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CHM 213 PHYSICAL CHEMISTRY

CHM 213 PHYSICAL CHEMISTRY. CHAPTER 2 CHEMICAL KINETICS. What is Chemical Kinetics?. The study of the speed or RATE at which a chemical reaction occurs. What is the importance of the knowledge of chemical kinetics ? to study the effectiveness of some medicine

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CHM 213 PHYSICAL CHEMISTRY

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  1. CHM 213PHYSICAL CHEMISTRY CHAPTER 2 CHEMICAL KINETICS

  2. What is Chemical Kinetics? The study of the speed or RATE at which a chemical reaction occurs. What is the importance of the knowledge of chemical kinetics ? to study the effectiveness of some medicine to know how rapidly food spoils to control the rate at which the fuel burns

  3. Rates of Reactions Rate of a chemical reaction – the change in concentration of a designated reactant or product per unit time. E.g.: Consider the reaction : A  B The rate of disappearance of reactant A is given by The rate of formation of a product B is given by Units Concentration = mol per dm3 (M) Time = seconds (s) Rate = mol dm-3 s-1 or M s-1

  4. Different types of rates • Initial rate : the rate at the start of reaction when infinitesimally small amount of the reactant has been used --- given by the gradient to the curve at time t=0. • Instantaneous rate : the rate at particular time --- given by the tangent to the curve at that time. • Average rate : the average change in concentration of reactant/product over a certain time interval.

  5. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) [C4H9Cl] M In this reaction, the concentration of butyl chloride, C4H9Cl, was measured at various times, t.

  6. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) • A plot of concentration vs. time for this reaction yields a curve like this. • The slope of a line tangent to the curve at any point is the instantaneous rate at that time.

  7. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) • The reaction slows down with time because the concentration of the reactants decreases.

  8. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) Average Rate, M/s The average rate of the reaction over each interval is the change in concentration divided by the change in time:

  9. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) • Note that the average rate decreases as the reaction proceeds. • This is because as the reaction goes forward, there are fewer collisions between reactant molecules.

  10. -[C4H9Cl] t Rate = = [C4H9OH] t Reaction Rates and Stoichiometry C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) • In this reaction, the ratio of C4H9Cl to C4H9OH is 1:1. • Thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH.

  11. Reaction Rates and Stoichiometry • What if the ratio is not 1:1? H2(g) + I2(g)  2 HI(g) • Only 1/2 HI is made for each H2 used.

  12. aA + bB cC + dD Reaction Rates and Stoichiometry • To generalize, for the reaction Reactants (decrease) Products (increase)

  13. Exercises • Write the reaction rate for the following reaction: • 2 N2O5 4 NO2 + O2 • H2 + I2  2 HI • 4 NH3 + 5O2  4 NO + 6 H20 • 2 HgCl2 +C2042-  2Cl- + 2 CO2 + Hg2Cl2

  14. Rate Law and Order of Reaction The rate law – an experimental determined equation which expresses the rate of reaction as a function of the concentrations of the reactants. aA + bB  cC + dD Rate α [A]x[B]y Rate = k[A]x[B]y Rate Constant, k • Experimentally determined value • Independent of concentrations but dependent of temperature • Magnitude of k indicates the speed of a reaction small k = a slow reaction large k = a fast reaction

  15. Order of reaction – the power to which the concentration of a reactant is raised in the rate equation. Rate = k[A]x[B]y x and y = integers = 0, 1, 2, 3……in most chemical reactions! • Order of reaction with respect to A = x • Order of reaction with respect to B = y • Overall order = x + y Overall order – sum of exponents of all reactants in the rate law

  16. The order of each reactant concentration explains how the rate of reaction varies with the concentration of particular reactant. Example: Rate = k[A]x[B]y ; when [A]=doubled If x = 0; the rate remains unchanged If x = 1; the rate doubles If x = 2; the rate quadruples/increases by factor of 4 (22) If x = 3; the rate increases eightfold/factor of 8 (23)

