1.A substance A is added at a constant rate r M s-¹ to a reaction vessel, in which it decays by massaction kinetics according to the reactionA2B.Let t be the time in seconds since the start of the reaction, and let [A] and [B] be measured in M.The concentration [A] is described by the ODE(a)(b)(c)d[A]dt= r - k[A].State the differential equation for [B] given by mass action kinetics.dtd[A]Use the Principle of Superposition to find the general solution of the ODE for AWhat values of the arbitrary constant C in your solution from (b) give physically realisticsolutions?(d)Given that the reaction vessel initially contains no A or B, find expressions for [A](t) and [B](t)in terms of t, k and r.

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(a) (b) (c) d[B] dt State the differential equation for given by mass action kinetics. Use the Principle of Superposition to find the general solution of the ODE for What values of the arbitrary constant C in your solution from (b) give physically realistic solutions? (d) Given that the reaction vessel initially contains no A or B, find expressions for [A](t) and [B](t) in terms of t, k and r.

(a) (b) (c) d[B] dt State the differential equation for given by mass action kinetics. Use the Principle of Superposition to find the general solution of the ODE for What values of the arbitrary constant C in your solution from (b) give physically realistic solutions? (d) Given that the reaction vessel initially contains no A or B, find expressions for [A](t) and [B](t) in terms of t, k and r.

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

1.
A substance A is added at a constant rate r M s-¹ to a reaction vessel, in which it decays by mass
action kinetics according to the reaction
A2B.
Let t be the time in seconds since the start of the reaction, and let [A] and [B] be measured in M.
The concentration [A] is described by the ODE
(a)
(b)
(c)
d[A]
dt
= r - k[A].
State the differential equation for [B] given by mass action kinetics.
dt
d[A]
Use the Principle of Superposition to find the general solution of the ODE for A
What values of the arbitrary constant C in your solution from (b) give physically realistic
solutions?
(d)
Given that the reaction vessel initially contains no A or B, find expressions for [A](t) and [B](t)
in terms of t, k and r.

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