Example 3.1. In certain cases, a reaction can proceed in either direction. For example, in the hydrogenation of ethylene (C2H4) to ethane (C2H6), a proposed mechanism is C2H4+H2- C2H6, H2 2H C2H4 + HC₂H C2H5 + H C2H6 where the first reaction can proceed in either direction. According to the law of mass action, we can model this mechanism with the following system of ODE, d[H2] =-k₁[H2]+k-1[H]2 dt d[H] 2k₁ [H2] 2k1[H]-ka[C₂Ha][H] - k3[C₂H][H] dt dC₂H] =-k₂[C₂H][H] dt d[C₂Hs] - ka[C₂Ha][H] ka[C₂Hs][H]. dt
Example 3.1. In certain cases, a reaction can proceed in either direction. For example, in the hydrogenation of ethylene (C2H4) to ethane (C2H6), a proposed mechanism is C2H4+H2- C2H6, H2 2H C2H4 + HC₂H C2H5 + H C2H6 where the first reaction can proceed in either direction. According to the law of mass action, we can model this mechanism with the following system of ODE, d[H2] =-k₁[H2]+k-1[H]2 dt d[H] 2k₁ [H2] 2k1[H]-ka[C₂Ha][H] - k3[C₂H][H] dt dC₂H] =-k₂[C₂H][H] dt d[C₂Hs] - ka[C₂Ha][H] ka[C₂Hs][H]. dt
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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Question
5
explain how chemical process can be represented in mathematical ordinary differential equations
![Example 3.1. In certain cases, a reaction can proceed in either direction. For example, in
the hydrogenation of ethylene (C₂H4) to ethane (C₂H6).
C₂H4 + H₂
C₂H6,
a proposed mechanism is
H₂2H
C₂H4+H2, C₂H5
k3
C₂H5 + H - C₂H6,
where the first reaction can proceed in either direction. According to the law of mass action,
we can model this mechanism with the following system of ODE,
d[H₂]
dt
- k₁ [H₂] + k_1[H]²
d[H]
= 2k₁ [H₂] - 2k1 [H²-k₂[C2H4] [H]- k3 [C₂H5] [H]
dt
d[C₂H₁]
-=-k₂[C₂H4][H]
dt
d[C₂Hs]
=k₂[C₂H4][H]-k3[C₂H5][H].
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbe292c5-5f71-4784-9613-ff64095fc49e%2F34318403-1c04-4f72-9a98-07eb08b463b8%2Fuv7j94r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example 3.1. In certain cases, a reaction can proceed in either direction. For example, in
the hydrogenation of ethylene (C₂H4) to ethane (C₂H6).
C₂H4 + H₂
C₂H6,
a proposed mechanism is
H₂2H
C₂H4+H2, C₂H5
k3
C₂H5 + H - C₂H6,
where the first reaction can proceed in either direction. According to the law of mass action,
we can model this mechanism with the following system of ODE,
d[H₂]
dt
- k₁ [H₂] + k_1[H]²
d[H]
= 2k₁ [H₂] - 2k1 [H²-k₂[C2H4] [H]- k3 [C₂H5] [H]
dt
d[C₂H₁]
-=-k₂[C₂H4][H]
dt
d[C₂Hs]
=k₂[C₂H4][H]-k3[C₂H5][H].
dt
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