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New Way Chemistry for Hong Kong A-Level Book 2 1 Rate Equations and Order of Reactions Increasing concentration of reactants can increase the rate of reaction. Is there any mathematical relationship between rate of reaction and concentration of reactants? YES!!!!!! 14

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Initial concentration / mol dm -3 Initial rate / mol dm -3 s -1 NOH2H For the reaction: 2NO(g) + 2H 2 (g) N 2 (g) + 2H 2 O (l) Rate [H 2 (g)] when [NO(g)] is constant Rate [NO 2 (g)] 2 when [H 2 (g)] is constant Rate [NO(g)] 2 [H 2 (g)] Rate = k[NO(g)] 2 [H 2 (g)]

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New Way Chemistry for Hong Kong A-Level Book 2 3 Rate Equations and Order of Reactions 14.1

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New Way Chemistry for Hong Kong A-Level Book 2 4 In general, for the reaction: mA + nB products (a rate equation) 14.1 Rate Equations and Order of Reactions (SB p.25 NB p.8) Rate Equation k = rate constant x = order of reaction with respect to reactant A y = order of reaction with respect to reactant B Overall order of reaction = x + y Rate= = k [A] x [B] y m n

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New Way Chemistry for Hong Kong A-Level Book 2 5 mA + nB products 14.1 Rate Equations and Order of Reactions (SB p.25) Rate Equation Rate= k [A] x [B] y experimentally.x and y are determined experimentally. NOTx and y may NOT equal to m and n. x and y may not be whole numbers!!! Rate of reaction is independent of products concentration

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New Way Chemistry for Hong Kong A-Level Book Rate Equations and Order of Reactions (SB p.26) Order of Reactions Usually integers (0, 1, 2, … …) If x = 1 first order with respect to reactant A If y = 2 second order with respect to reactant B The overall reaction is a third order reaction. Do Class Examples on p. 8

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New Way Chemistry for Hong Kong A-Level Book Rate Equations and Order of Reactions (SB p.25 NB p. 8) Rate Equation log rate = log k + x log[A] + y log[B] If B is kept large excess, its change in concentration will be negligible when compared with A. log[B] ~ constant log rate = c + x log[A] when is log rate plotted against log[A] straight line with slope = x Rate= k [A] x [B] y

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New Way Chemistry for Hong Kong A-Level Book 2 8 Zeroth, First and Second Order Reactions 14.2

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For the following reaction: A product [A] mol dm -3 Time (s) :: :: How can we find out the order of reaction with respects to [A]?

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New Way Chemistry for Hong Kong A-Level Book 2 10 Zeroth Order Reactions A products Rate = k [A] 0 = k 14.2 Zeroth, First and Second Order Reactions (SB p.27 NB p.10) e.g. CH 3 COCH 3 (aq) + I 2 (aq) + H + (aq) CH 3 COCH 2 I(aq) + I - (aq) + 2H + (aq) Rate = k[CH 3 COCH 3 (aq)][H + (aq)][I 2 (aq)] 0 The rate of reaction is independent of [I 2 ]!!! This means if we keep [CH 3 COCH 3 (aq)] and [H + (aq)] constant then measure the initial rate with various [I 2 (aq)], we will get the same initial rate.

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New Way Chemistry for Hong Kong A-Level Book 2 11 Zeroth Order Reactions 14.2 Zeroth, First and Second Order Reactions (SB p.27) [I 2 (aq)]

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New Way Chemistry for Hong Kong A-Level Book 2 12 Zeroth Order Reactions 14.2 Zeroth, First and Second Order Reactions (SB p.27) WHY??? The reaction is a multi-step reaction. Only the slowest step affect the overall reaction rate. A B C D Iodine is not involved in the slowest step of the reaction.

