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1 Chemical Kinetics Chapter 15 An automotive catalytic muffler. 2 Chemical Kinetics Chapter 15 • We can use thermodynamics to tell if a reaction is product or reactant favored. • But this gives us no info on HOW FAST reaction goes from reactants to products. • KINETICS — the study of REACTION RATES and their relation to the way the reaction proceeds, i.e., its MECHANISM. 3 Thermodynamics or Kinetics • Reactions can be one of the following: 1. Not thermodynamically favored (reactant favored) 2. Thermodynamically favored (product favored), but not kinetically favored (slow) 3. Thermodynamically favored (product favored) and kinetically favored (fast) 4 Thermodynamics or Kinetics • Not thermodynamically favored (reactant favored) • Sand (SiO2) will not decompose into Si and O2 5 Thermodynamics or Kinetics • Thermodynamically favored (product favored), but not kinetically favored (slow) • Diamonds will turn into graphite, but the reaction occurs very slowly 6 Thermodynamics or Kinetics • Thermodynamic ally favored (product favored) and kinetically favored (fast) • Burning of paper in air will turn to ash very quickly 7 Reaction Mechanisms The sequence of events at the molecular level that control the speed and outcome of a reaction. Br from biomass burning destroys stratospheric ozone. (See R.J. Cicerone, Science, volume 263, page 1243, 1994.) Step 1: Br + O3 ---> BrO + O2 Step 2: Cl + O3 ---> ClO + O2 Step 3: BrO + ClO + light ---> Br + Cl + O2 NET: 2 O3 ---> 3 O2 8 Reaction Rates Section 15.1 • Reaction rate = change in concentration of a reactant or product with time. • Know about initial rate, average rate, and instantaneous rate. See Screen 15.2. 9 10 Determining a Reaction Rate Blue dye is oxidized with bleach. Its concentration decreases with time. The rate — the change in dye conc with time — can be Dye Conc determined from the plot. Time 11 Factors Affecting Rates Section 15.2 • Concentrations and physical state of reactants and products (Screens 15.3 and 15.4) • Temperature (Screen 15.11) • Catalysts (Screen 15.14) 12 Factors Affecting Rates Section 15.2 • Concentrations Rate with 0.3 M HCl Rate with 6.0 M HCl 13 Factors Affecting Rates Section 15.2 • Physical state of reactants 14 Factors Affecting Rates Section 15.2 Catalysts: catalyzed decomp of H2O2 2 H2O2 --> 2 H2O + O2 15 Factors Affecting Rates Section 15.2 • Temperature 16 Concentrations and Rates To postulate a reaction mechanism, we study • reaction rate and • its concentration dependence 17 Concentrations and Rates Take reaction where Cl- in Cisplatin cisplatin [Pt(NH3)2Cl3] is replaced by H2O Rate of change of conc of Pt compd Am't of cisplatin reacting (mol/L) = elapsed time (t) 18 Cisplatin Concentrations and Rates Rate of change of conc of Pt compd Am't of cisplatin reacting (mol/L) = elapsed time (t) Rate of reaction is proportional to [Pt(NH3)2Cl2] We express this as a RATE LAW Rate of reaction = k [Pt(NH3)2Cl2] where k = rate constant k is independent of conc. but increases with T 19 Cisplatin Concentrations, Rates, and Rate Laws In general, for a A + b B ---> x X with a catalyst C Rate = k [A]m[B]n[C]p The exponents m, n, and p • are the reaction order • can be 0, 1, 2 or fractions • must be determined by experiment!!! Cisplatin 20 Interpreting Rate Laws Rate = k [A]m[B]n[C]p • If m = 