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Understanding Chemical Kinetics: Rates, Reactions, and Mechanisms

Explore the fundamentals of kinetics, reaction rates, and mechanisms in chemical reactions, including rate laws, integrated kinetics calculus, temperature effects, and catalysis. Learn to mathematically express reaction rates and understand key variables affecting reaction progress. Gain insights into reaction mechanisms, catalysis, and factors influencing reaction rates like concentration, physical state, and temperature. Discover essential concepts like activation energy and the role of energy in collisions to comprehend reaction rates comprehensively.

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Understanding Chemical Kinetics: Rates, Reactions, and Mechanisms

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  1. Kinetics

  2. Kinetics Rates and Mechanisms of Chemical Reactions Reaction Rate and Variables that Affect the Rate Mathematically Expressing Reaction Rates Rate Laws Integrated Rate Laws: the Calculus of Kinetics The Effect of Temperature on Reaction Rate Reaction Theory: Concentration and Temperature Reaction Mechanisms: How many steps?, 1?, 2?, more? Catalysis: Increasing Rates of Reaction

  3. A  B Reaction Progress Red  Blue t (min) 100 molecules 54 Red : 46 Blue 30 Red : 70 Blue

  4. A  B Moles A & B vs. Time

  5. QUESTION If we have the reaction A(g)  2B(g) and the number of moles of A follows: time 0 5 min 10 min moles A 0.100 0.085 0.070 What is the number of moles of B at 10 min? •   0.060 mol •   0.200 mol •   0.140 mol •   0.100 mol •   0.030 mol

  6. ANSWER If we have the reaction A(g) 2B(g) and the number of moles of A is as follows, time 0 5 min 10 min moles A 0.100 0.085 0.070 What is the number of moles of B at 10 min? • 0.060 mol •   0.200 mol •   0.140 mol •   0.100 mol •   0.030 mol 0.100 molA -0.070 molA 0.030 molA x 2 molB/1molA

  7. CONSIDER RATE of change for: A  B

  8. Expressions of a Rate of Reaction For the Chemical Reaction:aA + bB cC + dD

  9. QUESTION Chlorine dioxide (ClO2) is a disinfectant used in municipal water-treatment plants. It dissolves in basic solution producing ClO3– and ClO2–: 2ClO2 (aq) + 2OH– (aq)  ClO3– (aq) + ClO2– (aq) + H2O (l) Of the following, which would not be a proper expression to relate information about the rate of the reaction? –DClO2/Dt = 2DClO3–/Dt –DClO2/Dt = DOH–/Dt –DClO2/Dt = DClO2–/Dt –DOH–/Dt = 2DClO2–/Dt

  10. ANSWER C. The stoichiometry of the reaction indicates that ClO2 disappears twice as fast as ClO2– forms; so to determine the rate for ClO2 , the rate of ClO2– would have to be doubled or ½ of the rate of disappearance of ClO2.

  11. Rate of Reaction • C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) • The average rate can be expressed in terms of the disappearance of C4H9Cl. • The units for average rate are mol/L.s or M/s. • The average rate decreases over time. • Data and plotting [C4H9Cl] versus time:

  12. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)

  13. Plot of [C4H9Cl] vs. Time

  14. Rate of Reaction • C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) • The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve. • Instantaneous rate is different from average rate. • The instantaneous rate is usually the rate of reaction.

  15. QUESTION For: 2 NO2(g) O2(g) + 2 NO(g) Of the following, which is the approximate rate of O2 appearance at 50 sec? 0.0080 mol/Ls 0.000016 mol/Ls 0.00020mol/Ls 0.000030 mol/Ls

  16. ANSWER D is a reasonable estimate. Examine the interval for O2 concentration around the 250 second time. The Dy value shown is 0.0003. For that same rise at the 50 second mark, only about 10 seconds are needed. 0.0003/10 = 0.000030 Note: this is only an estimate of the tangent line at 50 seconds

  17. Important Factors that Effect Reaction Rates 1) Concentration: molecules must collide in order to react. The higher the concentration, the higher number of collisions. Rate = k (collision frequency) = k (concentration) k = rate constant 2) Physical state: molecules must physically mix in order to collide. The physical state (solid, liquid, gas) will affect frequency of collisions, as well as the physical size of droplets (liquid) or particles in the case of solids.(heterogeneous vs. homogeneous) 3) Temperature: molecules must collide with enough energy to react. (Activation Energy, Ea) Raising the temperature increases the K.E. of the molecules, the number of collisions and the energy of the collisions.

