3. In some circumstances, it is possible for a reactant to follow "half-order" kinetics, that is, d[A] k[A]¹/2. dt = (a) Find the integrated rate law for a half-order kinetics process, and express it as [A], given as a function of the initial concentration, [A]o, the rate constant, k, and the time, t. (b) Use your integrated rate law to derive an expression for the half-life of a half-order process, then compute the magnitude of the half-life for a process with [A]o = 0.24 M, and k = 0.003 (in appropriate units- this will result in time measured in seconds).

3. In some circumstances, it is possible for a reactant to follow "half-order" kinetics, that is, d[A] k[A]¹/2. dt = (a) Find the integrated rate law for a half-order kinetics process, and express it as [A], given as a function of the initial concentration, [A]o, the rate constant, k, and the time, t. (b) Use your integrated rate law to derive an expression for the half-life of a half-order process, then compute the magnitude of the half-life for a process with [A]o = 0.24 M, and k = 0.003 (in appropriate units- this will result in time measured in seconds).

Chemistry

9th Edition

ISBN:9781133611097

Author:Steven S. Zumdahl

Publisher:Steven S. Zumdahl

Chapter12: Chemical Kinetics

Section: Chapter Questions

Problem 3RQ: One experimental procedure that can be used to determine the rate law of a reaction is the method of...

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One experimental procedure that can be used to determine the rate law of a reaction is the method of initial rates. What data are gathered in the method of initial rates, and how are these data manipulated to determine k and the orders of the species in the rate law? Are the units for k. the rate constant, the same for all rate laws? Explain. If a reaction is first order in A, what happens to the rate if [A] is tripled? If the initial rate for a reaction increases by a factor of 16 when [A] is quadrupled, what is the order of n? If a reaction is third order in A and [A] is doubled, what happens to the initial rate? If a reaction is zero order, what effect does [A] have on the initial rate of a reaction?
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The plot below shows the number of collisions with a particular energy for two different temperatures. a. Which is greater, T2 or T1? How can you tell? b. What does this plot tell us about the temperature of the rate of a chemical reaction? Explain your answer.
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The hydrolysis of the sugar sucrose to the sugars glucose and fructose, C12H22O11+H2OC6H12O6+C6H12O6 follows a first-order rate equation for the disappearance of sucrose: Rate =k[C12H22O11] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.) (a) In neutral solution, k=2.11011s1 at 27 C and 8.51011s1 at 37 C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature). (b) When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is 1.65107M . How long will it take the solution to reach equilibrium at 27 C in the absence of a catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible. (c) Why does assuming that the reaction is irreversible simplify the calculation in pan (b)?
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The acid-catalyzed iodination of acetone CH3COCH3(aq) + I2(aq) CH3COCH2I(aq) + HI(aq) is a common laboratory experiment used in general chemistry courses to teach the method of initial rates. The reaction is followed spectrophotometrically by the disappearance of the color of iodine in the solution. The following data (J. P. Birk and D. L Walters, Journal of Chemical Education, Vol. 69, p. 585, 1992) were collected at 23 C for this reaction. Determine the rate law for this reaction.
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