Chapter 5_Chemical Kinetics_ GENERAL_ CHEMISTRY

CHEMICAL KINETICS

1. Chapter 5 Kinetic Chemistry PhD. Đặng Văn Hân Office: 112B2 or 804H3 Building Email: [email protected] Faculty of Chemical Engineering Department of Inorganic Technology General Chemistry

2. 2 Outline 1. Chemical Thermodynamics vs. Kinetics 2. Reaction Rate ( r rxn ) 3. Reaction Rate Constant (k) 4. Reaction Orders 5. Main Effects on the Reaction Rate 6. Catalyst and Mechanism

3. Thermodynamics vs. Kinetics THERMODYNAMICS Predicts direction and ‘driving force’ of chemical reactions based ONLY on the properties of reactants and products . KINETICS Predicts rate of chemical reaction depend on the pathway from reactants to products . Domain of thermodynamics (Initial & Final States) Reaction progress Energy Domain of kinetics Reactants Products The rate of chemical reactions; How to control or influence the rate (lower – faster); The mechanism of reaction.

4. Reaction Rate Reaction Rate: is expressed as the concentration of reactant consumed or the concentration of product formed per unit time t = 0 s t = 30 s t = 60 s Determination of Reaction Rates: Law of Mass Action Con. Change in the time Consider rxn : A → B UNIT of Reaction Rates: M/s or mol.l -1 s -1

5. 5 4 major factors strongly affect on the reaction rate : Concentration of reactant Temperature Surface area Catalyst Coefficients Coefficients in a chemical equation : are the simplest numbers used to balance chemical equations and are placed in front of a chemical symbols or formula. Example : 2 H 2 + 1 O 2 → 2 H 2 O

6. The average rate Definition : Is the concentration change of reactants or products that occurs in the unit of time. C [mol L -1 ]  aA + bB = cC   C A  C B  C C  C A < 0 C B < 0 C C > 0 - C A = - C B = + C C   A = -   The average rate of A , B , C : C = +   B = -   The average reaction rate: rxn = - = - = +   r rxn = = =  

7. The instantaneous Rate C [mol L -1 ]  aA + bB = cC   C A  C B  C C  dC A < 0 dC B < 0 dC C > 0 - C A = - C B = + C C   = -   Instantaneous rate of A , B , C : = +   = -   The instantaneous rate of reaction: = - = - = +   Definition : Is the reaction rate at any given point in time . T he instantaneous rate at a given time corresponds to the slope of a line tangent to the concentration-versus-time curve.

8. 8 Reaction Rate Based on Mass-Action Law Law of Mass Action (M. Guldberg and P. Waage ) aA (g) + bB (g) = cC (g) + dD (g) At T = const., consider the simple homogeneous reaction : Reaction rate: r = k [A] a [B] b With: r: reaction rate k: reaction rate constant 1. Reaction nature 2. Temperature 3. Catalysts Correct solution for simple reactions or for each step of a complex reaction

9. Simple vs. Complex Reaction Simple Reaction : only undergoes 1 stage (step) Each step is called a simple reaction ∑ Steps (simple reactions): reaction mechanism H 2 (g) + I 2 (g) = 2HI(g) k 1 In complex reaction , the overall reaction rate is determined by the lowest rate of simple rxn . Complex Reaction : undergoes many stages (steps) CH 4 (g) + Cl 2 (g) CH 3 Cl(g) + HCl (g)   Cl 2 Cl * + Cl * k 1   CH 4 + Cl * → CH 3 * + HCl k 2 CH 3 * + Cl 2 → CH 3 Cl + Cl * k 3 CH 3 * + Cl * → CH 3 Cl k 4

10. 10 Example 1 : Choose the CORRECT statement. The mechanism of complex reaction describes: 2NO 2 (g) + F 2 (g) → 2NO 2 F (g) Can be explained through 2 simple reactions : NO 2 (g) + F 2 (g)  NO 2 F (g) + F (g) (low) NO 2 (g) + F (g)  NO 2 F (g) (fast) The rate formula of this reaction will be depicted as : A.   B.   C.   D.   Complex reaction

11. 2N 2 O 5 (g) = 4NO 2 (g) + O 2 (g) N 2 O 5 = N 2 O 3 + O 2 (1) ; low reaction rate → r 1 = k 1 .[N 2 O 5 ] N 2 O 5 + N 2 O 3 = 4NO 2 (2) ; high reaction rate → r 2 = k 2 .[N 2 O 5 ].[N 2 O 3 ] The 1 st stage determines the overall rate → r rxn = v 1 = k 1 .[N 2 O 5 ] Example 2 : There are two successive stages : → The 1 st reaction order Complex reaction