  17. First order reaction • A first order reaction with respect to a reactant A, is a reaction in which the rate of reaction is directly proportional to the concentration of A. • If the concentration of a reactant is doubled, the rate of reaction is also doubled. • The rate equation for a first order reaction is, rate = k [A] where, k = rate constant [A] = concentration in mol dm-3 the unit of k is time-1 (that is s-1, min-1, h-1)

  18. First order reactions Examples of first order reactions: • Catalytic decomposition of hydrogen peroxide 2H2O (aq) 2H2O (l) + O2(g) ii. Thermal decomposition of dinitrogen pentoxide 2 N2O5 2N2O4 + O2 Units for rate constant for 1st order reaction

  19. Integrated rate equation for first order reaction • For the reaction: A products • Having the rate law : where [A] t = concentration of A at time t • Rearrange the expression: ln [A]t t A straight line with -ve slope Integrated form of the 1st order rate expression

  20. Intercept = ln[A]0 -slope = -k ln[A]t t / s Other useful forms t / s -slope = -k ln([A]t/[A]0) 20

  21. Second order reactions • A second order reaction is a reaction in which the reaction rate is proportional to the product of the concentrations of two reactants • The rate equation for a second order reaction is, rate = k [A] [B] or rate= k [A]2 where, k = rate constant [A] = concentration in mol dm-3 the unit of k is dm3 mol-1 time-1

  22. second order reactions • Examples of second order reactions: • The hydrolysis of iodomethane ii. The thermal decomposition of hydrogen iodide Units for rate constant for 2nd order reaction

  23. Integrated rate equation for 2nd reaction • Rate of reaction = - (rate of disappearance of A) = k [A]2 1/[A] t A straight line graph with a + ve slope

  24. zero order reactions • The rate of zero order reaction does not depend on the concentration of the reactants • For zero order reaction, the rate law is rate = k [A]0 = k where, k = rate constant [A] = concentration in mol dm-3 the unit of k is mol dm-3 time-1 • Examples of zero order reactions: • Reaction between iodine and propanone

  25. Integrated rate equation for zero order reaction [A] t A straight line graph with -ve slope

  26. DETERMINATION OF ORDER OF REACTION AND RATE CONSTANT • The order of reaction (x + y) and the rate constant (k) can be determined by using: • The reaction rate method/graph • The linear plots • The half-life method, t1/2 • Initial rate method

  27. I. REACTION RATE METHOD/GRAPH • The order of reaction can be found by plotting a ‘reaction rate against the concentration’ rate rate rate k [A] [A] [A] First order Second order Zero order

  28. Example: Bromine reacts with methanoic acid according to the equation: The table below shows the rates of reactions at specific concentrations Determine the order of reaction between bromine and methanoic acid

  29. Solution: Plot a graph rate vs concentration A straight line graph with positive slope is obtained when the rate of reaction is plotted against concentration. This shows that the reaction is first order with respect to bromine Rate  [Br2]

  30. II. LINEAR PLOTS METHOD • The order of reaction can be found by plotting linear plots with respect to a given reactant Lg [A]t 1/ [A]t [A]t y y y x x x time time time First order second order Zero order Slope = y / x = - k /2.303 Slope = y / x = k Slope = y / x = - k

  31. 12 10 8 6 4 2 t1/2 t”1/2 t”’1/2 0 2 4 6 Times (minutes) III. HALF LIFE METHOD life, t1/2 • The half-life, t½, of a reaction is the time taken for the concentration of a reactant to fall to half its initial value • For the first order reaction the half –life is independent of the initial concentration Thus first half-life (t 1/2) = Second half-life (t”1/2) [A], concentration

  32. First-order reactions – Remember that for a 1st order reaction: ln[A]t = ln[A]0 - kt At time t = 0, [A] = [A]0 Then at time t = t½ (half-life), [A]t½ = [A]0/2 Substituting into above equation, ln([A]0/2) = ln[A]o – kt½ ln([A]0/2) – ln[A]0 = -kt½ ln 1 – ln 2 = -kt½, where ln 1 = 0 Therefore, ln 2 = kt ½

  33. [A]0 t1/2 [A]0/2 t1/2 [A]0/4 t1/2 [A]0/8 Hence, or • For a 1st order reaction, the half-life is independent of reactant • concentration butdependent on k. • The half-life is constant for a 1st order reaction Recall: [A]t = [A]0e-kt concentration time

  34. Second-order reactions – At time t = 0, [A] = [A]0 And when t = t½, [A]t½ = [A]0/2 So t1/2 for 2nd order reactions depends on initial concentration

  35. [A]0 concentration t1/2 [A]0/2 t1/2 [A]0/4 t1/2 [A]0/8 time Therefore, larger initial concentrations imply shorter half-lives (so faster the reaction).

