NAME: Chapter 14Chemical Kinetics (Reaction Rate Law Concepts) 1. Go to the website : http://www.chm.davidson.edu/vce/kinetics/index.html, a. Go to reaction rates page, read the introductory paragraphs and then push start i. Write a brief summary of what the graphs look like after the experiment has run in part 1. b. Go to the second experiment and push start i. Write a brief summary (answering the questions above the graph) of what the graphs look like after the experiment has run in part 2. You can switch between the species and push the >>> or <<< button c. As we continue through this unit you may want to go to other pages on this website that have more experiments to explain multiple concepts in chemical kinetics. (or visit http://www.mrmchem.com/) 2. A wise, but sometime unwise AP chemistry student correctly determines ΔG to be a large negative value using, ΔG = ΔH - TΔS and then makes the following statement, this reaction must occur very fast with Gibbs free Energy being such a large negative number. Using several examples from your Zumdahl textbook (p. 527 and the introductory paragraphs of Chapter 12) w hat is wrong with this statement. 3. To completely understand a chemical reaction what three major concepts do we need to know and why? a. b. c. 4. Define each of the following terms a. Rate constant b. Rate-determining step c. Rate law (differential rate law) d. Reaction rate 1
Questions 5-9 are about the graph and equation shown above 5. Describe how the instantaneous rate of this reaction can be determined for this reaction based on any given reactant or any given product at any given time. a. Show an example of this on the graph above for finding the instantaneous rate for the reactant, nitrogen monoxide, after 80 seconds. b. What is happening to the rate of this reaction has time proceeds? 6. How is the graph going to look for each reactant and product after 400 seconds? a. Show the answer to this question by showing an extrapolation on the graph above. b. Why does the graph look like this after 400 s? 7. Write a hypothetical rate law for this reaction. a. Label the values n and k and how can each be determined? i. n can be found in two different ways, describe each method ii. Does the method you choose in 7(a-i) change what you find for the n value. iii. How do we determine which method to use? iv. Describe the method your favorite teacher (well maybe) use to determine the order for this reaction? v. Will the value found for n always equal the coefficient from the balanced equation? 2
8. How can the rate law be determined if the integrated rate law method was used for a reaction that has multiple reactants? 9. Define each of the following terms. a. Elementary step b. Intermediate c. Reaction Mechanism 10. What is the collision model and how does it help explain reaction rates? 11. Explain why unimolecular and bimolecular steps are common, but termolecular steps are not. a. What two things must be true about a molecular collision to be successful? i. ii. 12. What two things must be true about a reaction mechanism to be plausible? a. b. 13. How can activation energy be determined experimentally? 14. Finish the following statement, catalyst are a. What is the difference between a homogeneous and heterogeneous catalyst? Give examples of each? b. Which example above does increasing the area of a catalyst greatly increase the speed of the reaction and why? 3
A(aq) + 2 B(aq) Chapter 12 Reaction Rate Law Problems 3 C(aq) + D(aq) 1. For the reaction above, carried out in solution of 30 C, the following kinetic data were obtained: Experiment Initial Conc. of Reactants (mole. liter -1 ) Initial Rate of Reaction (mole. liter -1. hr -1 ) A o 1 0.240 0.480 8.00 2 0.240 0.120 2.00 3 0.360 0.240 9.00 4 0.120 0.120 0.500 5 0.240 0.0600 1.00 6 0.0140 1.35? B o a. Write the rate-law expression for this reaction. Explain b. Calculate the value of the specific rate constant k at 30 C and specify its units. c. Calculate the value of the initial rate of this reaction at 30 C for the initial concentrations shown in experiment 6. d. Assume that the reaction goes to completion. Under the conditions specified for experiment 2, what would be the final molar concentration of C? 2. Given the below initial rate data, determine the rate law and rate constant (including units) for the following reaction:. Support your answer with information from the data table. 4
3. Given the following rate data concerning the decomposition of sodium azide into nitrogen gas, determine its rate law including the rate constant with the appropriate units. 4. Graphical methods are frequently used to analyze data and obtain desired quantities. 2 HI(g) H 2 (g) + I 2 (g) a. The data below gives the value of the rate constant at various temperatures for the gas phase reaction above. Describe, without doing any calculations, how a graphical method can be used to obtain the activation energy for this reaction. Then find the E a for the reaction with the appropriate units. T (K) k (liter/mol sec) 647 8.58 10-5 666 2.19 10-4 683 5.11 10-4 700 1.17 10-3 716 2.50 10-3 A(g) B(g) + C(g) b. The following data give the partial pressure of A as a function of time and were obtained at 100 C for the reaction above. Describe, without doing any calculations, how graphs can be used to determine whether this reaction order for A and how these graphs are used to determine the rate constant. Then determine the order of A, include units with your answer. P A (mm Hg) t (sec) 348 0 247 600 185 1200 105 2400 58 3600 5