  18. Important Factors that Effect Reaction Rates Concentration: molecules must collide in order to react. The higher the concentration, the higher number of collisions. Rate = k (collision frequency) = k (concentration) http://chemconnections.org/general/movies/html-swf/reactionrate_conc.htm

  19. Physical state: molecules must physically mix in order to collide. The physical state (solid, liquid, gas) will affect frequency of collisions, as well as the physical size of droplets (liquid) or particles in the case of solids.(heterogeneous vs. homogeneous)

  20. Temperature: molecules must collide with enough energy to react. (Activation Energy, Ea) Raising the temperature increases the K.E. of the molecules, the number of collisions and the energy of the collisions.

  21. QUESTION Which of the following is a correct conclusion based on the information presented in this figure? The forward reaction is endothermic. The activation energy for the forward reaction is less than the activation energy of the reverse reaction. The transition state is at a lower energy than the products. The energy of the reactants represents a lower energy level than both the transition state and the products.

  22. ANSWER B. The activation energy of the forward reaction is lower than the reverse. From the reactants to the transition state the energy change is less than from the products to the transition state.

  23. Rate Constant (k) vs. Temperature

  24. Reaction Rate Expression / Rate Law For a Chemical Reaction:aA + bB cC + dD A Rate Expression for this reaction could be written as: Rate = k [A]m[B]n . . . k = the reaction rate constant m & n are called reaction orders. They define how the rate is effected by the concentration of each reactant, for example, if the rate doubles when the concentration of A doubles, the rate depends on [A]1, so a = 1; if the rate quadruples when the concentration of B doubles, the rate depends on [B]2, so b = 2. Can a reaction order equal zero? Yes, for Rate = k [A]m = 0 Rate = k

  25. Rate Laws http://chemconnections.org/general/movies/html-swf/rate_laws.htm

  26. QUESTION • A kinetic study of the reaction 2A + 2B  products was conducted yielding the following results: • Experiment [A], (M) [B], (M) Initial Rate, M/ s • 1 0.10 0.10 25 • 2 0.05 0.20 100 • 3 0.10 0.30 225 • 4 0.20 0.10 25 • What is the rate law for the reaction? •   Rate = k[A][B] •   Rate = k[B]2 •   Rate = k[A]2[B] •   Rate = k[A]2 •   Rate = k[A]2[B]2

  27. ANSWER • A kinetic study of the reaction 2A + 2B  products was conducted yielding the following results: • Experiment [A], (M) [B], (M) Initial Rate, M/ s • 1 0.10 0.10 25 • 2 0.05 0.20 100 • 3 0.10 0.30 225 • 4 0.20 0.10 25 • What is the rate law for the reaction? •   Rate = k[A][B] • Rate = k[B]2 •   Rate = k[A]2[B] •   Rate = k[A]2 •   Rate = k[A]2[B]2

  28. Review Lewis Structures & VSEPR Crystal Violet Phenolphthalein

  29. Reaction Plots: Zero Order

  30. http://chemconnections.org/%20general/movies/1st-order-rxn.movhttp://chemconnections.org/%20general/movies/1st-order-rxn.mov First Order Reaction Plots

  31. Second-Order Reaction Plots

  32. Integrated Rate Laws and Reaction Order

  33. Rate Laws http://chemconnections.org/general/movies/html-swf/rate_laws.htm

  34. First Order? or Second Order? First

  35. http://chemconnections.org/general/movies/html-swf/reactionhalflife.htmhttp://chemconnections.org/general/movies/html-swf/reactionhalflife.htm

  36. The thermal decomposition of N2O5(g) to form NO2(g) and O2(g) is a first-order reaction. The rate constant for the reaction is 5.1 x 10-4 s-1 at 318 K. What is the half-life of this process? •   2.00 x 103 s •   1.44 x 103 s •   2.62 x 10-1 s •   3.93 x 103 s • 1.00 x 10-1 s

