Chemical kinetics

B-Pharmacy
2nd year 4th sem
Physical Pharmacy

1. CHEMICAL KINETICS Presented by Gourav singh B-Pharmacy- 4th Semester (New PCI Syllabus) Gourav Singh 1

2. INTRODUCTION Reactions kinetics also known as Chemical kinetics. Chemical kinetics describe the mechanism of a chemical reaction . This give an ideas of an activation energy of a chemical reaction. Many properties such as the order of a chemical reaction, the rate of reaction or the concentration of the component can be easily calculated from the study of chemical kinetics . Rate of reaction is the speed at which chemical reaction take place and it is measured by change in concentration (dc) with respect to time ( dt ). It is expressed as Rate of reaction =   Gourav Singh 2

3. INTRODUCTION Where, Positive (+) sign- Increase in concentration over a period of time. Negative (-) sign – Decrease in concentration with respect to time. In general, a chemical reaction for kinetic study is written as cC + dD Products Rate = Rate =   Gourav Singh 3

4. INTRODUCTION Rate = Where K- rate constant or specific constant [C]and [D] – molar concentration of C and D respectively. Rate constant express the relationship between the rate of chemical reaction and the concentration of the reacting substances.   Gourav Singh 4

5. MOLECULARITY REACTION It is defined as number of reactant molecules or atoms that take part in chemical reaction to give the products. If number of reacting particle is one, then the reaction is considered to be Unimolecular . For example :- OR When two reactant molecules are involved to carry out the reaction, this reaction are called bimolecular reaction . For example -   Gourav Singh 5

6. MOLECULARITY REACTION When three reactant molecules are involved to carry out the reaction, this reaction are called trimolecular reaction . For example -   Gourav Singh 6

7. ORDER OF REACTION The sum of exponents or power of concentration term in the rate equation is known as order of reaction. Let us consider a general reaction. Thus the above order reaction is ( c+d ) If the value of ( c+d ) is 0, then it is called zero order reactions . If the value of ( c+d ) is 1, then it is called first order reactions . If the value of ( c+d ) is 2, then it is called second order reactions .   Gourav Singh 7

8. DIFFERENCE BETWEEN ORDER AND MOLECULARITY OF REACTION ORDER OF REACTION MOLECULARITY OF REACTION It is the sum of power of concentration of reactant, with respect to rate of reaction It is sum of reacting atom or molecule undergoing the chemical reaction to form product. It is determine experimentally It is a theoretical concept It may be fractional value It is always whole number Sometime, its value is zero It cannot have zero Order of reaction is based on the overall reaction The overall molecularity of a complex reaction has no significance It can be change with the parameter like, pressure, concentration, temperature Molecularity is not changes with external parametrs . Gourav Singh 8

9. ZERO ORDER REACTION When rate is independent of the reactant concentration, then it is called zero order reaction . Let us consider a reaction: For this Zero order reaction, x=0 Therefore rate =k Rate = Where, = change in concentration with respect to time negative (-) indicate decrease in concentration. K = specific rate constant for zero order.   Gourav Singh 9

10. ZERO ORDER REACTION Derivatives The rate of zero order reaction is expressed as On integrate equation   Gourav Singh 10

11. ZERO ORDER REACTION Or This is integrated rate of equation   t= 0 time (t) Slope = -k Concentration [A] Plot of concentration vs time Gourav Singh 11

12. ZERO ORDER REACTION Characteristics Half life It is the time required to reduce initial concentration of the reactant to become half of its value during the progress of the reaction. Initial concentration = Final concentration = /2 By putting this value in equation [ ] , we get:   Gourav Singh 12

13. ZERO ORDER REACTION Half life is directly proportional to the initial concentration of reactant. Shelf life: It is a time required for reactant concentration to decrease to 90% of the initial concentration. By putting this value in equation [ ] , we get:   Gourav Singh 13

14. ZERO ORDER REACTION This unit of k for zero order reaction is moles/litre/second Example Photochemical reaction between hydrogen and chlorine. Decomposition of on a hot platinum surface. =   Gourav Singh 14

15. ZERO ORDER REACTION Decomposition of in the presence of molybdenum or tungsten. Problems What is the value of rate constant if = 2.30M and half life is 7.30 min. Ans:- k=2.3 M/2 (7.3min) k = 0.157 mol /1.min   Gourav Singh 15

