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PRINCIPLES OF CHEMISTRY II CHEM 1212 CHAPTER 13

PRINCIPLES OF CHEMISTRY II CHEM 1212 CHAPTER 13. DR. AUGUSTINE OFORI AGYEMAN Assistant professor of chemistry Department of natural sciences Clayton state university. CHAPTER 13 CHEMICAL KINETICS. RATES OF REACTIONS. - Chemical reactions occur when reactant species strike

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PRINCIPLES OF CHEMISTRY II CHEM 1212 CHAPTER 13

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  1. PRINCIPLES OF CHEMISTRY II CHEM 1212CHAPTER 13 DR. AUGUSTINE OFORI AGYEMAN Assistant professor of chemistry Department of natural sciences Clayton state university

  2. CHAPTER 13 CHEMICAL KINETICS

  3. RATES OF REACTIONS - Chemical reactions occur when reactant species strike each other and interact to form products Reaction kinetics is studied to - improve production of materials - increase quality and quantity of products - increase energy efficiency - minimize pollution etc

  4. RATES OF REACTIONS Rate = change per unit time Rate of reaction = change in concentration per unit time

  5. RATES OF REACTIONS For a chemical reaction Reactant → Product - Rate at which reactants are consumed or products are formed in a given period of time is given as Units: M/s Square brackets represent molar concentrations [reactant] = reactant concentration [product] = product concentration

  6. RATES OF REACTIONS Rate of appearance of product = rate of disappearance of reactant - Reactant concentration decreases during reaction ∆[reactant] is negative - Product concentration increases during reaction ∆[product] is positive - Rate is always positive - Rate can be measured by following the concentrations of reactants or products

  7. INSTANTANEOUS AND AVERAGE RATES - Rate of reaction is generally not constant - Rate of reaction changes over the course of reaction - Concentration of reactants or products are measured at regular time intervals - A graph of concentration vs time may be plotted - Instantaneous rate at a given time is the slope of the tangent to the curve at that time - Average rate is measured rate over a time interval

  8. INSTANTANEOUS AND AVERAGE RATES ∆y ∆x

  9. REACTION STOICHIOMETRY - Rate depends on stoichiometry of the reaction - Rate is the ratio of rate of change of a substance to its coefficient Consider the reaction 2HBr(g) → H2(g) + Br2(g) 2 mol HBr : 1 mol of each product

  10. REACTION STOICHIOMETRY For the decomposition of HBr 2HBr(g) → H2(g) + Br2(g) If HBr concentration is decreasing at a rate of 0.52 M/s What is the rate of the reaction? What is the rate of appearance of H2 and Br2?

  11. RATES OF REACTIONS Factors Affecting Rate of Chemical Reaction - Concentration of reactants - Reaction temperature - Physical nature of reactants - Catalysts

  12. RATES OF REACTIONS Concentration of Reactants - An increase in the concentration of reactants causes an increase in the rate of reaction - Collisions are more frequent in a given time for higher concentrations

  13. RATES OF REACTIONS Reaction Temperature - An increase in temperature of a system increases the average kinetic energy of the reacting molecules - An increase in kinetic energy results in an increase in collisions in a given time - The rate of a chemical reaction normally doubles for every 10 oC raise in temperature

  14. RATES OF REACTIONS Physical State of Reactants: solid, liquid, or gas solid-state reactants liquid-state reactants gaseous-state reactants < < Increasing rate of reaction

  15. RATES OF REACTIONS Physical State of Reactants: solid, liquid, or gas - Most frequent collisions occur in the gaseous state (the most freedom of movement of particles) Solid-State Particle Size - Smaller particles have larger surface area and higher reaction rates - Extremely small particles may result in very fast reaction rates and may lead to explosion

  16. RATES OF REACTIONS • Catalysts • Catalysts increase the rate of a reaction without being used up

  17. RATE LAW - Rate of reaction is strongly influenced by concentrations of reacting species - Rate is proportional to the product of the concentrations of the reactants each raised to some power aA + bB → cC + dD Rate = k[A]x[B]y x and y are usually positive integers k = rate constant

