14.1 Factors That Affect Reaction Rates

Transcription

1 14.1 Factors That Affect Reaction Rates 1) 2) 3) 4) 14.2 Reaction Rates How does increasing the partial pressures of the reactive components of a gaseous mixture affect the rate at which the compounds react with one another? **note this P [ ], used throughout this, and subsequent chapters! Sample Exercise 14.1 From the data in the figure above, calculate the average rate at which A disappears over the time interval from 20s to 40s. Practice Exercise 14.1 For the reaction in the figure above calculate the average rate of appearance of B over the time interval from 0 to 40s. (see at figure captions)

2 Sample Exercise 14.2 Use figure 14.4 to calculate the instantaneous rate of disappearance of C 4H 9Cl at t=0s. (the initial rate) Practice Exercises 14.2 Use figure 14.4 determine the instantaneous rate of disappearance of C 4H 9Cl at t=600s The figure above shows two triangles that are used to determine the slope of the curve at two different times. How do you determine how large a triangle to draw when determining the slope of a curve at a particular point?

3 Look at the reaction below: 2O 3(g) 3O 2(g) A) How is the rate at which the ozone disappears related to the rate at which oxygen appears in the reaction? B) If the rate at which O 2 appears, Δ[O 2]/ Δt, is 6.0x10-5 M/s at a particular instant, at what rate is O 3 disappearing at this same time, - Δ[O 3]/ Δt? 14.3 Concentration and Rate We will now look at the way in which the rate at the beginning of a reaction (the i r ) depends on s c. For a reaction: aa + bb cc + dd we can write an expression, called the rate law expression (or rate law equation) that looks like this: A) What is a rate law? B) What is the name of the quantity k in any rate law? C) True of False: A rate law can always be determined directly from the balanced chemical equation. The experimentally determined rate law for the reaction 2NO(g) + 2H 2(g) N 2(g) +2H 2O(g) is rate = k[no] 2 [H 2] A) What are the reaction orders in this rate law? B) Does doubling the concentration of NO have the same effect on the rate as doubling the concentration of H 2?

4 Consider a reaction A + B C for which the rate = k[a][b] 2. Each of the following boxes represents a reaction mixture in which A is as red spheres and B as purple ones. Rank these mixtures in increasing rate of reaction. Assume the rate = k[a][b], rank the mixtures represented in this sample exercise in order of increasing rate. Eq 1: 2N 2O 5(g) 4NO 2(g) + O 2(g) rate = k(n 2O 5] Eq 2: CHCl 3(g) + Cl 2(g) CCl 4(g) + HCl(g) rate = k[chcl 3][Cl 2] 1/2 Eq 3: H 2(g) + I 2(g) 2HI(g) rate = k[h 2][I 2] What are the overall reaction orders for the reactions described in equation 1 and 2? What are the units of the rate constant for the rate law for equation 1? What is the reaction order for the reactant H 2 in equation 3? What are the units for the rate constant for equation 3?

5 The initial rate of a reaction A+B C was measured for several different concentrations of A and B the results are below. Using the data determine A) the rate law of the reaction. B) the magnitude of the rate constant. C) the rate of the reaction when [A]=0.050M and [B]=0.100M. Experiment Number [A] (M) [B] (M) Initial Rate (M/s) x x x 10-5 The following data were measured for the reaction of nitric oxide with hydrogen: 2NO(g) + 2H2(g) N2(g) + 2H2O(g) Experiment Number [NO] (M) [H2] (M) Initial Rate (M/s) x x x 10-3 A) Determine the rate law for the reaction. B) Calculate the rate constant. C) Calculate the rate when [NO]=0.050M and when [H2]=0.150M.

6 14.4 Change of Concentration With Time: Integrated Rate Laws Rate Law Equation Zero Order First Order Second Order Integrated Rate Law Equation Half- Life Equation Graphically, what makes it relate as a straight- line? What is k for the equation, and what are k s units? The decomposition of a certain insecticide in water follows first- order kinetics with a rate constant of 1.445yr - 1 at 12 C. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 x 10-7 g cm - 3. Assume that the average temperature of the lake is 12 C. A) What is the concentration of the insecticide on June 1 of the following year? B) How long will it take for the concentration of the insecticide to drop to 3.0 x 10-7 g cm - 3?

7 The decomposition of dimethyl ether, (CH 3) 2O, at 510 C is a first- order process with a rate constant of 6.8 x 10-4 s - 1 : (CH 3) 2O(g) CH 4(g) + H 2(g) + CO(g) If the initial pressure of (CH 3) 2O is 135 torr, what is its partial pressure after 1420 seconds? Look at the graphs below. What do the y- intercepts in the graphs (a) and (b) represent?

8 The following data were obtained for the gas- phase decomposition of nitrogen dioxide at 300 degrees Celsius, NO 2(g) NO(g)+ 1 / 2O 2(g): Time(s) [NO 2](M) Is the reaction zero, first or second order in NO 2? Some graphs to help: Consider again the decomposition of NO 2 discussed above. The reaction is second order in NO 2 with k=0.543 M - 1 s - 1. If the initial concentration of NO 2 in a closed vessel is M, what is the remaining concentration after h?