16. ZERO ORDER REACTION The amount of vitamin A oxidized in a certain period of time is 300 unit for a given dose of 3000 IU/ml. It mean that the decrease in potency is 10 percent. If the dose of the vitamin is 3,00,000, IU/ml, then shelf life = = ? Ans: - = 1136363.64 sec or 315.66 hrs or 13.15 days Self study— At the intensity of colour of drug preparation is reduced from 1.345 to 1.335 in 90 days. Estimate the reaction rate if colour fading follow zero order reaction? Answer – 0.011   Gourav Singh 16

17. PSEUDO ORDER REACTION An order of a chemical reaction that appears to be less than the true order due to experimental conditions; when a one reactant is in large excess. There are two types of reaction Pseudo first order reaction Pseudo second order reaction FIRST ORDER REACTION SECOND ORDER REACTION Pseudo first order kinetics 2 nd order rate law = k [A] or [B] Pseudo second order kinetic 3 rd order rate law = Reduce to first Pseudo first order if either [a] or [B] in large excess Reduce to pseudo first order if [A] is in excess, Pseudo second order if [B] is in excess FIRST ORDER REACTION SECOND ORDER REACTION Pseudo first order kinetics 2 nd order rate law = k [A] or [B] Reduce to first Pseudo first order if either [a] or [B] in large excess Reduce to pseudo first order if [A] is in excess, Pseudo second order if [B] is in excess Gourav Singh 17

18. FIRST-ORDER REACTION First order reaction is defined as a reaction in which the rate of reaction depends on the concentration of one reactant. Let us consider Rate = Rate = -d[A]/ dt equate both above equation, we get k[A] = -d[A]/ dt or k dt = -d[A]/[A]   Gourav Singh 18

19. FIRST-ORDER REACTION Integrating the above equation On integration As we know   Gourav Singh 19

20. FIRST-ORDER REACTION Or k This equation is integrated rate law of equation In exponential form, the equation becomes,   Gourav Singh 20

21. FIRST-ORDER REACTION Or For first order equation, when we plot concentration against time, a curve is obtained. The curve shows that concentration decrease exponentially with time. The can be written as-   Gourav Singh 21

22. FIRST-ORDER REACTION Where, a is initial concentration and equal to X is decrease in concentration with time a-x is the concentration remained at time t and equal to The unit of k for first order reaction is   Gourav Singh 22

23. FIRST-ORDER REACTION Half life: To calculate half life As we know rate equation for first order reaction is By putting value of into above equation, we get Or 693/k   Gourav Singh 23

24. FIRST-ORDER REACTION This equation shows that in first order reaction the half life is independent of the initial concentration Shelf life: As per definition By putting these value in equation { }, we get   Gourav Singh 24

25. FIRST-ORDER REACTION Problems The half life of drug which decompose according to first order kinetics, is 75 days. Calculate shelf life and K Ans:- = 0.693/k 75 = 0.693/k k = 0.0092 shelf life   Gourav Singh 25

26. FIRST-ORDER REACTION The initial concentration of drug was found to be 0.075 M. The concentration after 12 hours was 0.055 M. Calculate the reaction rate constant if decomposition of drug follows first order reaction. Solution:- The first order reactions is k = 0.02527   Gourav Singh 26

27. SECOND-ORDER REACTION The reaction is said to be second order when rate of reaction is directly proportional to the concentration of two reactants. In second order reaction two condition are possible When A Products When A + B Products   Gourav Singh 27

28. SECOND-ORDER REACTION Case 1 When there is one reactant or concentration of both reactants are same A + A products At time = 0, initial concentration a a At time = t, Concentration (a-x)(a-x) x Where K is second order rate constant.   Gourav Singh 28

29. SECOND-ORDER REACTION On integrating between x=0 at t=0 and x=dx at t=t, we obtain   Gourav Singh 29

30. SECOND-ORDER REACTION The plot of x/a(a-x) versus time give straight line having slope = k Plot of x/a(a - x) vs time in case of second order reaction   Time Slope = k Gourav Singh 30

31. SECOND-ORDER REACTION Half life By putting these value in above equation, we get or According to this equation half life is inversely proportional to initial concentration.   Gourav Singh 31

32. SECOND-ORDER REACTION Case 2 When concentration of both reactant are different or not same A + B Product At time = 0, initial Concentration A B 0 At time = t, Concentration (a - x)(b - x) X Where a and b are initial concentrations of A and B respectively and x is amount of each of A and B reacting in time t, (a - x) and (b – x ) represent concentration of A and B remaining unreacted at time t.   Gourav Singh 32

33. SECOND-ORDER REACTION Or Rearrange the equation On integration By using partial fraction of , we get   Gourav Singh 33

34. SECOND-ORDER REACTION Put this value of partial fraction into above equation, we get By putting t = 0 and x = 0 in above equation, the value of C will be   Gourav Singh 34