  18. RATE LAW aA + bB → cC + dD Rate = k[A]x[B]y - x and y are not necessarily coefficients of A and B - x and y are the orders of the reaction - Described as xth order in A and yth order in B If x = 1 and y = 2 The reaction is first order in A and second order in B Overall order = 1 + 2 = 3

  19. RATE LAW Example For the reaction 2NO2(g) + F2(g) → 2NO2F(g) Rate = k[NO2][F2] The reaction is first order in NO2 and first order in F2

  20. INITIAL RATE OF REACTION The decomposition of nitrosyl chloride was studied: 2NOCl(g) ↔ 2NO(g) + Cl2(g) The following data were obtained [NOCl]0 (molecules/cm3) 3.0 x 1016 2.0 x 1016 1.0 x 1016 4.0 x 1016 Initial Rate (molecules/cm3·s) 5.98 x 104 2.66 x 104 6.64 x 103 1.06 x 105 What is the rate law? Calculate the rate constant Rate = k[NOCl]2, k = 6.64 x 10-29 cm3/molecules∙s

  21. INITIAL RATE OF REACTION The reaction below was studied at -10 oC 2NO(g) + Cl2(g) → 2NOCl(g) The following data were obtained [NO]0 (mol/L) 0.10 0.10 0.20 [Cl2]0 (mol/L) 0.10 0.20 0.20 Initial Rate (mol/L) 0.18 0.36 1.45 What is the rate law? Calculate the rate constant Rate = k[NO]2[Cl2], k = 1.8 x 102 L2/mol2

  22. CONCENTRATION AND TIME - Rate of reaction decreases with time - Rate of reaction eventually goes to zero - Concentrations of reactants decrease - Concentrations of products increase

  23. ZERO-ORDER RATE LAW - Rates are independent of the concentrations of the reactants R → product Rate = k[R]0 Rate = k - Called differential rate law Unit of k = unit of reaction rate = M/s

  24. ZERO-ORDER RATE LAW - Graph of concentration vs time Concentration Time

  25. ZERO-ORDER RATE LAW - Rates are independent of the concentrations of the reactants R → product [R]t = [R]0 - kt - Called integrated rate law Unit of k = unit of reaction rate = M/s Examples Metabolism of ethyl alcohol in the body Biochemical reactions involving enzymes

  26. ZERO-ORDER RATE LAW - Graph of concentration vs time is a straight line Slope = −k Intercept = [R]0 Concentration Time

  27. ZERO-ORDER RATE LAW HALF - LIFE - A large value of k implies a fast reaction - The half-life (t1/2) is also used to describe the speed of a reaction - Half-life is the time needed for the concentration of a reactant to decrease to half its original value - A short half-life indicates a fast reaction

  28. ZERO-ORDER RATE LAW HALF - LIFE At t = 0 Initial concentration = [R]0 At half-life t = t1/2 [R]t = ½[R]0 - Substitute in zero-order equation and simplify

  29. ZERO-ORDER RATE LAW HALF - LIFE - Using the zero-order rate equation [R]t = [R]0 – kt - Simplifying gives - Half-life for zero-order depends on concentration

  30. ZERO-ORDER RATE LAW The reaction A → B + C is known to be zero order in A and to have a rate constant of 5.0 x 10-2 mol/L·s at 25 oC. An experiment was run at 25 oC where [A]0 = 1.0 x 10-3 M. a) What is the integrated rate law for this reaction? b) Calculate the half-life for the reaction. c) Calculate the concentration of B after 5.0 x 10-3 s has elapsed. a) [A] = [A]0 - kt b) 1.0 x 10-2 s c) 2.5 x 10-4 M

  31. FIRST-ORDER RATE LAW - Rate is proportional to the concentration of the reactant R → product - Called the differential form of the rate law - Relates differences in concentration and time Unit of k = s-1

