Chemical Kinetics Part 2

1. Chemical KineticsPart 2 Chapter 13

2. The Change of Concentration with Time

3. Zero-Order Reactions (or zeroth order) • Goal: convert rate law into a convenient equation to give concentrations as a function of time. • For a zero order rxn, the rate is unchanged or is independent of the concentration of a reactant. • However, you must have some of the reactant for the rxn to occur!

4. Zero-Order Reactions (or zeroth order) • One example of a rxn which is 0 order is: • 2HI(g) H2(g) + I2(g) • The rate law for this rxn has been determined experimentally and is: • rate = k[HI]0 = k or rate = k • What are the k units? • Rate = M/s so k units are M/s or M•s-1

5. Zero-Order Reactions (or zeroth order) • But the rate is also equal to the change in [reactant] over the change in time: • But if rate = k, this means that this is true:

6. Zero-Order Reactions (or zeroth order) • We rearrange this equation: • We then integrate:

7. Zero-Order Reactions (or zeroth order) • This eq. means that a graph of [HI] vs. time is a straight line with a slope of -k and a y-intercept of [HI]0. • Here are typical 0-order graphs:

8. Zero-Order Reactions (or zeroth order) • We can find the half-life, t1/2, for a 0-order rxn. • The t1/2 is defined as the time it takes for half of the reactant to disappear. • But this is the time required for [A] to reach • 0.5[A]0 • Mathematically, this is:

9. First-Order Reactions • For a first order rxn, the rate doubles as the concentration of a reactant doubles. • We can show that • A plot of ln[A]t versus t is a straight line with slope -k and y-intercept ln[A]0. • In the above we use the natural logarithm, ln, which is log to the base e.

10. First-Order Reactions

11. Half-Life for 1st-Order Rxns • Half-life is the time taken for the concentration of a reactant to drop to half its original value. • That is, half life, t1/2 is the time taken for [A]0 to reach ½[A]0. • Mathematically, • Note the half-life is independent of the [reactant]0.

12. The Change of Concentration with Time Half-Life

13. Second-Order Reactions • For a second order reaction with just one reactant • A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0 • For a second order reaction, a plot of ln[A]t vs. t is not linear.

14. Second-Order Reactions

15. Second-Order Reactions • We can show that the half life is: • The half-life of a 2nd-order rxn changes as the rxn progresses. • Each half-life is twice as long as the one before! • This makes these problems harder (and less common).

16. Second-Order Reactions • A reaction can also have a rate constant expression of the form: • rate = k[A][B] • This is second order overall, but has first order dependence on A and B. • This is more complicated and you won’t have to solve for half-lives of these rxns.

17. Temperature and Rate

18. Temperature and Rate • Most reactions speed up as temperature increases. (E.g. food spoils when not refrigerated.) • When two light sticks are placed in water: one at room temperature and one in ice, the one at room temperature is brighter than the one in ice. • The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light. • As temperature increases, the rate increases.

19. Temperature and Rate • As temperature increases, the rate increases. • Since the rate law has no temperature term in it, the rate constant must depend on temperature. • Consider the first order reaction CH3NC→CH3CN. • As temperature increases from 190°C to 250°C the rate constant increases from 2.52x10-5 s-1 to 3.16x10-3 s-1. • A rule of thumb is that for every 10°C increase in temperature, the rate doubles! • The temperature effect is quite dramatic. Why?

20. Temperature and Rate

21. The Collision Model • Observations: rates of reactions are affected by concentration and temperature. • Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases. • The collision model: in order for molecules to react they must collide. • The greater the number of collisions the faster the rate.

22. The Collision Model • The more molecules present, the greater the probability of collision and the faster the rate. • The higher the temperature, the more energy available to the molecules and the faster the rate. • However, not all collisions lead to products. In fact, only a small fraction of collisions lead to product. • In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products. • These are called effective collisions.

23. The Collision Model

24. The Collision Model

25. Orientation Factor in Effective Collisions • The orientation of a molecule during collisions is critical in whether a rxn takes place. • Consider the reaction between Cl and NOCl: • Cl + NOCl→NO + Cl2 • If the Cl collides with the Cl of NOCl then the products are Cl2 and NO. • If the Cl collided with the O of NOCl then no products are formed.

26. Orientation Factor in Effective Collisions

27. Activation Energy • Arrhenius: molecules must possess a minimum amount of energy to react. Why? • In order to form products, bonds must be broken in the reactants. • Breaking bonds always requires energy. • Activation energy, Ea, is the minimum energy required to initiate a chemical reaction. • It is also called the Energy of Activation.

28. Activation Energy

29. Activation Energy • Consider the rearrangement of methyl isonitrile to form acetonitrile: • In H3C-N≡C, the C-N≡C bond bends until the C-N bond breaks and the N≡C portion is perpendicular to the H3C portion. This structure is called the activated complex or transition state. • The energy required for the above twist and break is the activation energy, Ea. • Once the C-N bond is broken, the N≡C portion can continue to rotate forming a C-C≡N bond.

30. Activation Energy

31. Activation Energy • The change in energy for the reaction is the difference in energy between CH3NC and CH3CN. • The activation energy is the difference in energy between reactants, CH3NC and transition state. • The rate depends on Ea. • The higher the Ea, the slower the rate!

32. Activation Energy • Notice that if a forward reaction is exothermic (CH3NC→CH3CN), then the reverse reaction is endothermic (CH3CN→CH3NC). • What is theΔH and the Ea for the reverse rxn? • Is Ea revjust -Ea?

34. Activation Energy • How does the Ea relate to temperature? • At any particular temperature, the molecules (or atoms) have an average kinetic energy. • However, somemolecules have less energy while others have more energy than the average value. • This gives us an energy distribution curve where we plot the fraction of molecules with a given energy. • We can graph this for different temperatures as well.

36. Activation Energy • We can see on the graph that some molecules do have enough kinetic energy to react. • This is called f, the fraction of molecules with an energy ≥ Ea. • The equation for f is:

37. Activation Energy • Molecules with an energy ≥ Ea have sufficient energy to react. • What happens to the kinetic energy as we increase the temperature? • It increases! • So, as we increase the temperature, more molecules have an energy ≥ Ea. • So more molecules react per unit time, and the rate increases.

38. Arrhenius Equation • Arrhenius discovered that most rxn-rate data obeyed an equation based on 3 factors: • The number of collisions per unit time. • The fraction of collisions that occur with the correct orientation. • f, the fraction of colliding molecules with an energy ≥ Ea. • From this, he developed the Arrhenius Equation.

39. Arrhenius Equation • In the above, k is the rate constant: it depends on temperature! • R is the Ideal Gas Constant, 8.314J/mol•K • Ea is the Energy of Activation in J • T is the temperature in Kelvin • A is the frequency factor

40. Arrhenius Equation • A is related to the frequency of collisions & the probability that a collision occurs with the correct orientation. • This is related to the molecular size, mass, and shape. • Usually the larger or more complicated the shape, the lower A is. • Important: Both Ea and A are rxn-specific!

41. Arrhenius Equation • How do we find Ea and A? By experiments! • You will do this in the lab! • If we have data from 2 different temperatures, we can find Ea mathematically:

42. Arrhenius Equation • But we can’t find A with only 2 temperatures. • If we have data from 3 or more different temperatures, we can find Ea and A graphically. • According to the Arrhenius Equation: • If we graph lnk vs. 1/T, we get a straight line with a slope of -Ea/R and a y-intercept of lnA.

43. Arrhenius Equation • Here’s a typical graph of the Arrhenius Equation.