1. Chemical Kinetics © 2009, Prentice-Hall, Inc. First-Order Processes Therefore, if a reaction is first-order, a plot of ln [A] vs. t will yield a straight line, and the slope of the line will be -k. ln [A] t = -kt + ln [A] 0

2. Chemical Kinetics Ex. 14.7 The decomposition of certain insecticide in water follows first- order kinetics with rate constant of 1.45 /y at 12 c. A quantity of this insecticide is washed into alake on june 1, leading to concentration of 5.0 X 10-7 g/cm3. assume that the average tempreture of the lake is 12 A- what is the concentration of the insecticide on june of the following year B- how long will it take for the concentration of the insecicide to decrease to 3.0 x 10 -7 g/ cm3

3. Chemical Kinetics © 2009, Prentice-Hall, Inc. First-Order Processes Consider the process in which methyl isonitrile is converted to acetonitrile. CH 3 NCCH 3 CN

4. Chemical Kinetics © 2009, Prentice-Hall, Inc. First-Order Processes This data was collected for this reaction at 198.9 °C. CH 3 NCCH 3 CN

5. Chemical Kinetics © 2009, Prentice-Hall, Inc. First-Order Processes When ln P is plotted as a function of time, a straight line results. Therefore, –The process is first-order. –k is the negative of the slope: 5.1  10 -5 s −1.

6. Chemical Kinetics * The reaction 2A → B is first order in A with a rate costant of 2.8x10 -2 s -1 at 80 0 C. How long will it take for A to decrease from 0.88 to 0.14 M, then calculate half life time (s) Solve: ln[A] = ln[A] 0 - kt, ln 0.14 = ln 0.88 - 2.8x10 -2 x t t = ln 0.14 – ln 0.88 / 2.8x10 -2 = 66 s Half life time ( t 1/2 ) = 0.693/ k = 0.693 / 2.8x10 -2 = 24.74 s.... * Given : CH 3 - N= N – CH 3 (g) → N 2(g) + C 2 H 6 (g) Time P N=N-CH3 mmHg -------------- ---------------------------- 0 284 ln P t = -kt + ln P 0 100 220 ln 220 = -k x 100 + ln 284 150 193 5.394 = - k x 100 + 5.649 200 170 k = - ( 5.394-5.649) /100 ______________ 2.55x10 -3 s -1 © 2009, Prentice-Hall, Inc.

7. Chemical Kinetics © 2009, Prentice-Hall, Inc. Second-Order Processes Similarly, integrating the rate law for a process that is second-order in reactant A, we get 1 [A] t = kt + 1 [A] 0 also in the form y = mx + b

8. Chemical Kinetics © 2009, Prentice-Hall, Inc. Second-Order Processes So if a process is second-order in A, a plot of vs. t will yield a straight line, and the slope of that line is k. Zero order reaction : Rate ( - ∆[A] / ∆t ) = k [A] 0 = k [A] = [A] 0 – k t, t 1/2 = [A] 0 /2 k 1 [A] t = kt + 1 [A] 0 1 [A]

9. Chemical Kinetics © 2009, Prentice-Hall, Inc. Second-Order Processes The decomposition of NO 2 at 300°C is described by the equation NO 2 (g) NO (g) + O 2 (g) and yields data comparable to this: Time (s)[NO 2 ], M 0.00.01000 50.00.00787 100.00.00649 200.00.00481 300.00.00380 1212

10. Chemical Kinetics © 2009, Prentice-Hall, Inc. Second-Order Processes Plotting ln [NO 2 ] vs. t yields the graph at the right. Time (s)[NO 2 ], Mln [NO 2 ] 0.00.01000−4.610 50.00.00787−4.845 100.00.00649−5.038 200.00.00481−5.337 300.00.00380−5.573 The plot is not a straight line, so the process is not first-order in [A].

11. Chemical Kinetics © 2009, Prentice-Hall, Inc. Second-Order Processes Graphing ln vs. t, however, gives this plot. Time (s)[NO 2 ], M1/[NO 2 ] 0.00.01000100 50.00.00787127 100.00.00649154 200.00.00481208 300.00.00380263 Because this is a straight line, the process is second- order in [A]. 1 [NO 2 ]

12. Chemical Kinetics © 2009, Prentice-Hall, Inc. Half-Life Half-life is defined as the time required for one-half of a reactant to react. Because [A] at t 1/2 is one-half of the original [A], [A] t = 0.5 [A] 0.

13. Chemical Kinetics © 2009, Prentice-Hall, Inc. Half-Life For a first-order process, this becomes 0.5 [A] 0 [A] 0 ln = −kt 1/2 ln 0.5 = − kt 1/2 −0.693 = − kt 1/2 = t 1/2 0.693 k NOTE: For a first-order process, then, the half-life does not depend on [A] 0.

14. Chemical Kinetics © 2009, Prentice-Hall, Inc. Half-Life For a second-order process, 1 0.5 [A] 0 = kt 1/2 + 1 [A] 0 2 [A] 0 = kt 1/2 + 1 [A] 0 2 − 1 [A] 0 = kt 1/2 1 [A] 0 == t 1/2 1 k[A] 0

15. Chemical Kinetics Ex 14.9 The reaction of C4H9Cl with water is first order reaction. Figure shows How the concentration changes with time at particular temp. A- from the graph estamate the t1/2 B- use t1/2 and calculate the rate constant