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Problem 4. In this problem, we will walk through how to derive the Kremser equation from component mass balances. (a) In class, we showed that, when CMO assumption is valid, for any stage n and any component i, the term Vy,n+1- LXin is a constant throughout the column (we denoted this constant as di in class, which stands for the net material upward flow for component i). Meanwhile, we know that yn+1 = K;Xin+1 and yn-Kixia as well (VLE relation), assuming that the K-value K; is constant throughout the column. Based en these twe sets of relations, show that: YiN+1 - YLN = ("K – "19) () Hint: Start by writing down Vyn+1- Lx,n for n = N and n= N - 1 and apply the VLE relation. Note that, once we convert yiy and yio respectively to KixiN and KiXLo (which are physically present in the absorption column) using the VLE relation, we will recover the first form of the Kremser equation introduced in lecture.

Problem 4. In this problem, we will walk through how to derive the Kremser equation from component mass balances. (a) In class, we showed that, when CMO assumption is valid, for any stage n and any component i, the term Vy,n+1- LXin is a constant throughout the column (we denoted this constant as di in class, which stands for the net material upward flow for component i). Meanwhile, we know that yn+1 = K;Xin+1 and yn-Kixia as well (VLE relation), assuming that the K-value K; is constant throughout the column. Based en these twe sets of relations, show that: YiN+1 - YLN = ("K – "19) () Hint: Start by writing down Vyn+1- Lx,n for n = N and n= N - 1 and apply the VLE relation. Note that, once we convert yiy and yio respectively to KixiN and KiXLo (which are physically present in the absorption column) using the VLE relation, we will recover the first form of the Kremser equation introduced in lecture.

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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Problem 4. In this problem, we will walk through how to derive the Kremser equation from component mass balances. (a) In class, we showed that, when CMO assumption is valid, for any stage n and any component i, the term Vyi,n+1- Lx,n is a constant throughout the column (we denoted this constant as di in class, which stands for the net material upward flow for component î). Meanwhile, we know that y,n+1 = K;X¡n+1 and yin = K;xin as well (VLE relation), assuming that the K-value K; is constant throughout the column. Based on these two sets of relations, show that: YiN+1 - Yin = (Vi1 - Yio) Hint: Start by writing down Vy;,n+1- Lxi,n for n = N and n = N - 1 and apply the VLE relation. Note that, once we convert yiy and yio respectively to Krši,n and Kjxi,0 (which are physically present in the absorption column) using the VLE relation, we will recover the first form of the Kremser equation introduced in lecture. (b) Following the same procedure in Part a), derive the second form of the Kremser equation in tems of liquid compositions: YiN+1 XiN Yi.1
Transcribed Image Text:Problem 4. In this problem, we will walk through how to derive the Kremser equation from component mass balances. (a) In class, we showed that, when CMO assumption is valid, for any stage n and any component i, the term Vyi,n+1- Lx,n is a constant throughout the column (we denoted this constant as di in class, which stands for the net material upward flow for component î). Meanwhile, we know that y,n+1 = K;X¡n+1 and yin = K;xin as well (VLE relation), assuming that the K-value K; is constant throughout the column. Based on these two sets of relations, show that: YiN+1 - Yin = (Vi1 - Yio) Hint: Start by writing down Vy;,n+1- Lxi,n for n = N and n = N - 1 and apply the VLE relation. Note that, once we convert yiy and yio respectively to Krši,n and Kjxi,0 (which are physically present in the absorption column) using the VLE relation, we will recover the first form of the Kremser equation introduced in lecture. (b) Following the same procedure in Part a), derive the second form of the Kremser equation in tems of liquid compositions: YiN+1 XiN Yi.1
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