9 The reaction of C 4H 9Cl with water is a first- order reaction. The figure above shows how the concentration of C 4H 9Cl changes with time at a particular temperature. (a) From that graph, estimate the half- life for this reaction. (b) Use the half- life from (a) to calculate the rate constant. Using the 1 st - order half- life equation t 1/2 = 0.693/k

10 (a) calculate t 1/2 for the decomposition of the insecticide described in a sample exercise above. The insecticide follows first- order kinetics with a rate constant of 1.445yr - 1 at 12 C. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 x 10-7 g cm - 3. (b) how long does it take for the concentration of the insecticide to reach one- quarter of the initial value. How does the half- life of a second order reaction change as the reaction proceeds? 14.5 Temperature and Rate What is the central Why isn t collision idea of the collision frequency the only model? factor affecting a reaction rate? This is called an E P Diagram. The vertical axis is E, and the horizontal axis is R P.

11 Consider a series of reactions having the following energy profiles: Assuming that all three reactions have nearly the same frequency factors, rank the reactions from slowest to fastest. Imagine that these reactions are reversed. Rank these reverse reactions from slowest to fastest. Arrhenius noted that for most reactions the increase in the rate with increasing temperature is nonlinear. He developed an equation, the Arrhenius Equation, that related three factors that affect the rate of a reaction: a) b) c) When the natural log of both sides of the equation is taken, the result is: Note it is in the form of y=mx+b a line

12 The following table shows the rate constants for the rearrangement of methyl isonitrile at various temperatures: a) From these data, calculate the activation energy for the reaction b) What is the value of the rate constant at 430.0K? Help for answering (a): What is the sign of the slope of the line graphed above? What quantities are on the vertical and horizontal axes of the graph? What data was collected to determine the activation energy of the reaction?

13 14.6 Reaction Mechanisms Reactions that occur in a single event or step are called elementary reactions (or elementary processes). The number of molecules that participate as reactants in an elementary reaction defines the molecularity of the reaction. Three types of molecularity: a) b) c) The net change represented by a balanced chemical equation often occurs by a multistep mechanism, which consists of a sequence of elementary reactions. It has been proposed that the conversion of ozone into O 2 proceeds by a two- step mechanism: O 3(g) O 2(g) + O(g) O 3(g) + O(g) 2O 2(g) a) describe the molecularity of each elementary reaction in this mechanism. b) Write the equation for the overall reaction. c) Identify the intermediates. The proposed mechanism for a reaction is: Mo(CO) 6 Mo(CO) 5 + CO Mo(CO) 5 + P(CH 3) 3 Mo(CO) 5P(CH 3) 3 a) Write is the equation for the overall reaction? b) What is the molecularity of each step in the mechanism? c) Identify the intermediates. If we know that a reaction is an elementary reaction, then we know its rate law. Questions you answer, must TELL YOU that it is an elementary process or reaction otherwise you don t know.

14 If the follwing reaction occurs in a single elementary reaction, predict the rate law: H 2(g) + Br 2(g) 2HBr(g) Consider the following reaction: 2NO(g) + Br 2(g) 2NOBr(g) a) write the rate law for the reaction, assuming it involves a single elementary reaction. b) Is a single- step mechanism likely for this reaction? Justify your answer. Why can t the rate law for a reaction generally be deduced from the balanced chemical equation? The decomposition of nitrous oxide, N 2O, is believed to occur by a two- step mechanism: N 2O(g) N 2(g) + O(g) slow N 2O(g) + O(g) N 2(g) + O 2(g) fast a) write the equation for the overall reaction. b) write the rate law for the overall reaction. Ozone reacts with nitrogen dioxide to produce dinitrogen pentoxide and oxygen: O 3(g) + 2NO 2(g) N 2O 5(g) + O 2(g) The reaction is believed to occur in two steps: O 3(g) + NO 2(g) NO 3(g) + O 2(g) NO 3(g) + NO 2(g) N 2O 5(g) The experimental rate law is: Rate = k[o 3][NO 2] What can you say about the relative rates of the two steps of the mechanism (e.g., which step is fast and which step is slow )?

15 Show that the following mechanism for 2NO(g) + Br 2(g) 2NOBr(g) also produces a rate law consistent with the experimentally observed one: Step 1: NO(g) + NO(g) N 2O 2(g) (fast, equilibrium) Step 2: N 2O 2(g) + Br 2(g) 2NOBr(g) (slow) The first step of a mechanism involving the reaction of bromine is Br 2(g) 2Br(g) (fast, equilibrium) What is the expression relating the concentration of Br(g) to that of Br 2(g)? A reaction has a known multi-step mechanism of: (1) NO + NO N2O2 (fast, equilibrium) (2) N2O2 + O2 2NO2 (slow) a) Write the overall reaction b) Identify any intermediates in reaction steps c) Write the rate expression for the slow step of the reaction. d) Write the rate law for the overall reaction, eliminating any intermediates from the rate expression.

16 14.7 Catalysis homogeneous catalyst: heterogeneous catalyst: How does a catalyst increase the rate of a reaction? In the energy profile diagram above, label: a) the activation energy without a catalyst b) the activation energy with a catalyst c) the enthalpy of the overall reaction Determine the number of elementary steps (reactions) during the catalyzed reaction. Label them. Is the activation energy for the reverse of the uncatalyzed reaction greater, smaller or equal to the activation energy for the forward reaction? Justify your answer.