(I) A 2 + B 2 2 AB (II) X 2 + Y 2 2 XY 5. Two reactions are represented above. The potential-energy diagram for reaction I is shown below. The potential energy of the reactants in reaction II is also indicated on the diagram. Reaction II is endothermic, and the activation energy of reaction I is greater than that of reaction II. a. Complete the potential-energy diagram for reaction II on the graph above. b. For reaction I, predict how each of the following is affected as the temperature is increased by 20 C. Explain the basis for each prediction. i. Rate of reaction ii. Heat of reaction c. For reaction II, the form of the rate law is rate = k[x 2 ] m [Y 2 ] n. Briefly describe an experiment that can be conducted in order to determine the values of m and n in the rate law for the reaction. d. From the information given, determine which reaction initially proceeds at the faster rate under the same conditions of concentration and temperature. Justify your answer. 6
6. Answer the questions a-e below given the following information: 7
7. Answer the following questions regarding the kinetics of chemical reactions. a. The diagram below shows the energy pathway for the reaction O 3 + NO NO 2 + O 2. Clearly label the following directly on the diagram. i. The activation energy (E a ) for the forward reaction ii. The enthalpy change ( H) for the reaction b. The reaction 2 N 2 O 5 4 NO 2 + O 2 is first order with respect to N 2 O 5. Using the axes below, complete the graph that represents the change in [N 2 O 5 ] over time as the reaction proceeds. Initial [ N O ] Time i. Describe how the graph in (i) could be used to find the reaction rate at a given time, t. ii. Considering the rate law and the graph in (i), describe how the value of the rate constant, k, could be determined. iii. If more N 2 O 5 were added to the reaction mixture at constant temperature, what would be the effect on the rate constant, k? Explain c. Data for the chemical reaction 2A B + C were collected by measuring the concentration of A at 10- minute intervals for 80 minutes. The following graphs were generated from analysis of the data. d. Use the information in the graphs above to answer the following. i. Write the rate-law expression for the reaction. Justify your answer. ii. Describe how to determine the value of the rate constant for the reaction. 8
Answer #1: (a) Rate = k [A] 2 [B] k rate [ A ] 2 [ B ] 8. 00mo l L 1 hr ( 0. 2 4 0 mo l L 1 ) 2 ( 0. 48 0 mol L 1 ) 1 (b) = 289 L 2 mol -2 hr -1 (c) Rate = k [A] 2 [B] = (289 L 2 mol -2 hr -1 )(0.0140 mol L -1 ) 2 (1.35 mol L -1 ) = 0.0766 mol L -1 hr -1 (d) According to the equation: 2 mol B reacts with 1 mol A, therefore, B is the limiting reagent, while only 0.006 mole/l of A reacts. 0.1 20 mol/l B 3 mol/l C 2 mol/l B 0. 18 0 mol/l C Answer #2: Using the method of initial rates, we take the ratio of rates between reactions 2 and 1 to determine the order of the reaction in permanganate. By taking the ratios of the rates of experiments 3 and 1 we can obtain the order of the reaction in chlorite. Finally, by taking the ratios of the rates of experiments 4 and 1 we can obtain the order of the reaction in H +. Now that we know the order of the reaction in permanganate is 2, chlorite is 1, and H + is 1/2, we can use the rate and concentration data in experiment 1 to calculate the rate constant. Answer #3: The graph of ln [HN 3 ] versus time is linear: That means the reaction is a first order decay process with a rate law rate = k [NaN 3 ]. The value of k is the negative of the value of the slope, so k = 0.056 s -1. 9
Answer #4: (a) Plot ln k vs. 1 / T ; E act = -R (slope) OR Plot log k vs. 1 / T ; E act = -2.303 R (slope) (b) Plot ln P A or log P A vs. time Plot 1 / PA vs. time If the former is linear, the reaction is 1 st order. If the latter is linear, the reaction is 2 nd order. If the reaction is 1 st order, slope = -k 1 or -k 1 2.303. If 2 nd order, slope = k 2. Answer #5: (a) 2 XY (b) (i) Rate increases. At temperature increases, the molecules move faster and collide more frequently resulting in more possible reactions in the same time span as before. Also, and more importantly, they have more kinetic energy which results in a higher percentage of molecules that have sufficient activation energy when they collide, resulting in more effective collisions and reactions. (ii) Heat of reaction is increased. The energy of the reactants is increased so the H (difference between reactants and products) is larger. (c) Conduct a series of experiments in which the [Y 2 ] is kept constant and the [X 2 ] is varied by a specific amount and measure the initial reaction rate. Repeat keeping [X 2 ] constant and varying [Y 2 ] as in the table below. Expt. # [X 2 ] [Y 2 ] Initial reaction rate 1 1 1 R 1 2 2 1 R 2 3 1 2 R 3 If R 1 = R 2 then m = 0, if R 2 = 2R 1 then m= 1, and if R 2 = 4R 1 then m = 2. Use similar logic to compare R 3 with R 1 and determine the value of n. (d) Reaction II will initially be faster since it has the lower activation energy, a higher % of its molecules (since they are at the same temperature) will have sufficient energy to create the activated complex resulting in more effective collisions. OR It is not possible to determine which reaction has a faster rate without knowledge of other (preexponential) factors. It cannot be assumed these factors will be the same for X 2, Y 2 as for A 2, B 2, or that a similar mechanism is involved. 10
Answer #6: Answer #7 E _ H (a) Initial [ N O ] (b) i ii iii Time the rate at time, t, is the slope of the tangent to the curve at time t since the reaction is 1 st order: ln[n 2 O 3 ] t - ln[n 2 O 3 ] o = -kt ln [N 2 O 3 ] t [N 2 O 3 ] o t k = iv k would remain unchanged, it is temperature dependent, not concentration dependent. (c)i since the graph of ln[a] is a straight line, this indicates that it its 1 st order with respect to A, = k [A] ii k = - slope of the straight line of the ln[a] vs. time graph, rate 11