: 1) Reaction between NO and O2 to give NO2 2NO + O2--------> 2NO2 r = k[NO]2[O2] 2) Reaction between NO and Cl2 to give NOCl 2NO + Cl2  2NOCl r = k[NO]2 [Cl2]

Chemical kinetics

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Problems : 1) What is the order of the reaction if the rate law for the reaction A + 2B r = k [A]1/2[B]2

products is

Rate constant (k): The rate of a reaction at the unit concentrations of all the reactants of the reaction is called specific rate (or) rate constant. rate = k when [reactants] = 1 Units of rate constant For a general reaction, A  products Rate expression can be written as dc n  k A dt where n = order of the reaction

 Units of k =

mole / litre 1 x n sec  mole / litre  1-n

=

 mole / litre  sec - n-1

For 1st order reaction

For zero order reaction Molecularity

-1   sec -1 -1   L.mole sec

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For 2nd order reaction For 3rd order reaction

.sec-1

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= Ln-1 .mole 

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dc 1 x dt  A n

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k=

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rate =

2 -2 -1   L .mole sec -1 -1   mole .L sec

Elementary reactions: The chemical reactions which occur in one single step are called elementary reactions. But most of the reactions occur in more than one step. The sequence of elementary steps that occur during a reaction is referred to as mechanism of that reaction. Rate determining step: The elementary step or reaction with slowest rate is called rate determining step or rate limiting step. The rate of overall reaction depends on this step. Molecularity: Total number of atoms or molecules or ions taking part in an elementary reaction is called molecularity of that elementary reaction (or step). It is only possible to define the molecularity of an elementary step. But the molecularity of the overall reaction which involves more than one step cannot be defined. Molecularity is an integer. It cannot be zero or fractional. The maximum value observed is 3. It can be deduced theoretically from the proposed mechanism

Chemical kinetics

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Differences between Order and Molecularity

Order Molecularity 1) Sum of the powers of concentration terms 1) Total number of atoms or molecules or in rate expression is called order. ions taking part in an elementary reaction is called molecularity 2) It may have zero or positive or negative or 2) It can only have integral values (1,2 or 3). integer or fractional values. Its value cannot be zero or fractional. 3) It is determined experimentally 3) It is deduced theoretically from the mechanism of the reaction.

dc dx = =kco dt dt

dx o =k  a-x   k dt

or

 dx = k  dt

or

x = kt

or

k=

First order reaction

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x t k = specific rate x = amount of reactant consumed or reacted in time 't'.

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Where

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or

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-

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Integrated rate equations for zero and first order reactions Zero order rate equation: Reactions in which the rate is independent of the concentrations of reactants are called Zero order reactions. The integrated rate equation for zero order reactions is derived as follows.

P For a first order reaction R 

Let

The initial concentration of reactant = a mol. dm-3. Amount of reactant decomposed in 't' sec = x mol. dm-3. The concentration of reactant after 't' sec = (a - x ) mol. dm-3.  dx  The rate   at time 't' is proportional to the concentration of reactant (a - x) at that time. Since the  dt  reaction is a first order reaction, dx   a-x  dt dx  k  a-x  dt

dx =k.dt  a-x  On integration

[where k = specific rate]

Chemical kinetics

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dx

  a-x    k .dt -ln (a-x) = k.t + c when t = 0 then x = 0  -ln a = c Hence -ln(a-x) = kt-ln a

kt = ln

or

k=

1 a ln t  a-x 

or

k=

2.303 a log t  a-x 

a = initial concentration of reactant x = concentration reacted in an interval of time 't' (a-x) = concentration of reactant after time 't'

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Where

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a  a-x 

or

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Half life (t1/2) of a reaction :The time required for initial concentration of reactants to become half is called half life.

a-x = a-

Therefore

k=

or

a = a/2 2

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Then

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Half life of first order reaction can be derived as given below. x = a/2 when t = t1/2

2.303  a  2.303 log  log2 = 2.303 x 0.3010 (  log2 = 03010)  t t1/2 a/2   t1 1/2

t1/2 

2

0.693 k

Methods of determination of order of a reaction : 1) Integrated equation method or Trial and error method * The initial concentration (a) and the concentrations at various intervals of time (a - x) are measured during the progress of reaction by suitable analytical methods. These values are substituted in the rate equations of different rate orders. The order corresponding to the rate equations, which gives constant 'k' values is taken as the order of reaction. Rate equations For a Zero order reaction x = kt or

k=

P R 

x a-  a-x  R o -R t = = t t t

Chemical kinetics

P R 

For first order reaction k=

2.303 a 2.303 R log = log o t a-x t Rt P 2R 

For second order reaction k=

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1 x 1 R o -R t = . at a-x R o t R t

P For second order reaction R1 + R2 

2.303 b( a  x ) log t(a-b) a (b  x ) The order can also be ascertained graphically as follows For a zero order reaction, the graph of 'x' versus 't' must be a straight line parallel to time (t) axis.