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New Way Chemistry for Hong Kong A-Level Book 2 13 Zeroth Order Reaction [A] = -kt + [A] Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37) A product Rate equation is: A Plot of [A] against time will give a straight line

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New Way Chemistry for Hong Kong A-Level Book Zeroth, First and Second Order Reactions (SB p.28) First Order Reaction 2H 2 O 2 (aq) 2H 2 O(l) + O 2 (g) Rate = k [H 2 O 2 (aq)] Though the stoichiometric coefficient of H 2 O 2 (aq) is 2 Order of reaction with respect to H 2 O 2 (aq) is 1 (determined experimentally) e.g Decomposition of H 2 O 2 (aq) to H 2 O and O 2

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New Way Chemistry for Hong Kong A-Level Book 2 15 First Order Reaction In A = -k 1 t + In [A] Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37 NB p. 9)) A product Rate equation is: A Plot of ln [A] against time will give a straight line

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New Way Chemistry for Hong Kong A-Level Book 2 16 Half-life of First Order reaction 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) The time taken for half of the reactant to be converted to the product is known as the half-life of the reaction. After time t, [A] = [A] 0 t is called the half life of the reaction.

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New Way Chemistry for Hong Kong A-Level Book 2 17 Half-life of First Order Reaction 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) ln[A] = -k 1 t + ln[A] 0 k 1 t = ln[A] 0 - ln[A] If t = half-life (t 0.5 ), then [A] 0 = 2[A]: k 1 t 0.5 = ln 2 t 0.5 = constant

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New Way Chemistry for Hong Kong A-Level Book 2 18 Half-life of a First Order Reaction 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.39) For a first order reaction: Half-life is a constant Do Class Examples 1, 3 on p.10

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New Way Chemistry for Hong Kong A-Level Book 2 19 Second Order Reaction 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.40 NB p.11) A product Rate equation is: Integrating the above rate equation, obtain: A plot of 1/[A] vs time will give a straight line

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New Way Chemistry for Hong Kong A-Level Book 2 20 Summary Steps to determine the order of reaction 1.Plot a concentration-time graph a straight line zeroth order a curve with constant half life first order Confirmation: ln[A] vs time straight line 2.Plot a second graph of vs time a straight line second order Do Q. 5 on p. 77 Do Q. 14 on p. 80 Q. 13 (more difficult) Do Q. 3 on NB p.17 Q. 2 on NB p. 21

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New Way Chemistry for Hong Kong A-Level Book 2 21 Determination of Simple Rate Equations by Graphical Method Notes p – 14.5

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New Way Chemistry for Hong Kong A-Level Book Determination of Simple Rate Equations from Differential Rate Equations (SB p.32) log (rate)-log (concentration) Graph rate = k[A] n log (rate) = n log [A] + log k Plotting log (rate) against log [A], a straight line is obtained for any orders Slope of straight line = Order of reaction (n) y-intercept = log k Do Q. 1 on NB p. 16

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New Way Chemistry for Hong Kong A-Level Book 2 23 We need to plot two graphs: (1)[A] vs time to find the rate at different [A] (by slope to the curve) (2) log (rate) vs log[A] to find the order and k

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New Way Chemistry for Hong Kong A-Level Book Determination of Simple Rate Equations from Differential Rate Equations (SB p.36) (a)Decide which curve in the following graph corresponds to (i)a zeroth order reaction; (ii)a first order reaction. (a)(i)(3) (ii)(2)

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New Way Chemistry for Hong Kong A-Level Book Determination of Simple Rate Equations from Differential Rate Equations (SB p.33) Isolation technique When two or more substances react: A + B products Order of reaction with respect to reactant A can be found by keeping concentration of B constant (by using much excess B – isolation technique) Rate = k[A] x [B] y Rate = k [A] x Do Q. 1, 3 on p. 27 Do Q 13 on p.80

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New Way Chemistry for Hong Kong A-Level Book 2 26 The END

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Q.13 on p. 80 t(s)v(cm 3 ) Products (not reactants) vol. of N 2 (a) in reactant/cm ln (a)

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