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Chemical Kinetics

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  1. Chemical Kinetics The area of chemistry concerned with the speeds, or rates, at which a chemical reaction occurs. Chemical Kinetics 2009-2010

  2. Reaction Rate The reaction rate is the change in the concentration of a reactant or a product with time, (M/s or M . s-1), where M is molarity and s represents seconds. Another way to represent rate is mol . L-1 s-1 Chemical Kinetics 2009-2010

  3. Factors that Influence Reaction Rate Under a given set of conditions, each reaction has its own characteristic rate, which is ultimately determined by the chemical nature of the reactants. (You will remember this from Chem I - potassium and water have a different rate of reaction than iron and oxygen.) For a given reaction (using the same reactants), we can control four factors that affect its rate: the concentration of reactants, their physical state, the temperature at which the reaction occurs, and the use of a catalyst. Chemical Kinetics 2009-2010

  4. Means “proportional to” The Collision Theory of Chemical Kinetics The kinetic molecular theory of gases postulates that gas molecules frequently collide with one another. Therefore, it seems logical to assume – and it is generally true - that chemical reactions occur as a result of collisions between reacting molecules. In terms of the collision theory of chemical kinetics, then, we expect the rate of a reaction to be directly proportional to the frequency of the collisions (number of molecular collisions per second). Rate collision frequency Chemical Kinetics 2009-2010

  5. Rate collision frequency concentration Concentration Since molecules must collide in order to react, the more frequently they collide, the more often a reaction occurs. Thus, reaction rate is proportional to the concentration of reactant Therefore, if we increase the concentration… we increase the collision frequency, which… increases the rate Chemical Kinetics 2009-2010

  6. Physical State Molecules must mix in order to collide. When reactants are in the same phase, as in aqueous solution, occasional stirring keeps them in contact. When they are in different phases, more vigorous mixing is needed. The more finely divided a solid or liquid reactant, the greater the surface are per unit volume, the more contact it makes with the other reactant, and the faster the reaction. Chemical Kinetics 2009-2010

  7. Speed of a molecule Number of collisions Temperature Molecules must collide in order to react. Since the speed of a molecule depends on its temperature, more collisions will occur if the temperature is increased. Chemical Kinetics 2009-2010

  8. Temperature Molecules must also collide with enough energy to react. Increasing the temperature increases the kinetic energy of the molecules, which in turn increases the energy of the collisions. Therefore, at a higher temperature, more collisions occur with enough energy to react. Thus, raising the temperature increases the reaction rate by increasing the number and especially the energy of the collisions. Chemical Kinetics 2009-2010

  9. Temperature Two familiar kitchen appliances employ this effect: a refrigerator slows down chemical processes that spoil food, whereas an oven speeds up other chemical processes to cook it. Chemical Kinetics 2009-2010

  10. Expressing Reaction Rate Before we can deal quantitatively with the effects of concentration and temperature on reaction rate, we must be able to express the rate mathematically. A rate is a change in some variable per unit of time. For example, the rate of motion of a car is the change of position of the car divided by time. A car that travels 57 miles in 60. minutes is traveling at… 57 miles/60. minutes = .95 miles/min In the case of chemical reactions, the positions of the substances do not change over time, but their concentrations do. Chemical Kinetics 2009-2010

  11. We know that any reaction can be represented by the general equation reactants  products This equation tells us that during the course of a reaction, reactants are consumed while products are formed. As a result, we can follow the progress of a reaction by monitoring either the decrease in concentration of the reactants or the increase in concentration of the products. Chemical Kinetics 2009-2010

  12. The following figure shows the progress of a simple reaction in which A molecules are converted to B molecules: A  B B A Chemical Kinetics 2009-2010

  13. The decrease in number of A molecules and the increase in the number of B molecules with time are shown below. Chemical Kinetics 2009-2010

  14. D[A] Dt Because the concentration of A decreases during the time interval, D[A] is a negative quantity. Because the rate of a reaction is always a positive quantity, a minus sign is needed in the rate expression to make the rate positive. In general, it is more convenient to express the reaction rate in terms of the change in concentration with time. Thus, for the reaction A  B we can express the rate as: [A]final – [A]initial Rate = -

  15. Rate = The rate of product formation does not require a minus sign because D[B], ([B]final – [B]initial) is a positive quantity (the concentration increases with time), so rate is a positive value already. or D[B] Dt Chemical Kinetics 2009-2010

  16. Rate = - Rate = or D[A] Dt D[B] Dt These rates are average rates because they are averaged over a certain time period (Dt). Rate can be expressed as M/s, M . s-1, or mol . L-1 . s-1 Chemical Kinetics 2009-2010

  17. Reaction Rates and Stoichiometry We have seen that for stoichiometrically simple reactions of the type A  B, the rate can either be expressed in terms of the decrease in reactant concentration with time, -D[A]/Dt, or the increase in product concentration with time, D[B]/Dt. For more complex reactions, we must be careful in writing the rate expressions. Consider the reaction 2A  B Two moles of A disappear for each mole of B that forms Chemical Kinetics 2009-2010