1, rxn. is 1st order in A Rate = k [A]1 If [A] doubles, then rate goes up by factor of ? • If m = 2, rxn. is 2nd order in A. Rate = k [A]2 Doubling [A] increases rate by ? • If m = 0, rxn. is zero order. Rate = k [A]0 If [A] doubles, rate ? Cisplatin 21 Deriving Rate Laws Derive rate law and k for CH3CHO(g) ---> CH4(g) + CO(g) from experimental data for rate of disappearance of CH3CHO Expt. [CH3CHO] Disappear of CH3CHO (mol/L) (mol/L•sec) 1 0.10 0.020 2 0.20 0.081 3 0.30 0.182 4 0.40 0.318 Cisplatin 22 Deriving Rate Laws Rate of rxn = k [CH3CHO]2 Here the rate goes up by ______ when initial conc. doubles. Therefore, we say this reaction is _________________ order. Now determine the value of k. Use expt. #3 data— 0.182 mol/L•s = k (0.30 mol/L)2 k = 2.0 (L / mol•s) Using k you can calc. rate at other values of [CH3CHO] at same T. Cisplatin Concentration/Time 23 Relations Need to know what conc. of reactant is as function of time. Consider FIRST ORDER REACTIONS For 1st order reactions, the rate law is - (D [A] / D time) = k [A] Cisplatin Concentration/Time 24 Relations Integrating - (D [A] / D time) = k [A], we get Cisplatin Concentration/Time 25 Relations Integrating - (D [A] / D time) = k [A], we get [A] = - k t ln [A]o natural logarithm [A] at time = 0 [A] / [A]0 =fraction remaining after time t has elapsed. Cisplatin Concentration/Time 26 Relations Integrating - (D [A] / D time) = k [A], we get [A] = - k t ln [A]o natural logarithm [A] at time = 0 [A] / [A]0 =fraction remaining after time t has elapsed. Called the integrated first-order rate law. 27 Concentration/Time Relations Sucrose Sucrose decomposes to simpler sugars Rate of disappearance of sucrose = k [sucrose] k = 0.21 hr-1 Initial [sucrose] = 0.010 M How long to drop 90% (to 0.0010 M)? 28 Concentration/Time Relationships Rate of disappear of sucrose = k [sucrose], k = 0.21 hr-1. If initial [sucrose] = 0.010 M, how long to drop 90% or to 0.0010 M? Use the first order integrated rate law 29 Concentration/Time Relationships Rate of disappear of sucrose = k [sucrose], k = 0.21 hr-1. If initial [sucrose] = 0.010 M, how long to drop 90% or to 0.0010 M? Use the first order integrated rate law 30 Concentration/Time Relationships Rate of disappear of sucrose = k [sucrose], k = 0.21 hr-1. If initial [sucrose] = 0.010 M, how long to drop 90% or to 0.0010 M? Use the first order integrated rate law ln (0.100) = - 2.3 = - (0.21 hr-1) • time 31 Concentration/Time Relationships Rate of disappear of sucrose = k [sucrose], k = 0.21 hr-1. If initial [sucrose] = 0.010 M, how long to drop 90% or to 0.0010 M? Use the first order integrated rate law ln (0.100) = - 2.3 = - (0.21 hr-1) • time time = 11 hours 32 Using the Integrated Rate Law The integrated rate law suggests a way to tell if a reaction is first order based on experiment. 2 N2O5(g) ---> 4 NO2(g) + O2(g) Rate = k [N2O5] Time (min) [N2O5]0 (M) ln [N2O5]0 0 1.00 0 1.0 0.705 -0.35 2.0 0.497 -0.70 5.0 0.173 -1.75 33 Using the Integrated Rate Law 2 N2O5(g) ---> 4 NO2(g) + O2(g) Rate = k [N2O5] Data of conc. vs. time plot do not fit straight line. 34 Using the Integrated Rate Law 2 N2O5(g) ---> 4 NO2(g) + O2(g) Rate = k [N2O5] Data of conc. vs. Plot of ln [N2O5] vs. time plot do not fit time is a straight straight line. line! 35 Using the Integrated Rate Law Plot of ln [N2O5] vs. time is a straight line! Eqn. for straight