. Show that the half-life for a first-order reaction is inversely proportionalto the rate constant, and determine the constant of proportionality.

Half life of a reaction is the time required for a reactant to reach one-half of its initial…

Answered: . Show that the half-life for a…

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter20: Kinetics

Section: Chapter Questions

Problem 20.31E: The decomposition of NH3: 2NH3N2+3H2 is a zeroth-order reaction that, at elevated temperatures, has...

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For the chemical reaction Mn2+(aq)+H2O2(aq)products The following data are collected: [Mn2+],M [H2O2],M Initial rate (M/s) 0.740 0.556 3.43102 0.219 0.556 3.01103 0.740 0.662 4.86102 Determine the order with respect to Mn2+ and H2O2, and construct the complete rate law, including the value of the rate law constant.
The decomposition of NH3: 2NH3N2+3H2 is a zeroth-order reaction that, at elevated temperatures, has a rate constant of 1.04101M/s. If the initial concentration of NH3 is 1.00M, how long will it take for the concentration to drop to a 0.75M; b 0.50M; c 0.00M?
If a reaction has the same rate constant, what time does it take for a reactant to decrease by 5 that is, still near the beginning of the reaction process if the kinetics are zeroth-order, first-order, and second-order with respect to that reactant?
Nitric oxide, NO, is known to break down ozone, O3, by the following bimolecular reaction: NO(g)+O3(g)NO2(g)+O2(g) If the activation energy of this reaction is 10.5kJ/mol and the pre-exponential factor is 7.91011cm3/(mols), a what is the rate constant of this reaction at 298K? b If the ozone concentration were 5.41012mol/cm3 and the NO concentration were 2.01012mol/cm3 conditions that might exist in a high-pollution area, what is the rate of this reaction?
Digestive processes are first-order processes. The absorption of Fe2+ by the small intestine has a rate law constant of 3.09102s1. If the initial concentration of Fe2+ in food is 5.5M, how long before the concentration drops to 1.0M?
For the reaction 2H2(g)+2NO(g)N2(g)+2H2O(g) the experimental rate expression is rate rate=k[ NO ]2[ H2 ]. The following mechanism is proposed: 2NON2O2(fast) N2O2+H2H2O+N2O(slow) N2O+H2N2+H2O(fast) Is this mechanism consistent with the rate expression?
In a first-order reaction, suppose that a quantity X of a reactant is added at regular intervals of time, t. At first the amount of reactant in the system builds up; eventually, however, it levels off at a saturation value given by the expression a saturation value saturationvalue= x110a where a=0.30tt1/2 This analysis applies to prescription drugs, of which you take a certain amount each day. Suppose that you take 0.100 g of a drug three times a day and that the half-life for elimination is 2.0 days. Using this equation, calculate the mass of the drug in the body at saturation. Suppose further that side effects show up when 0.500 g of the drug accumulates in the body. As a pharmacist, what is the maximum dosage you could assign to a patient for an 8-h period without causing side effects?
For the reaction between hydrogen and iodine, H2(g)+I22HI(g) the experimental rate expression is rate=k[ H2 ][ I2 ]. Show that this expression is consistent with the mechanism I2(g)2I(g)(fast) H2(g)+I(g)+I(g)2HI(g)(slow)
An aqueous reaction that uses the solvent H2O as a reactant has a given rate law of rate=k[H2O][A] Where A is the other reactant species. Explain why, in most circumstances, this reaction can be defined in terms of pseudo first-order kinetics. What are the units on the rate constant?
An interesting pair of consecutive reactions involve the absorption of ethyl alcohol by the body, which is a first-order process, and the consequent oxidation of alcohol to acetaldehyde by liver alcohol dehydrogenase LADH, which is a zeroth order process. The differential changes in the three states of ethanol can therefore be described as d[A]dt=k1[A]td[B]dt=k1[A]tk2d[C]dt=k2 which are slightly modified from equations 20.46. The integrated form of the first equation is the same as for two consecutive first-order reactions, but for the second and third reactions, they will not be. a What do A, B and C stand for in this example? b Determine an integrated form for [B] over time. Do this by finding an integrated expression for [A]t Hint: Refer to the chapter, substitute for [A]t in the second expression, rearrange the infinitesimals, and integrate one side over [B] as the variable and the other side over time, t, as the variable. The integrations are actually simpler than for the consecutive first-order reaction example in the chapter itself. c Determine an integrated form for [C] over time. d Rough values of k1 and k2 for people are 3.00103s1 and 4.44105mol/s, respectively. Use your expressions for the amounts over time to plot a graph of [A]t, [B]t, and [C]t versus time. A graphing calculator or a computer with a graphing program would be useful. Use 1.00mol of C2H5OH as [A]0. Vary this value and see how it affects the graphs of [A]t, [B]t, and [C]t.
Consider the chemical reaction A+B+Cproducts Determine the order with respect to A,B,andC, and construct the complete rate law including the value of the rate law constant from the following experimental data. Initial rate (M/s) [A],M [B],M [C],M 6.76106 0.550 0.200 1.15 9.82107 0.210 0.200 1.15 1.68106 0.210 0.333 1.15 9.84107 0.210 0.200 1.77
Many gas-phase reactions require some inert body, usually represented as M, to absorb or supply energy in a collision in order to proceed. In the spontaneous decomposition of ozone, O3, we can suggest the mechanism O3+MO3*+MO3RDSO2+OO+O32O2 for the overall reaction 2O33O2 In the mechanism, O3* refers to an ozone molecule in some energetically excited state that can react spontaneously to form O2 and O atoms. Determine the rate law of the proposed mechanism in terms of O3 and M, where the second step is the rate-determining step. Will adding an inert gas like Ar to a sample of ozone increase or decrease the rate of the reaction?

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. Show that the half-life for a first-order reaction is inversely proportional to the rate constant, and determine the constant of proportionality.