2. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 1 Chapter 14 Rates Equations and Order of Reactions 14.1Rates Equations and Order of Reactions 14.2Zeroth, First and Second Order Reactions 14.3Determination of Simple Rate Equations from Initial Rate Method from Initial Rate Method

3. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 2 14.4Determination of Simple Rate Equations from Differential Rate Equations from Differential Rate Equations 14.5Determination of Simple Rate Equations from Integrated Rate Equations from Integrated Rate Equations 14.6 Carbon-14 Dating

4. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 3 Consider a reaction: aA + bB  C Rate of reaction = k[A] x [B] y (a rate law) 1. x and y can only be determined experimentally and bear NO direct relationships with a and b (stoichiometric ratios) 2. x = order of reaction with respect to reactant A y = order of reaction with respect to reactant B x + y = overall order of reaction k is called the rate constant Note: unit of k depends on x and y Unit: mol dm -3 s -1 14.1 Rates Equations and Order of Reactions (SB p.25) Rate Equations

5. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 4 Zeroth Order Reactions 14.2 Zeroth, First and Second Order Reactions (SB p.26) A product Rate = k[A]º = k

6. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 5 Example of Zeroth Order Reaction At high pressure, gold surface saturated with adsorbed HI(g) 14.2 Zeroth, First and Second Order Reactions (SB p.27) 2HI(g) H 2 (g) + I 2 (g) gold surface Rate = k[HI(g)] n (where n = 0) ∴ Rate = k Hence, the rate is independent of the concentration of HI(g) and is a constant.

7. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 6 First Order Reactions 14.2 Zeroth, First and Second Order Reactions (SB p.27) A product Rate = k [A]

8. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 7 Examples of First Order Reaction 14.2 Zeroth, First and Second Order Reactions (SB p.27) 2H 2 O 2 (aq) 2H 2 O(l) + O 2 (g) Rate = k[H 2 O] Rate = k[N 2 O 5 (g)] Rate = k [SO 2 Cl 2 (l)] Rate = k [(CH 3 ) 3 CCl(l)] 2N 2 O 5 (g) 4NO 2 (g) + O 2 (g) SO 2 Cl 2 (l) SO 2 (g) + Cl 2 (g) (CH 3 ) 3 CCl(l) + OH - (aq) (CH 3 ) 3 COH(l) + Cl - (aq) Rate equationReaction

9. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 8 Second Order Reactions (Case 1) Example: 14.2 Zeroth, First and Second Order Reactions (SB p.28) 2NOCl(g) 2NO(g) + Cl 2 Rate = k[NOCl] 2 A products Rate = = k[A] 2

10. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 9 Second Order Reactions (Case 2) Examples 14.2 Zeroth, First and Second Order Reactions (SB p.28) A + B products Rate = k[A][B] H 2 (g) + I 2 (g) 2HI(g) Rate = k[H 2 (g)][I 2 (g)] ReactionRate equation 2NO 2 (g) 2NO(g) + O 2 (g) CH 3 Br(l) + OH - (aq) CH 3 OH(l) + Br - (aq) CH 3 COOC 2 H 5 (l) + OH - (aq) CH 3 COO - (aq) + C 2 H 5 OH(l) Rate = k[NO 2 (g)] 2 Rate =k[CH 3 Br(l)][OH - (aq)] Rate = k[CH 3 COOC 2 H 5 (l)][OH - (aq)]

11. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 10 14.3 Determination of Simple Rate Equations from Initial Rate Method (SB p.29) By determining the initial rates of reactions with different initial concentrations of reactants experimentally: For a reaction between two substances A and B, experiments with different initial concentrations of A and B were carried out. The results were as follows: ExperimentInitial concentration of A (mol dm -3 ) Initial concentration of B (mol dm -3 ) Initial rate (mol dm -3 s -1 ) 1 2 3 0.01 0.02 0.01 0.02 0.04 0.0005 0.0010 0.0020

12. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 11 14.3 Determination of Simple Rate Equations from Initial Rate Method (SB p.29) (a) What is the order of reaction with respect to A and with respect to B? Let m be the order of reaction with respect to A, and n be the order of reaction with respect to B. Then, the rate equation for the reaction can be expressed as: Rate = k[A] m [B] n Therefore, 0.0005 = k(0.01) m (0.02) n ………………(1) 0.0010 = k (0.02) m (0.02) n ………………(2) 0.0020 = k(0.01) m (0.04) n ……………….(3) Dividing (1) by (2), 0.0005/0.0020 = (0.01/0.02) m ∴ m =1 Dividing (1) by (3), 0.0005/0.0020 = (0.02/0.04) n ∴ n = 2 Answer

13. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 12 14.3 Determination of Simple Rate Equations from Initial Rate Method (SB p.29) (b) Calculate the rate constant using the result of experimental 1. Using the result of experiment (1), Rate = k[A][B] 2 0.0005 = k x 0.01 x 0.02 2 k = 125 mol -2 dm 6 s -1 (c) What is the rate equation for the reaction? Rate = 125[A][B] 2 Answer

14. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 13 Consider aA +bB  products By keeping B in large excess, we have rate = k[A] n i.e. log(rate) = nlog[A] + logk 14.4 Determination of Simple Rate Equations from Differential Rate Equations (SB p.32) Reactions Involving More Two Reactants

15. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 14 Zeroth Order Reaction 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37) [A] = -k 0 t + [A] 0 A product Rate = = k 0

16. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 15 First Order Reaction Integrating the above equation gives 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37) In A = -k 1 t + In[A] 0 A product Rate = = k 1 [A]

17. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 16 Half-life for First Order Reactions Rearranging, we have The time taken for half of the reactant to be converted to the product is known as the half-life of the reaction (t ½ ) 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) In A = -k 1 t + In[A] 0 In( ) = k 1 t t 1/2 = In 2/ k 1 = 0.693/ k 1 In( ) = k 1 t In 2 =

18. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 17 Remark: All radioactivity decays are 1st order reaction and thus have constant half-lives. 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) Half-life of a first order reaction

19. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 18 Integrating the above equation gives Half-life for Second Order Reactions 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.40) A product Rate = = k 2 [A] 2

20. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 19 In the upper atmosphere As long as an organism is alive, the ration of carbon-14 to carbon-12 remains constant. When the organism dies and incorporation of carbon ceases, the ratio of carbon-14 to carbon-12 decreases. Thus the age of fossil can be deduced by comparing the carbon-14 to carbon-12 with that in living tissue. 14.6 Carbon-14 Dating (SB p.44) Carbon-14 Dating +  +

21. H+H+ H+H+ H+H+ OH - New Way Chemistry for Hong Kong A-Level Book 2 20 The END