line: y = ax + b ln [N 2O5] = - kt + ln [N 2O5]o conc at rate const conc at time t = slope time = 0 All 1st order reactions have straight line plot for ln [A] vs. time. (2nd order gives straight line for plot of 1/[A] vs. time) 36 Graphical Methods for Determining Reaction Order and Rate Constant • Zero-order [ A]t [ A]o kt y b mx • Straight line plot of [A]t vs. t • Slope is –k (mol/L*s) 37 Graphical Methods for Determining Reaction Order and Rate Constant • First-order ln[ A]t ln[ A]o kt y b mx • Straight line plot of ln[A]t vs. t • Slope is – k (s-1) 38 Graphical Methods for Determining Reaction Order and Rate Constant • Second-order 1 1 kt [ A] [ A]o t y b mx • Straight line plot of 1/[A]t vs t • Slope is k (L/mol*s) 39 Half-Life Section 15.4 and Screen 15.8 HALF-LIFE is the time it takes for 1/2 a sample is disappear. For 1st order reactions, the concept of HALF- LIFE is especially useful. 40 Half-Life • Reaction is 1st order decomposition of H2O2. 41 Half-Life • Reaction after 654 min, 1 half-life. • 1/2 of the reactant remains. 42 Half-Life • Reaction after 1306 min, or 2 half-lives. • 1/4 of the reactant remains. 43 Half-Life • Reaction after 3 half-lives, or 1962 min. • 1/8 of the reactant remains. 44 Half-Life • Reaction after 4 half-lives, or 2616 min. • 1/16 of the reactant remains. 45 Half-Life Section 15.4 and Screen 15.8 Sugar is fermented in a 1st order process (using an enzyme as a catalyst). sugar + enzyme --> products Rate of disappear of sugar = k[sugar] k = 3.3 x 10-4 sec-1 What is the half-life of this reaction? 46 Half-Life Section 15.4 and Screen 15.8 Rate = k[sugar] and k = 3.3 x 10-4 sec-1. What is the half- life of this reaction? Solution [A] / [A]0 = 1/2 when t = t1/2 Therefore, ln (1/2) = - k • t1/2 - 0.693 = - k • t1/2 t1/2 = 0.693 / k So, for sugar, t1/2 = 0.693 / k = 2100 sec = 35 min 47 Half-Life Section 15.4 and Screen 15.8 Rate = k[sugar] and k = 3.3 x 10-4 sec-1. Half-life is 35 min. Start with 5.00 g sugar. How much is left after 2 hr and 20 min? Solution 2 hr and 20 min = 4 half-lives Half-life Time Elapsed Mass Left 1st 35 min 5.00 g 2nd 70 2.50 g 3rd 105 1.25 g 4th 140 0.625 g 48 Half-Life Section 15.4 and Screen 15.8 Radioactive decay is a first order process. Tritium ---> electron + helium 3H 0 e 3He -1 If you have 1.50 mg of tritium, how much is left after 49.2 years? t1/2 = 12.3 years Solution Half-Life 49 Section 15.4 and Screen 15.8 Start with 1.50 mg of tritium, how much is left after 49.2 years? t1/2 = 12.3 years Solution ln [A] / [A]0 = -kt [A] = ? [A]0 = 1.50 mg t = 49.2 years Need k, so we calc k from: k = 0.693 / t1/2 Obtain k = 0.0564 y-1 Now ln [A] / [A]0 = -kt = - (0.0564 y-1) • (49.2 y) = - 2.77 Take antilog: [A] / [A]0 = e-2.77 = 0.0627 0.0627 is the fraction remaining! Half-Life 50 Section 15.4 and Screen 15.8 Start with 1.50 mg of tritium, how much is left after 49.2 years? t1/2 = 12.3 years Solution [A] / [A]0 = 0.0627 0.0627 is the fraction remaining! Because [A]0 = 1.50 mg, [A] = 0.094 mg But notice that 49.2 y = 4.00 half-lives 1.50 mg ---> 0.750 mg after 1 ---> 0.375 mg after 2 ---> 0.188 mg after 3 ---> 0.094 mg after 4 51 Half-Lives of Radioactive Elements Rate of decay of radioactive isotopes given in terms of 1/2-life. 238U --> 234Th + He 4.5 x 109 y 14C --> 14N + beta 5730 y 131I --> 131Xe + beta 8.05 d Element 106 - seaborgium 263Sg 0.9 s