AP * Chemistry. Kinetics: Integrated Rate Law & Determining Ea. René McCormick
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1 AP * Chemistry Kinetics: Integrated Rate Law & Determining Ea René McCormick *AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product by René McCormick. All rights reserved.
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3 Kinetics These terms may be used in a question testing your understanding of KINETICS Rate; time; concentration; order; rate constant; mechanisms; rate determining step; intermediate; catalyst; halflife; instantaneous rate; relative rate; activation energy; integrated rate law; rate expression; rate law Key Formulas and Relationships Δ in some measurable quantity Rate = time and is measured in units of M time or M 1 time 1 Instantaneous rate: rate at an instant of time. Draw a line tangent to the curve of concentration vs. time and calculate the slope of the tangent line. Relative rate: Start with the balance equation, next make each coefficient in the balanced equation the denominator of a fraction and assign the numerator a value of 1. Now, all of the terms in the balanced chemical equation can be set relative to each other. Example: 2A + 3B C + 2D becomes 1 A+ 1 B C+ 1 D where it follows that ΔA 1 ΔB ΔC 1 ΔD rate = = =+ =+ 2 Δt 3 Δt Δt 2 Δt You ll only be asked to relate two terms to each other, not all of the terms that can be generated. Take caution to assign reactants a negative sign since they are disappearing and products a positive sign since they are appearing. Your clue as to when to use this is rate in terms of which is code for relative rates as well as statements such as: In experiment 2 or anything that asks about the rate of a different reactant or product than that listed in the table of concentration-rate data. Differential Rate Law (concentration vs. rate data): Rate = k [A] x [B] y and graphical methods are simplest. We linearize data to avoid calculus! Memorize the graphical pattern: Set up your axes so that time is always on the x-axis. Plot the concentration of the reactant on the y-axis of the first graph. Plot the natural log of the concentration (ln [A], NOT log[a]) on the y-axis of the second graph and the reciprocal of the concentration on the y-axis of the third graph. You are in search of linear data! Here comes the elegant part If you do the set of graphs in this order with the y-axes being concentration, natural log of concentration and reciprocal concentration, the alphabetical order of the y-axis variables leads to 0, 1, 2 orders respectively for that reactant. Zero order k = negative slope First order k = negative slope Second order k = the slope
4 You can now easily solve for either time or concentration once you know the order of the reactant. Just remember y = mx + b. Choose the set of variables that gave you the best straight line (r value closest to ±1) and insert them in place of x and y in the generalized equation for a straight line. A is reactant A and A o is the initial concentration of reactant A at time zero [the y-intercept]. y = mx + b zero order [A] = kt + [A o ] first order ln[a] = kt + ln [A o ] second order 1/[A] = kt + 1/[A o ] Also recognize that slope = k, since the rate constant is NEVER negative. If you are asked to write the rate order you determined from analyzing the graphs expression [or rate law] it is simply Rate = k[a] Also half-life plays a role in kinetics: t 1 = for first order reactions and all nuclear decay 2 k To calculate the activation energy we use the Arrhenius equation relates k and temperature: Ea 1 ln k = + ln A, so a graph of lnk vs. 1 R T T is linear and the E a = slope R( the energy R) Key Concepts Be able to explain with algebraic equations or words how an order is determined. It is important to state which concentration(s) is held constant and which concentration is varied as well the effect that has on the rate of the reaction if you choose not to justify with algebraic equations. Mechanisms must agree with the stoichiometry of the reaction and the summary rate law must agree up to and including the slow step; identify intermediates and catalysts and clearly state that the correct mechanism agrees with the experimentally determined rate law. Discuss number of effective collisions in relation to increasing or decreasing rates Arrhenius magnitude of k relates directly to the speed of the reaction; large = fast; small = slow E a also predicts speed but the relationship is an inverse one; high = slow rate; low = fast rate instantaneous rate = slope of the line tangent to the time point in question Connections to Other Chapters Stoichiometry -- using up one component of the system might indicate a limiting reactant in effect Electrochemistry -- if reaction is redox in nature you could be asked to bridge to this concept Potenial Pitfalls and Unit Warnings Units on k = always time -1 and one less M -1 than overall order. Ex: 2 nd order overall has a k with units of M -1 s -1 liter = = liter mol s = mol s M s
5 Figures or graphs you may need to interpret Change in [Conc] over time; notice stoich ratio in effect Instantaneous Rate Energy diagram; locate activation energy, overall energy, transition state, endo./exo, effect of adding a catalyst. Be able to evaluate energy quantities for BOTH the forward and reverse reactions. Zero Order First Order Second Order WHY increasing the temperature increases the rate of a reaction Arrhenius plot to determine activation energy E a = energy R slope Catalysts increase the rate of reaction by lowering the activation energy and providing an alternate mechanism
6 Kinetics Concept Map graph [A] vs. time graph ln[a] vs. time graph 1/[A] vs. time graph lnk vs. 1/[T] Page 9
7 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 3. The first-order decomposition of a colored chemical species, X, into colorless products is monitored with a spectrophotometer by measuring changes in absorbance over time. Species X has a molar absorptivity constant of cm 1 M 1 and the path length of the cuvette containing the reaction mixture is 1.00 cm. The data from the experiment are given in the table below. [X] ( M ) Absorbance Time (min)? ? (a) Calculate the initial concentration of the colored species. (b) Calculate the rate constant for the first-order reaction using the values given for concentration and time. Include units with your answer. (c) Calculate the number of minutes it takes for the absorbance to drop from to (d) Calculate the half-life of the reaction. Include units with your answer. (e) Experiments were performed to determine the value of the rate constant for this reaction at various temperatures. Data from these experiments were used to produce the graph below, where T is temperature. This graph can be used to determine the activation energy, E a, of the reaction. (i) Label the vertical axis of the graph. (ii) Explain how to calculate the activation energy from this graph. STOP If you finish before time is called, you may check your work on this part only. Do not turn to the other part of the test until you are told to do so. Copyright 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). Page 12
8 2005 AP CHEMISTRY FREE-RESPONSE QUESTIONS (Form B) X 2 Y + Z 3. The decomposition of gas X to produce gases Y and Z is represented by the equation above. In a certain experiment, the reaction took place in a 5.00 L flask at 428 K. Data from this experiment were used to produce the information in the table below, which is plotted in the graphs that follow. Time [X] [X] (minutes) (mol L 1 ln [X] ) (L mol 1 ) ,110 Copyright 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). 8 GO ON TO THE NEXT PAGE. Page 13
9 2005 AP CHEMISTRY FREE-RESPONSE QUESTIONS (Form B) (a) How many moles of X were initially in the flask? (b) How many molecules of Y were produced in the first 20. minutes of the reaction? (c) What is the order of this reaction with respect to X? Justify your answer. (d) Write the rate law for this reaction. (e) Calculate the specific rate constant for this reaction. Specify units. (f) Calculate the concentration of X in the flask after a total of 150. minutes of reaction. STOP If you finish before time is called, you may check your work on this part only. Do not turn to the other part of the test until you are told to do so. Copyright 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). 9 Page 14
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