  36. IV. THE INITIAL RATE METHOD Where: r1 and r2 = initial rates of experiment 1 and 2 respectively A1 and A2 = initial concentration of A for experiment 1 and 2 respectively, n = order of reaction with respect to A

  37. Example; Reaction A + 2B C have been studying at 25°C and the result are shown below. Determine the a) rate law, b) order of reaction and c) rate constant

  38. To find order of reaction for A consider exp. 1 and 2, where [B] is keep constant that is [B] = 0.1 • r1=5.5 x 10-6, r2 = 2.2 x 10-5 A1=0.1 A2=0.2

  39. To find order of reaction for B consider exp. 4 and 5, where [A] is keep constant that is [A] = 0.1 r1=1.65 x 10-5, r2 = 3.3 x 10-5 B1=0.3 B2=0.6 a) So, rate of reaction = k [A]m[B]n=k [A]2[B]1 b) And order of reaction = m+ n = 2 +1 =3

  40. c) Rate constant, k

  41. Exercise: From the following reaction rates observed in experiments, derive the rate law for the reaction A + B + C productswhere reaction rates are measured as soon as the reactants are mixed. Expt 1 2 3 4 [A]o0.100 0.200 0.200 0.100 [B]o0.100 0.100 0.300 0.100 [C]o0.100 0.100 0.100 0.400rate0.100 0.800 7.200 0.400

  42. Exercises First order reaction Q1: N2O5 decomposes according to 1st order kinetics, and 10% of it decomposed in 30 s. Estimate k, t½and percent decomposed in 500 s. Answers: k = 0.00351 s – 1 , t½ = 197 s percent decomposed 82.7 %

  43. Exercises Q2: The decomposition of A is first order, and [A] is monitored. The following data are recorded: t / min 0 2 4 8[A]/[M] 0.100 0.0905 0.0819 0.0670 Calculate k (k = 0.0499) Calculate the half life (Half life = 13.89) Calculate [A] when t = 5 min. Calculate t when [A] = 0.0100.

  44. Exercises Second order reaction Dimerization of butadiene is second order: 2 C4H6(g) = C8H12(g). The rate constantk at some temperature is 0.100 /min. The initial concentration of butadiene [B] is 2.0 M. Calculate the time required for [B] = 1.0 and 0.5 M Calculate concentration of butadiene when t = 1, 5, 10, and 30.

  45. Collision Theory This theory developed from kinetic theory to account for the effects of concentration and temperature on reaction rates. Collision theory is based on the 3 ideas • Molecules must collide to react. • Molecules must possess a certain minimum kinetic energy, called activation energy (Ea) to initiate a chemical reaction. • Molecules must collide in the right orientation for the collisions to result in a reaction. This is sometimes called the steric factor.

  46. Activation energy, (Ea) – minimum amount of energy required to initiate a chemical reaction Ea enables breakage of chemical bonds and rearrangement of atoms and valence electrons as reaction proceeds.

  47. Molecular orientation Consider the following reaction CH2= CH2 + HCl  CH3CH2Cl

  48. Collision Theory Effective collision – reactants molecules which collide successfully and lead to the formation of products. Two requirements for effective collisions • The reacting molecules must collide with energy which must be equal or greater than activation energy of the reaction • The relative orientation of the reactants must allow formation of any new bonds necessary to produce products.

  49. Collision Theory • The rate of a reaction is directly proportional to the number of effective molecular collisions per second or the frequency of effective collisions. Rate αzfp z = collision frequency f = fraction of collisions having energy > Ea p = steric factor or fraction of collision that occur in reactant molecules properly orientated.

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