  37. The thermal decomposition of N2O5(g) to form NO2(g) and O2(g) is a first-order reaction. The rate constant for the reaction is 5.1 x 10-4 s-1 at 318 K. What is the half-life of this process? •   2.0 x 103 s • 1.4 x 103 s •   2.6 x 10-1 s •   3.9 x 103 s •   1.0 x 10-1 s or t 1/2 = ln 2 / k t 1/2 = 0.69 / 5.1 x 10 -4

  38. QUESTION

  39. ANSWER A Between trial #1 and #2 the rate changed in the same ratio as [ClO2], whereas OH– remained constant. Therefore, the reaction is first order with respect to ClO2. The same happens between trial #2 and #3 for OH–. Dividing the rate of any trial by the concentrations of ClO2 and OH– provides the rate constant. Note that the units for k must cancel out mol2/L2 to provide mol/L s

  40. Zero Order rate = k mol/L . s [A] = [A]0 – kt [A] vs.t -k, [A]0 [A]0 / 2k

  41. Unimolecular (1st Order) Reaction One treatment of hyperthyroidism is the oral administration of radioactive iodine, which concentrates in the thyroid and slows the thyroid’s hormone production. 131I decays by a first order reaction with the emission of a Beta particle, which has a half life of ~8 days. The biological half life of iodine is ~100 days. Write the rate law for the 131I decay. If 1.00 gram of 131I is taken by a patient, how much remains after 1 week? After 1 month? After 1 year? Rate = k[131I]; t1/2 = 0.693/k k = ln 2 /8 days = 1.00 x 10-6 s-1 k = 1.00 x 10-6 s-1; ln(Ao/A) = kt; 604800s = 0.54g; 2.59 x 106s = 0.075g 3.15 x 107s = 2 x 10-14 g

  42. QUESTION Consider the hydrolysis of t-butyliodide, the equation for which is (CH3) 3C-I + H2O  (CH3) 3COH + HI. The equation governing the rate of this reaction is rate = k[(CH3) 3C-I]. What is the order of each reactant and the overall order of the reaction? The order of t-butyliodide is 0, the order of water is 1, and the reaction order is 1. The order of t-butyliodide is 1, the order of water is 1, and the reaction order is 1. The order of t-butyliodide is 1, the order of water is 0, and the reaction order is 2. The order of t-butyliodide is 1, the order of water is 0, and the reaction order is 1. The order of t-butyliodide is 1, the order of water is 1, and the reaction order is 2.

  43. ANSWER Consider the hydrolysis of t-butyliodide, the equation for which is (CH3) 3C-I + H2O  (CH3) 3COH + HI. The equation governing the rate of this reaction is rate = k[(CH3) 3C-I]. What is the order of each reactant and the overall order of the reaction? The order of t-butyliodide is 0, the order of water is 1, and the reaction order is 1. The order of t-butyliodide is 1, the order of water is 1, and the reaction order is 1. The order of t-butyliodide is 1, the order of water is 0, and the reaction order is 2. The order of t-butyliodide is 1, the order of water is 0, and the reaction order is 1. The order of t-butyliodide is 1, the order of water is 1, and the reaction order is 2.

  44. QUESTION A reaction is shown to be first order with respect to one reactant, with a second order dependency on another reactant. Which statement makes an accurate comment about these two observations? Assuming no temperature change, doubling the concentration of both reactants would cause the reaction rate to double. Assuming no temperature change, doubling the concentration of both reactants would cause the reaction rate to increase by a factor of four. Assuming no temperature change, doubling the concentration of both reactants would cause the reaction rate to increase by a factor of five. Assuming no temperature change, doubling the concentration of both reactants would cause the reaction rate to increase by a factor of eight.

  45. ANSWER D. Doubling the concentration for a first order dependency would double the rate. However, doubling the concentration when there is a second order dependency would quadruple the rate. The combined effect would then be an eight-fold increase.

  46. The Arrhenius Equation • k is the rate constant, Eais the activation energy, R is the thermodynamic constant (8.314 J/K mol) and T is the temperature in K. • A is called the frequency factor. • A is a measure of the probability of a favorable collision. • Both A and Ea are specific to a given reaction.

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