  32. FIRST-ORDER RATE LAW - A graph of concentration vs time describes an exponential decay Concentration Time

  33. FIRST-ORDER RATE LAW - Rate is proportional to the concentration of the reactant R → product - Called the integrated form of the rate law (describes an exponential decay) - Relates instantaneous concentrations [R]t = concentration of R at any time [R]0 = initial concentration at t = 0 e = base of natural logarithms ≈ 2.718

  34. FIRST-ORDER RATE LAW From the first-order rate equation Take natural logarithm on both sides and simplify or

  35. FIRST-ORDER RATE LAW A graph of ln[R]t vs time is a straight line Slope = −k Intercept = ln[R]0 ln[Concentration] Time

  36. FIRST-ORDER RATE LAW HALF - LIFE At t = 0 Initial concentration = [R]0 At half-life t = t1/2 [R]t = ½[R]0 Substitute in first-order equation and simplify

  37. FIRST-ORDER RATE LAW HALF - LIFE From the first-order rate equation Substitute and simplify

  38. FIRST-ORDER RATE LAW HALF - LIFE - Half-life of a first-order reaction is independent of the concentration of the reactant - Depends on only the rate constant (k) - Constant half-life from concentration vs time plot indicates first-order reaction Example Radioactive decay processes

  39. FIRST-ORDER RATE LAW The radioactive isotope 32P decays by first-order kinetics and has a half-life of 14.3 days. How long does it take for 95% of a sample of 32P to decay? k = 0.0485 1/day t = 61.8 days

  40. FIRST-ORDER RATE LAW A first-order reaction is 75.0% complete in 320 second. a) What are the first and second half-lives for this reaction? b) How long does it take for 90% completion? a) 160 s for both first and second half-lives b) 532 s

  41. FIRST-ORDER RATE LAW Calculate the half-life of a first order reaction if the concentration of the reactant is 0.0451 M at 30.5 seconds after the reaction starts and is 0.0321 M at 45.0 seconds after the reaction starts. How many seconds after the start of the reaction does it take for the reactant concentration to decrease to 0.0100 M? a) 29.5 s b) 94.9 s

  42. SECOND-ORDER RATE LAW - Rate is proportional to the concentration of the reactant raised to the second power R → product - Called the differential form of the rate law - Relates differences in concentration and time Unit of k = M-1s-1 or L/mol·s

  43. SECOND-ORDER RATE LAW - Graph of concentration vs time Concentration Time

  44. SECOND-ORDER RATE LAW - Rate is proportional to the concentration of the reactant raised to the second power R → product - Called the integrated form of the rate law Unit of k = M-1s-1 or L/mol·s

  45. SECOND-ORDER RATE LAW - A graph of 1/concentration vs time is a straight line 1/[Concentration] Slope = k Intercept = 1/[R]0 Time

  46. SECOND-ORDER RATE LAW HALF-LIFE Half-life depends on starting concentration

  47. SECOND-ORDER RATE LAW For the reaction A → products successive half-lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which [A]0 = 0.10 M. Calculate the concentration of A at a) 30.0 min b) 70.0 min c) 80.0 min a) 0.025 M b) 0.013 M c) 0.011 M

  48. SECOND-ORDER RATE LAW Consider the following initial rate data for the decomposition of compound AB to give A and B [AB]0, mol/L: 0.200 0.400 0.600 Initial rate, mol/L·s: 3.20 x 10-3 1.28 x 10-2 2.88 x 10-2 Determine the half-life for the decomposition reaction initially having 1.00 M AB present Rate = k[AB]2 k = 0.0800 L/mol·s t1/2 = 12.5 s

  49. RATE AND TEMPERATURE - Almost all reactions go faster at higher temperatures - The rate of most reactions increase at increasing temperature - The order of the reaction usually does not change with temperature

  50. RATE AND TEMPERATURE Example For the reaction NO(g) + O3(g) → NO2(g) + O2(g) The rate constant increases with increasing temperature k (L/mol·s) T (K)

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