12. Complex reaction Example 3 (5.4) : The chemical reaction, 2NO( g ) + Br 2 (g)  2NOBr( g ) proceeds as the following elementary steps: Step 1: NO( g ) + Br 2 ( g ) ⇌ NOBr 2 ( g ) (fast) Step 2: NOBr 2 ( g ) + NO( g )  2NOBr( g ) (low) The rate law expression will be: A. rate = k [NO][Br 2 ] B. rate = k [NO] C. rate = k [Br 2 ] 2 . D. rate = k [NO] 2 [Br 2 ] Slow stage → r L = k L [NO][NOBr 2 ] Solution : unstable Fast stage → K = → [NOBr 2 ] = K[NO][Br 2 ]   r = k [NO] 2 [Br 2 ] D: correct

13. 13 The general reaction rate Consider the homogeneous rxn : aA + bB = cC + dD The general reaction rate: r = k . C A m . C B n m + n : the overall reaction order which can be a negative value, integer, fraction or zero. Values of m & n are calculated by experiments m: the reaction order of A, m the reaction order of B. Simple reactions n = a ; m = b Complex reactions n  a ; m  b 1 st and 2 nd reaction orders are common, whereas zero or 3 rd reaction order is uncommon and reaction orders larger 3 hardly occur.

14. 14 Reaction Orders The 3 rd order respects to NO and the overall rxn = 3 The 1 st order respects to NO 2 and F 2 ; the overall rxn order = 2 The 1 st order for H 2 O 2 and I - ; Zero order for H + ; the overall rxn = 2 3NO (g) → N 2 O (g) + NO 2 (g) r = k[NO] 3 2NO 2 (g) + F 2 (g) → 2NO 2 F (g) r = k[NO 2 ] [ F 2 ] H 2 O 2 (l) + 3I - (l) + 2H + ( aq ) → 2H 2 O (l) + I 3 - (l) r = k[H 2 O 2 ] [ I - ]

15. 15 Example : Choose the CORRECT statement. Consider reaction: 2NO (g) + O 2 (g) = 2NO 2 (g) The formula of the overall reaction rate is So, we can conclude that: The 1 st order for O 2 and the 2 nd order for NO Complex reaction The overall reaction order is 3 The above reaction rate is the average reaction rate   A. 2, 3 and 4 B. 1, 2 and 3 C. 1, 3 and 4 D. Only 1 and 3 Reaction Orders

16. 16 The Effects of Reaction Order on Reaction Rate Consider the simple rxn : A  B + C r rxn = k   Rxn order n = 0 → r rxn = k[A] = k → the rxn rate unchanges as the concentration of reactant A change in time ; Rxn order n = 1 → r rxn = k[A] 1 = kA → the rxn rate doubles as the concentration of reactant A increases double times ; Rxn order n = n → r rxn = k[A] n → the rxn rate increases 2 n times as the concentration of reactant A doubles ;

17. 17 Determination of Reaction Orders and Rates 1. CHEMICAL METHODS: Using the quantative analysis : No. of analytic samples are large  titration 2. PHYSICAL METHODS: Using some method to calculate the change of reactant com. in times : spectrometer, pH, pressure, currency, turbidity measurements, etc. H 2 SO 4 + Na 2 S 2 O 3 = H 2 O + Na 2 SO 4 + S + SO 2  The general-reaction rate: r = k . C A m . C B n The overall reaction rate ( m+n ) must be experimentally calculated even not only based on reaction mechanism :

18. 18 Reaction-Order Cal. based on [Reactant] Change r 1 =k[A 1 ] m [B 1 ] n r 2 =k[A 2 ] m [B 2 ] n   In experiments : The change of reactant A or B Example : A + B  C We have: r rxn = kC A m C B n   r 2 /r 1 = 2 = [A 2 /A 1 ] m [B 2 /B 1 ] n = 1 m 2 n  n=1 r 3 /r 1 = 4 = 2 m 1 n  m=2 r rxn = kC A 2 C B Exp. 1 & 2: Exp. 2 & 3:

19. 19 The Rate Constant (k) Unit: [k] = . = [mol/l] (1-orders) .[s] -1   The zero reaction order: k = M.s -1 or mol.l -1 .s -1 [k] = [mol/l] (1-orders) .[ s ] -1 = M 1-orders .s -1 The 1 st reaction order: k = s -1 The 2 nd reaction order: k = M -1 .s -1 or l.mol -1 s -1 The n th reaction order: k = M 1-n .s -1 or mol 1-n .l n-1 .s -1

