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Chemical rate equations The reaction of certain chemical com- pounds can be modeled using a differential equation of the form y' (t) = -ky" (t), where y(t) is the concentration of the com- pound, for t = 0, k > 0 is a constant that determines the speed of the reaction, and n is a positive integer called the order of the reaction. Assume the initial concentration of the compound is y(0) = yo > 0. a. Consider a first-order reaction (n = 1) and show that the solu- tion of the initial value problem is y(t) = y,e¬. b. Consider a second-order reaction (n = 2) and show that the Yo Yokt + 1° solution of the initial value problem is y(t) c. Let yo = 1 and k = 0.1. Graph the first-order and second- order solutions found in parts (a) and (b). Compare the two reactions.

Chemical rate equations The reaction of certain chemical com- pounds can be modeled using a differential equation of the form y' (t) = -ky" (t), where y(t) is the concentration of the com- pound, for t = 0, k > 0 is a constant that determines the speed of the reaction, and n is a positive integer called the order of the reaction. Assume the initial concentration of the compound is y(0) = yo > 0. a. Consider a first-order reaction (n = 1) and show that the solu- tion of the initial value problem is y(t) = y,e¬. b. Consider a second-order reaction (n = 2) and show that the Yo Yokt + 1° solution of the initial value problem is y(t) c. Let yo = 1 and k = 0.1. Graph the first-order and second- order solutions found in parts (a) and (b). Compare the two reactions.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.4: Solving Nonlinear Equations
Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...
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Chemical rate equations The reaction of certain chemical com- pounds can be modeled using a differential equation of the form y' (t) = -ky" (t), where y(t) is the concentration of the com- pound, for t = 0, k > 0 is a constant that determines the speed of the reaction, and n is a positive integer called the order of the reaction. Assume the initial concentration of the compound is y(0) = yo > 0. a. Consider a first-order reaction (n = 1) and show that the solu- tion of the initial value problem is y(t) = y,e¬. b. Consider a second-order reaction (n = 2) and show that the Yo Yokt + 1° solution of the initial value problem is y(t) c. Let yo = 1 and k = 0.1. Graph the first-order and second- order solutions found in parts (a) and (b). Compare the two reactions.
Transcribed Image Text:Chemical rate equations The reaction of certain chemical com- pounds can be modeled using a differential equation of the form y' (t) = -ky" (t), where y(t) is the concentration of the com- pound, for t = 0, k > 0 is a constant that determines the speed of the reaction, and n is a positive integer called the order of the reaction. Assume the initial concentration of the compound is y(0) = yo > 0. a. Consider a first-order reaction (n = 1) and show that the solu- tion of the initial value problem is y(t) = y,e¬. b. Consider a second-order reaction (n = 2) and show that the Yo Yokt + 1° solution of the initial value problem is y(t) c. Let yo = 1 and k = 0.1. Graph the first-order and second- order solutions found in parts (a) and (b). Compare the two reactions.
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