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k=

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x

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t

For a first order reaction, the graph of log

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and should pass through the origin

a versus 't' should be a straight line with positive slope a-x

a

V. AD VA I AG T log

a-x

t

x For a second order reaction, the graph of a  a-x  vs 't' must be a straight line passing through the origin with a positive slope.

x a(a-x)

OR

t

  is inversely proportional to a

n-1

2

a(b-x)

t

Half life method Half life t 1

b(a-x) log

Chemical kinetics

t1  2

where

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1 a n -1

a = initial concentration n = order

  The order 'n' of a reaction can be calculated by comparing two half lives - t 1 & t 1 with initial 2

2

concentrations a & a respectively.. t 1

 a   =  t 1  a  

n -1

2

2

3) Van't Hoff differential method

dc1 =kc1n dt

-

;

dc 2 =kc n2 dt

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 dc   log  - 1   log k + nlogc1  dt 

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-

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dc dc n for a reaction of nth order is given by the equation, - =kc dt dt For two initial concentrations c1,c2, we have

The rate -

 dc   dc  log  - 1  - log  - 2   n log c1  nlogc 2  n  log c1  logc 2   dt   dt 

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or

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 dc  log  - 2   log k + nlogc 2  dt 

 dc   dc  log  - 1  - log  - 2   dt   dt  n   log c1  logc2 

concentration of reactants

concentration of reactants

For two different initial concentrations c1 and c2, the rates are determined at any given time from c-t graph. These are substituted in the above equation and 'n' is calculated.

c1

Time (t)

c2

Time (t)

4) Ostwald's Isolation Method In this method, order with respect to each reactant is determined separately by taking other reactants in larger quantity. For example, for the given reactions A + B   products, the order is determined as follows: 1) First the concentration of 'B' is taken in larger excess and the order (nA) with respect to 'A' is determined by any of the other three methods.

Chemical kinetics

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2) In the second experiment the order (nB) with respect to 'B' is determined by taking 'A' in large excess. The order of the overall reaction is taken as nA + nB. Kinetic Molecular Theory of Reaction Rates or Collision theory of reaction rates :

products

A = normal molecule A* = Activated molecule 7) The number of binary collisions per unit time (Z) is given by

where

8 kT .n A .n B 

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2 Z    AB

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Where

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 

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A* + A*

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This theory was proposed by Arrhenius. The main postulates of this theory are 1) Chemical reactions occur due to collisions between reactant molecules. 2) But all the collisions do not lead to the formation of products. 3) Only those collisions taking place between molecules possessing certain minimum amount of energy can form the products. This minimum amount of energy is called Threshold Energy (ET). 4) The energy possessed by the normal molecules under STP conditions is called 'Average Energy'. The difference between threshold energy and average energy of the reacting molecules is called Activation energy (Ea). Ea = Threshold energy (ET) - Average energy (ER) 5) Some molecules will get threshold energy during collisions and are called activated molecules and denoted by asterick(*). 6) The collisions taking place between activated molecules are called activated collisions. The reaction occurs only during the activated collisions. Activated molecules constitute a small fraction of total molecules. Similarly activated collisions constitute small fraction of total collisions. Hence all the chemical reactions do not occur in fraction of second. A+A A* + A  

 AB = Collision diameter  = reduced mass

n A & n B are number of molecules of A & B 8) The relation between specific rate (k), temperature (T) and activation energy Ea can be given as follows k = A.e -Ea /RT or where

k = p.Z.e-Ea /RT p = probability factor

The concept of activation energies of both forward and backward reactions (Ea and Ea') can be shown graphically as follows.

Chemical kinetics

Energy barrier

Ea ET ER

ET E1a

H

Ep

ER = Energy of reactants EP = Energy of products ET = Threshold energy Ea = Activation energy of forward reaction Ea1 = Activation energy of backward reaction H = Enthalpy of reaction

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Where

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Problems : 1) The rate constant of a first order reaction is 1.386 sec-1. What is it's half life. 2) The initial concentration of A is 0.5 moles/litre. If the concentration becomes 0.25 mole/litre in 5 sec. What is the value of rate constant. TEST YOUR UNDERSTANDING

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State whether the following statements are true or false.

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1) The rate of a reaction increases with time as the concentration of reactants decreases. 2) The order of a reaction is always determined experimentally. 3) The units of rate constants for the following reaction are (L / mol /sec). 2NO(g) + Cl2 (g)  2NOCl (g) 4) The half life of zero order reaction is proportional to the initial concentration. 5) The rate of consumption of hydrogen gas is thrice of formation of Ammonia in the following reaction. N2 (g) + 3H2 (g)  2 NH3 (g) 6) In Ostwald isolation method, the reactant for which the order is going to be determined is taken in excess when compared to the concentrations of other reactants. 7) A positive catalyst increases the activation energy of both forward and backward reactions. 8) In exothermic reaction the activation energy of forward reaction is always greater than that of back ward reaction. a is plotted against time (t) ax 10) Rate of reaction increases with increasing temperature as the threshold energy increases.

9) For a second order reaction, a straight line is obtained when log