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9. Chemical Reactions. A second order chemical reaction involves the interaction (collision) of one molecule of a substance P with one molecule of a substance Q to produce one molecule of a new substance X; this is denoted by P+Q→ X. Suppose that p and q, where p / q, are the initial concentrations of P and Q, respectively, and let r(t) be the concentration of X at time t. Then p- r(t) and q- x(t) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation dx/dt = a(px) (q − x), (i). where a is a positive constant. (a) If x (0) = 0, determine the limiting value of x (t) as t → ∞ without solving the differential equation. Then solve the initial value problem and find ä(t) for any t. (b) If the substances P and Q are the same, then p = q and Eq. (i) is replaced by dx/dt = a(p - x)². (ii)

9. Chemical Reactions. A second order chemical reaction involves the interaction (collision) of one molecule of a substance P with one molecule of a substance Q to produce one molecule of a new substance X; this is denoted by P+Q→ X. Suppose that p and q, where p / q, are the initial concentrations of P and Q, respectively, and let r(t) be the concentration of X at time t. Then p- r(t) and q- x(t) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation dx/dt = a(px) (q − x), (i). where a is a positive constant. (a) If x (0) = 0, determine the limiting value of x (t) as t → ∞ without solving the differential equation. Then solve the initial value problem and find ä(t) for any t. (b) If the substances P and Q are the same, then p = q and Eq. (i) is replaced by dx/dt = a(p - x)². (ii)

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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9. Chemical Reactions. A second order chemical reaction involves the interaction (collision) of one molecule of a substance P with one molecule of a substance Q to produce one molecule of a new substance X; this is denoted by P+Q→ X. Suppose that p and q, where p / q, are the initial concentrations of P and Q, respectively, and let r(t) be the concentration of X at time t. Then p- r(t) and q- x (t) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation dx/dt = a(px) (q − x), (1) where a is a positive constant. (a) If x (0) = 0, determine the limiting value of x (t) as t → ∞ without solving the differential equation. Then solve the initial value problem and find z(t) for any t. (b) If the substances P and Q are the same, then p = q and Eq. (i) is replaced by dx/dt = a(p - x)². If x (0) = 0, determine the limiting value of r(t) as t→ ∞ without solving the differential equation. Then solve the initial value problem and determine x(t) for any t.
Transcribed Image Text:9. Chemical Reactions. A second order chemical reaction involves the interaction (collision) of one molecule of a substance P with one molecule of a substance Q to produce one molecule of a new substance X; this is denoted by P+Q→ X. Suppose that p and q, where p / q, are the initial concentrations of P and Q, respectively, and let r(t) be the concentration of X at time t. Then p- r(t) and q- x (t) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation dx/dt = a(px) (q − x), (1) where a is a positive constant. (a) If x (0) = 0, determine the limiting value of x (t) as t → ∞ without solving the differential equation. Then solve the initial value problem and find z(t) for any t. (b) If the substances P and Q are the same, then p = q and Eq. (i) is replaced by dx/dt = a(p - x)². If x (0) = 0, determine the limiting value of r(t) as t→ ∞ without solving the differential equation. Then solve the initial value problem and determine x(t) for any t.
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