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 x(t) be the concentration of X at time t. Then p − x(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 (32) dxdt=α(p−x)(q−x), where α 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 x(t) for any t.
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 x(t) be the concentration of X at time t. Then p − x(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 (32) dxdt=α(p−x)(q−x), where α 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 x(t) for any t.
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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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 x(t) be the concentration of X at time t. Then p − x(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
(32)
dxdt=α(p−x)(q−x), where α 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 x(t) for any t.
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