20. 20 But, independent on concentration of reactants The activation energy (J): is the minimum energy necessary for reaction occurrence . Nature of reaction and Temp. The activation energy Catalysts Frequency factor ( measure a favorable collision ) k depends on: Arrhenius Equation: The Rate Constant (k)

21. 21 Based on Arrhenius Eq. , At T 1 → we had k 1 T 2 → What is the value of k 2 ? )   The Effect of Temperature on Rate Constant (k)

22. 22 Main effects on the reaction rate Stirring, light, … The general reaction rate: r rxn = k . C A n . C B m with Nature reaction. [Reactants]  r rxn  Temperature Catalysts Surface area (homogeneous rxn ): S  r rxn  Solvent (solution reaction). r rxn depends on

23. 23 The effects of concentration 0. THE ZERO REACTION ORDER Consider a simple rxn : A  Products Reaction rate: Integrate from 0 (corresponding to 0 s and ) to t (corresponding to t s and C A )  

24. 24 Half-life Time of Reaction (t 1/2 ) HALF-LIFE TIME, t 1/2 , is the amount of time required for the reactant to be reduced to exactly half of its starting concentration ( [A] t=1/2 = ½ [A] t=0 ) In the case of the zero order: and C A,t = 1/2  

25. 25 1. THE 1 ST REACTION ORDER Consider a simple rxn : A  Products Reaction rate: The half-life time of 1 st rxn order ONLY depends on rate constant (k) Half-life time: The effects of concentration

26. The GRAPH FORM of the 1 st RXN ORDER Corresponds to the graph: y = ax + b Determination of Rate Constant base on Graph k value is the slope this equation (*) k (*)

27. 27 2. The 2 nd REACTION ORDER Consider a simple rxn : 2A  Products Reaction rate: Half-life time: The effects of concentration

28. 28 Consider a simple rxn : A + B  Products Reaction rate: After integration: The effects of concentration 2. The 2 nd REACTION ORDER

29. 29 Consider a simple rxn : 3A  Products Reaction rate: The effects of concentration 3. The 3 rd REACTION ORDER

30. 30 Short Summary

31. 31 The effect of Temperature Van’t Hoff Principle As the temperature increase of 10 o C , the rxn rate increases 2 - 4 times This principle is ONLY CORRECT in small or mediate temp. ranges   At T 1 → we had k 1 T 2 → What is the value of k 2 ? Based on Arrhenius Eq. : : is the temperature coefficient     General

32. 32 Example 1: The decomposition rxn of N 2 O 5, given and . Calculate We have : The effect of Temperature

33. 33 Example 2: (5.31) A chemical reaction was terminated after 3 hours at 20 o C. At what temperature will the reaction be terminated after 20 min? Given that the temperature coefficient of the reaction is 3. A. at 30 o C B. at 40 o C C. at 50 o C D. at 60 o C We have : The effect of Temperature   n = 2 ⇢ T 2 = 20 + 2*10 = 40 o C B: Correct

34. Reaction Mechanism Once molecules collide they may react together or they may not. So, t he primary requirements for a reaction to occur is that: 1. The reactants must collide and interact with each other. 2 . The molecules must have sufficient energy to initiate the reaction. 3. The molecules must have the proper orientation . Reaction: 2NOBr → 2NO + Br 2 Reaction ⇢No Reaction

35. 35 Catalyst Catalyst is a substance that change the rate of chemical rxn or cause the rxn occurrence Participate in chemical interactions in them intermediate steps After reaction, catalysts usually restores and remains the similar amount as well as chemical properties; ONLY CHANGE rxn rate and times, UNCHANGES the equilibrium constant The roles of catalysts : Reduce the activation energy in reaction through mechanism changes → increase the reaction rate Properties :

36. 36 2 common types of catalysts: 1. Homogeneous Catalysts 2. Heterogeneous Catalysis Catalysts & Reactants have same phases Catalysts & Reactants have different phases Selective properties : Each catalyst is ONLY suitable for a specific reaction With the SAME REACTANT and DIFFERENT CATALYSTS , they can form VARIOUS PRODUCTS Examples :     Catalyst

37. 37 Catalytic Mechanism Example : Consider reaction: A + B = AB Without a catalyst: A + B → A…B → AB , low   In presence of catalyst K: A + K → A…K → AK , fast   AK + B → AK-B → AB + K , fast   Where: and < , so the reaction rate increase in presence of catalyst   A + B + K → AB + K The overall rxn :