35. SECOND-ORDER REACTION Put the value of C in above equation, we get The unit of rate constant for second order reaction is litre.   Gourav Singh 35

36. SECOND-ORDER REACTION In the saponification of methylacetate at , the concentration of sodium hydroxide remaining after 75 minutes was 0.00552 M. The initial concentration of ester and the base was 0.01 molar. Calculate the second order rate constant and half life of the reaction. Solution:- Given:- a = 0.01 molar; (a - x) = 0.00552; t= 75 min; To find:- = ? x = a – (a - x) = 0.01 – 0.00552 x = 0.00448   Gourav Singh 36

37. SECOND-ORDER REACTION Half life = ? Examples: Hydrolysis of ester by an alkali (saponification) Decomposition of into NO and Conversion of ozone into oxygen at Thermal Decomposition of choline monoxide.   Gourav Singh 37

38. DETRMINATION OF REACTION ORDER Order of a reaction can be determine by any one of the following methods: Substitution Method: In this method, the data obtained from a kinetic experiment is substituted in the appropriate rate equation. The equation gives a fairly constant value of k and indicates the order of a reaction. The rate and half-life equation for different order reaction are given in table:- Order Rate Law Rate=k 1 Rate=k[A] 2 Rate=k Order Rate Law Rate=k 1 Rate=k[A] 2 Gourav Singh 38

39. DETRMINATION OF REACTION ORDER Graphical Method: In this method,, the data obtained from a kinetics experiment is plotted in the appropriate form for determining the order of a reaction. For Example, If a plot of concentration versus time (t) yield a straight line, the reaction is of zero-order . If a plot of log (a - x)versus t yield a straight line, the reaction is of first –order. If a plot of versus t yields a straight line (provided the initial concentration are equal), the reaction is of second-order .   Gourav Singh 39

40. DETRMINATION OF REACTION ORDER Half-Life Method: by calculating value of k by above method, value can be estimate for each time period in Kinetic study.   Order of reaction 1 2 Order of reaction 1 2 Gourav Singh 40

41. DETRMINATION OF REACTION ORDER A general expression for the determination of the half –life of a reaction can be given as: Where, n= Order of the reaction. If two reactions are initiated with two different initial concentrations ( and , respectively), the half-lives are determined as:   Gourav Singh 41

42. DETRMINATION OF REACTION ORDER And, On dividing (1) with (2): On taking log: log   Gourav Singh 42

43. DETRMINATION OF REACTION ORDER + 1 Where, n = order of reaction. Half- lives are calculated by plotting a graph between ‘a’ and ‘t’ at two different initial concentration (a1 and a2). The half- life times are then read at a1 and a2 respectively from the graph. The values of half life and the initial concentration are then substituted in the above equation and the order of reaction (n) is calculated directly.   Gourav Singh 43

44. IMPORTANT DEFINITIONS Chemical Kinetics- It include the study of the speed or rate of chemical processes that occur during chemical reactions. Rate of reaction- It is a speed at which chemical reaction take place. Molecularity of reaction- It is defines as number of reactant molecules or atom that take part in chemical reactions to give the products. Unimolecular reaction- When only one reactant molecule participate to carry out the reaction, this reaction are called Unimolecular reaction. Bimolecular reaction- When two reactants molecules are involved to carry out the reaction these reactions are called Bimolecular reaction. Gourav Singh 44

45. IMPORTANT DEFINITIONS Order of reaction- The sum of exponents or power of concentration terms in the rate equation is known as order of reactions. Zero order reactions- When rate is independent of the reactant concentration, that is called as Zero order reactions. Half life- It is the time required to reduce initial concentration of the reactant to become half of its value during the progress of the reaction. Shelf life- It is the time required for reactant concentration to decrease to 90% of the initial concentrations. Gourav Singh 45

46. SUMMARY OF THE KINETICS Order Rate Law Concentration-time Equation Half –Life M/t Unit of k Rate=k [A] = - kt k m/s, m/min, m/ hrs , etc 1 Rate=k[A] In[A] = In - kt kM 2 Rate=k Order Rate Law Concentration-time Equation Half –Life M/t Unit of k Rate=k k m/s, m/min, m/ hrs , etc 1 Rate=k[A] kM 2 Gourav Singh 46

47. Reference Subramanyam C.V.S, First edition, “Chemical Kinetics” Text Book of Physical Pharmaceutics, Page No. 13 – 49 Martin Physical Pharmacy and Pharmaceutical Science, Sixth edition, “Chemical Kinetics and Stability ” Text Book of Physical Pharmaceutics, Page No. 328 -- 354 Gourav Singh 47