  18. 1 D[A] 2 Dt D[B] Dt Another way to think of this is to say that the rate of disappearance of A is twice as fast as the rate of appearance of B. We write the rate as either Rate = - or Rate = For the reaction 2A  B Chemical Kinetics 2009-2010

  19. 1 D[A] a Dt 1 D[B] b Dt 1 D[C] c Dt 1 D[D] d Dt 1 D[A] a Dt 1 D[C] c Dt In general, for the reaction aA + bB  cC + dD The rate is given by Rate = - = - = = Chemical Kinetics 2009-2010

  20. 1 D[O3] 2 Dt 1 D[O2] 3 Dt - Write the expression for the following reactions in terms of the disappearance of the reactants and the appearance of the products: 3O2(g)  2O3(g) Rate = = Chemical Kinetics 2009-2010

  21. 1 D[O3] 2 Dt 1 D[O2] 3 Dt - 1 -.25M 3 s 1 x 2 s - If O2 is disappearing at .25 M/s, what is the rate of formation of O3? = = .50Ms = 3(x)s x = .17M Chemical Kinetics 2009-2010

  22. By definition, we know that to determine the rate of a reaction we have to monitor the concentration of the reactant (or product) as a function of time. • For reactions in solution, the concentration of a species can often be measured by spectroscopic means. • If ions are involved, the change in concentration can also be detected by an electrical conductance measurement. • Reactions involving gases are most conveniently followed by pressure measurements. Chemical Kinetics 2009-2010

  23. Reddish-brown colorless colorless colorless colorless Reaction of Molecular Bromine and Formic Acid In aqueous solutions, molecular bromine reacts with formic acid (HCOOH) as follows: Br2(aq) + HCOOH(aq)  2Br-(aq) + 2H+(aq) + CO2(g) The rate of Br2 disappearance can be determined by monitoring the color over time. As the reaction proceeds, the color of the solution … goes from brown to colorless Chemical Kinetics 2009-2010

  24. Reaction of Molecular Bromine and Formic Acid Br2(aq) + HCOOH(aq) 2Br-(aq) + 2H+(aq) + CO2(g) As the reaction proceeded, the concentration of Br2 steadily decreased and the color of the solution faded. Chemical Kinetics 2009-2010

  25. D[Br2] Dt [Br2]t – [Br2]0 tfinal – tinitial Measuring the change (decrease) in bromine concentration at some initial time ([Br2]0) and then at some other time, ([Br2]t)allows us to determine the average rate of the reaction during that interval: Average rate = Average rate = Chemical Kinetics 2009-2010

  26. Use the data in the following table to calculate the average rate over the first 50 second time interval. Chemical Kinetics 2009-2010

  27. (0.0101 – 0.0120)M (50.0 – 0.0)s Average rate = = 3.80 x 10-5 M/s Notice, this average rate is slower than rate at time 0, but faster than the rate at time 50 Chemical Kinetics 2009-2010

  28. Now use the data in the same table to calculate the average rate over the first 100 second time interval. Chemical Kinetics 2009-2010

  29. (0.00846 – 0.0120)M (100.0 – 0.0)s Avg rate = = 3.54 x 10-5 M/s Notice, this average rate is slower than rate at time 0, but faster than the rate at time 100 Chemical Kinetics 2009-2010

  30. These calculations demonstrate that the average rate of the reaction depends on the time interval we choose. By calculating the average reaction rate over shorter and shorter intervals, we can obtain the rate for a specific instant in time, which gives us the instantaneous rate of the reaction at that time. Chemical Kinetics 2009-2010

  31. The figure below shows the plot of [Br2] versus time, based on the data table given previously. Graphically, the instantaneous rate at 100 seconds after the start of the reaction is the slope of the line tangent to the curve at that instant. Unless otherwise stated, we will refer to the instantaneous rate as simply “the rate”. The instantaneous rate at any other time can be determined in a similar manner. Chemical Kinetics 2009-2010

  32. k, the Rate Constant At a specific temperature, a rate constant (k) is a constant of proportionality between the reaction rate and the concentrations of reactants. rate [Br2] rate = k[Br2] k is specific for a given reaction at a given temperature; it does not change as the reaction proceeds. Chemical Kinetics 2009-2010

  33. Rate [Br2] Rearrange the equation rate = k[Br2] To solve for k Since reaction rate has the units M/s, and [Br2] is in M, the unit of k for this first order reaction is 1/s or s-1. k = Chemical Kinetics 2009-2010

  34. Calculate the rate constant for the following reaction Br2(aq) + HCOOH(aq)  2Br-(aq) + 2H+(aq) + CO2(g) Chemical Kinetics 2009-2010

  35. 4.20 x 10-5 0.0120 rate [Br2] k = = 3.50 x 10-3 k = Because k is a constant (for this reaction at this specific temperature), it doesn’t matter which row we consider, so let’s consider the data at time 0.0 seconds… 3.50 x 10-3 rate = k[Br2]

