Show that if A reacts to form either B or C according to elementary unimolecularreactionsthenShow that the half-life of A isAB or=[A]t =[A]oe-(k₁+k₂)tt1/2or A C=In 2k₁ + k2Show that [B]/[C]t = k₁/k₂ for all times t. For the set of initial conditions [A]o = 1,[B]o [C]o = 0, and k₁ = 1, and k₂ = 4 plot [A], [B], and [C] as functions of time onthe same graph.

Unimolecular reactions involve the transformation of a single molecule into products, typically through processes like decomposition or isomerization. The most common representation for unimolecular reactions is the first-order reaction kinetics.For a simple unimolecular reaction, let's denote a reactant A undergoing a decomposition reaction to form products B:A→ProductsThe rate law for a unimolecular reaction is expressed using the rate constant k and the concentration of the reactant A as:Rate = -k[A]This rate law signifies that the rate of the reaction is directly proportional to the concentration of the reactant A. The rate constant k is specific to each reaction and represents the speed at which the reaction proceeds at a particular temperature.The integrated rate law for a first-order reaction, such as a unimolecular reaction, can be written as:ln([A]/[A]0)=−ktWhere:[A] is the concentration of reactant A at time t.[A]0 is the initial concentration of reactant A.k is the rate constant.t is time.This equation shows the relationship between the concentration of the reactant A at any given time t and the initial concentration of A at t=0. It demonstrates the characteristic linear behavior of a first-order reaction when the natural logarithm of the ratio of concentrations is plotted against time.Experimental determination of the rate constant (k) and the concentration of the reactant (A) at different time intervals helps in verifying the rate law and the order of the reaction. The slope of the plot of ln([A]/[A]0) against time will be equal to−k in accordance with the integrated rate law for a first-order reaction.Understanding the kinetics of elementary unimolecular reactions is fundamental in studying the rates of various chemical processes and predicting how different factors such as temperature, pressure, and catalysts affect the reaction rates.See the above explanation

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Show that if A reacts to form either B or C according to elementary unimolecular reactions then Show that the half-life of A is AB А В = Ак3, С or A ог [A]t =[A]oe¯(k1+k₂)t In 2 k₁ + k₂ t1/2 Show that [B]t/[C]t = k₁/k₂ for all times t. For the set of initial conditions [A]o [B]o [C]o = 0, and k₁ = 1, and k₂ 1, and k₂ = 4 plot [A], [B], and [C] as functions of time on =

Show that if A reacts to form either B or C according to elementary unimolecular reactions then Show that the half-life of A is AB А В = Ак3, С or A ог [A]t =[A]oe¯(k1+k₂)t In 2 k₁ + k₂ t1/2 Show that [B]t/[C]t = k₁/k₂ for all times t. For the set of initial conditions [A]o [B]o [C]o = 0, and k₁ = 1, and k₂ 1, and k₂ = 4 plot [A], [B], and [C] as functions of time on =

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

Show that if A reacts to form either B or C according to elementary unimolecular
reactions
then
Show that the half-life of A is
AB or
=
[A]t =[A]oe-(k₁+k₂)t
t1/2
or A C
=
In 2
k₁ + k2
Show that [B]/[C]t = k₁/k₂ for all times t. For the set of initial conditions [A]o = 1,
[B]o [C]o = 0, and k₁ = 1, and k₂ = 4 plot [A], [B], and [C] as functions of time on
the same graph.

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