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**Rate Equations and Order of Reactions**

14 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!!!!!!

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**2NO(g) + 2H2(g) N2(g) + 2H2O (l)**

For the reaction: 2NO(g) + 2H2(g) N2(g) + 2H2O (l) Initial concentration / mol dm-3 Initial rate / mol dm-3 s-1 NO H2 0.0250 0.100 2.4 10-6 0.050 1.2 10-6 0.0125 0.6 10-6 Rate a [H2(g)] when [NO(g)] is constant Rate a [NO2(g)]2 when [H2(g)] is constant Rate a [NO(g)]2 [H2(g)] Rate = k[NO(g)]2 [H2(g)]

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**Rate Equations and Order of Reactions**

14.1 Rate Equations and Order of Reactions

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**Rate Equation In general, for the reaction: mA + nB products Rate =**

14.1 Rate Equations and Order of Reactions (SB p.25 NB p.8) Rate Equation In general, for the reaction: mA + nB products Rate = = k [A]x [B]y m n (a 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

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**Rate Equation mA + nB products Rate = k [A]x [B]y**

14.1 Rate Equations and Order of Reactions (SB p.25) Rate Equation mA + nB products Rate = k [A]x [B]y x and y are determined experimentally. x 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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**Order of Reactions Usually integers (0, 1, 2, … …) If x = 1**

14.1 Rate Equations and Order of Reactions (SB p.26) Order of Reactions Do Class Examples on p. 8 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.

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**Rate Equation Rate = k [A]x [B]y**

14.1 Rate Equations and Order of Reactions (SB p.25 NB p. 8) Rate Equation Rate = k [A]x [B]y 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

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**Zeroth, First and Second Order Reactions**

14.2 Zeroth, First and Second Order Reactions

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**For the following reaction: A product**

[A] mol dm-3 Time (s) 1.00 0.80 10 0.70 20 0.65 30 0.53 40 : How can we find out the order of reaction with respects to [A]?

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**Zeroth Order Reactions**

14.2 Zeroth, First and Second Order Reactions (SB p.27 NB p.10) Zeroth Order Reactions A products Rate = k [A]0 = k e.g. CH3COCH3(aq) + I2(aq) + H+(aq) CH3COCH2I(aq) + I-(aq) + 2H+(aq) Rate = k[CH3COCH3(aq)][H+(aq)][I2(aq)]0 The rate of reaction is independent of [I2]!!! This means if we keep [CH3COCH3(aq)] and [H+(aq)] constant then measure the initial rate with various [I2(aq)], we will get the same initial rate.

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**Zeroth Order Reactions**

14.2 Zeroth, First and Second Order Reactions (SB p.27) Zeroth Order Reactions [I2(aq)]

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**Zeroth Order Reactions WHY???**

14.2 Zeroth, First and Second Order Reactions (SB p.27) Zeroth Order Reactions 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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**A Plot of [A] against time will give a straight line**

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37) Zeroth Order Reaction A Plot of [A] against time will give a straight line A product Rate equation is: [A] = -kt + [A]0

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**First Order Reaction e.g Decomposition of H2O2(aq) to H2O and O2**

14.2 Zeroth, First and Second Order Reactions (SB p.28) First Order Reaction e.g Decomposition of H2O2(aq) to H2O and O2 2H2O2(aq) 2H2O(l) + O2(g) Rate = k [H2O2(aq)] Though the stoichiometric coefficient of H2O2(aq) is 2 Order of reaction with respect to H2O2(aq) is 1 (determined experimentally)

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**A Plot of ln [A] against time will give a straight line**

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37 NB p. 9)) First Order Reaction A Plot of ln [A] against time will give a straight line A product Rate equation is: In A = -k1t + In [A]0

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**Half-life of First Order reaction**

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) Half-life of First Order reaction 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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**Half-life of First Order Reaction**

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) Half-life of First Order Reaction ln[A] = -k1t + ln[A]0 k1t = ln[A]0 - ln[A] If t = half-life (t0.5), then [A]0 = 2[A]: k1t0.5 = ln 2 t0.5 = constant

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**Half-life of a First Order Reaction**

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.39) Half-life of a First Order Reaction For a first order reaction: Half-life is a constant Do Class Examples 1, 3 on p.10

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**Second Order Reaction A product Rate equation is:**

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.40 NB p.11) Second Order Reaction A plot of 1/[A] vs time will give a straight line A product Rate equation is: Integrating the above rate equation, obtain:

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**Summary Plot a second graph of vs time**

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 Summary Steps to determine the order of reaction 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 Plot a second graph of vs time a straight line second order

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**Determination of Simple Rate Equations by Graphical Method**

14.4 – 14.5 Determination of Simple Rate Equations by Graphical Method Notes p. 18

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**log (rate)-log (concentration) Graph**

14.4 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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**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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**14.4 Determination of Simple Rate Equations from Differential Rate Equations**

(SB p.36) Check Point 14-4 Decide which curve in the following graph corresponds to (i) a zeroth order reaction; (ii) a first order reaction. (i) (3) (ii) (2)

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**Isolation technique When two or more substances react:**

14.4 Determination of Simple Rate Equations from Differential Rate Equations (SB p.33) Do Q. 1, 3 on p. 27 Do Q 13 on p.80 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

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The END

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Q.13 on p. 80 Products (not reactants) t(s) v(cm3) 5 33 10 56 15 73 25 92 3600 110 5400 ln (a) vol. of N2 (a) in reactant/cm3 110 77 54 37 18

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