  36. To prove that k is a constant, calculate k at time 200.0 seconds 3.50 x 10-3 3.51 x 10-3 The slight variations in the values of k are due to experimental deviations in rate measurements. Chemical Kinetics 2009-2010

  37. Filling in the rest of the table… 3.50 x 10-3 3.49 x 10-3 3.50 x 10-3 3.51 x 10-3 3.51 x 10-3 3.50 x 10-3 3.52 x 10-3 3.48 x 10-3 3.51 x 10-3 Chemical Kinetics 2009-2010

  38. As we will see in the next section, the label for k is determined by the overall reaction order Chemical Kinetics 2009-2010

  39. It is important to understand that k is NOT affected by the concentration of Br2. • The rate is faster at a higher concentration and slower at a lower concentration of Br2, but the ratio of rate/[Br2] remains the same provided the temperature doesn’t change. Chemical Kinetics 2009-2010

  40. The Rate Law The rate law expresses the relationship of the rate of a reaction to the rate constant (k) and the concentrations of the reactants raised to a power. For the general reaction aA + bB  cC + dD The rate law takes the form Rate = k[A]x[B]y Wherex and y are numbers that must be determined experimentally. Note – in general, x and y are NOT equal to the stoichiometric coefficients a and b from the overall balanced chemical equation. When we know the values of x, y and k, we can use the rate equation shown above to calculate the rate of the reaction, given the concentrations of A and B. Chemical Kinetics 2009-2010

  41. Rate = k[A]x[B]y The reaction orders define how the rate is affected by the concentration of each reactant. This reaction is xth order in A, yth order in B. Chemical Kinetics 2009-2010

  42. The following rate law was determined for the formation of nitrogen (VI) oxide and molecular oxygen from nitrogen (IV) oxide and ozone Rate = k[NO2][O3] How would the rate of this reaction be affected if the concentration of NO2 increased from 1.0 M to 2.0 M? Chemical Kinetics 2009-2010

  43. Rate = k[NO2][O3] This reaction is first order with respect to both NO2 and O3. This means that doubling the concentration of either reactant would double the rate of the reaction. (2)1 = 2 How many times greater the rate of the reaction will be How many times greater the concentration is What the order is for that reactant Chemical Kinetics 2009-2010

  44. The reaction between nitrogen monoxide and molecular oxygen is described by a different rate law. Rate = k [NO]2[O2] How would the rate of this reaction be affected if the concentration of NO increased from 1.0 M to 2.0 M? Chemical Kinetics 2009-2010

  45. Rate = k[NO]2[O2] This reaction is second order with respect to NO and first order with respect to O2. Doubling the concentration NO would increase the rate by a factor of four (2)2 = 4 How many times greater the rate of the reaction will be How many times greater the concentration is What the order is for that reactant Chemical Kinetics 2009-2010

  46. Rate = k [NO]2[O2] How would the rate of this reaction be affected if the concentration of NO increased from 1.0 M to 5.0 M? In this case, when the concentration of NO is multiplied by 5, the rate increases by a factor of 25! (5)2 = 25 Chemical Kinetics 2009-2010

  47. The exponents x and y specify the relationships between the concentrations of reactants A and B and the reaction rate. Added together, they give us the overall reaction order, defined as the sum of the powers to which all reactant concentrations appearing in the rate law are raised. For the equation Rate = k[A]x[B]y The overall reaction order is x + y. Chemical Kinetics 2009-2010

  48. For the following reaction (CH3)3CBr(l) + H2O(l)  (CH3)3COH(l) + HBr(aq) The rate law has been found to be rate = k[(CH3)3CBr] This reaction is first order in 2-bromo-2-methylpropane. Note that the concentration of H2O does not even appear in the rate law. Thus, the reaction is zero order with respect to H2O. This means that the rate does not depend on the concentration of H2O; we could also write the rate law for this reaction as rate = k[(CH3)3CBr][H2O]0 What is the overall order of this reaction? 1st order overall (1+0=1) Chemical Kinetics 2009-2010

  49. Reaction orders are usually positive integers or zero, but they can also be fractional or negative. In the reaction CHCl3(g) + Cl2(g)  CCl4(g) + HCl(g) A fractional order appears in the rate law: rate = k[CHCl3][Cl2]1/2 This order means that the reaction depends on the square root of the Cl2 concentration. If the initial Cl2 concentration is increased by a factor of 4, for example, the rate increases by V4 (= 2), therefore the rate would double.

  50. A negative exponent means that the reaction rate decreases when the concentration of that component increases. Negative orders are often seen for reactions whose rate laws include products. For example, in the atmospheric reaction 2O3(g) 3O2(g) The rate law has been shown to be Rate = k[O3]2[O2]-1 ; or [O3]2 rate = k [O2] If the [O2] doubles, the reaction proceeds half as fast. Chemical Kinetics 2009-2010