z = Z2 Consider the diffusion system shown on the right. Liquid A is evaporating into gas B, and we imagine that there is some device which maintains the liquid level at z = z1. Right at the liquid-gas interface the gas-phase concentration of A, expressed as mole fraction, is xa1. We further assume that the solubility of B in liquid A is negligible. At the top of the tube (at z = z2) a stream of gas mixture A-B of concentration XA2 flows past slowly; thereby the mole fraction of A at the top of the column is maintained at xA2. The entire system is presumed to be held at constant temperature and pressure. Gases A and B are NAl:+ Az NAl: assumed to be ideal. By performing a mass balance over an incremental column height Az, at steady state: z = z1 dN A =0 dz where Na: is the molar flux of A with respect to a fixed axis z. The molar flux Na: is equivalent to the following expression: cD AB dx, N. Az 1-x, dz where c is the molar density of the solution, and DAB is the mass diffusivity of A to B. For ideal gas mixtures at constant temperature and pressure, c and Dab can be assumed to be constant. By solving the differential equation above, show that 1-XA 1-X42 1-XA 1-xA A2 or 1-X A1 1-X A1 1-XA1 A2
z = Z2 Consider the diffusion system shown on the right. Liquid A is evaporating into gas B, and we imagine that there is some device which maintains the liquid level at z = z1. Right at the liquid-gas interface the gas-phase concentration of A, expressed as mole fraction, is xa1. We further assume that the solubility of B in liquid A is negligible. At the top of the tube (at z = z2) a stream of gas mixture A-B of concentration XA2 flows past slowly; thereby the mole fraction of A at the top of the column is maintained at xA2. The entire system is presumed to be held at constant temperature and pressure. Gases A and B are NAl:+ Az NAl: assumed to be ideal. By performing a mass balance over an incremental column height Az, at steady state: z = z1 dN A =0 dz where Na: is the molar flux of A with respect to a fixed axis z. The molar flux Na: is equivalent to the following expression: cD AB dx, N. Az 1-x, dz where c is the molar density of the solution, and DAB is the mass diffusivity of A to B. For ideal gas mixtures at constant temperature and pressure, c and Dab can be assumed to be constant. By solving the differential equation above, show that 1-XA 1-X42 1-XA 1-xA A2 or 1-X A1 1-X A1 1-XA1 A2
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Consider the diffusion system shown on the right. Liquid A is evaporating into gas B, and we imagine that there is some device which maintains the liquid level at z = z1. Right at the liquid-gas interface the gas-phase concentration of A, expressed as mole fraction, is xA1. We further assume that the solubility of B in liquid A is negligible. At the top of the tube (at z = z2) a stream of gas mixture A-B of concentration xA2 flows past slowly;
thereby the mole fraction of A at the top of the column is maintained at xA2. The entire system is presumed to be held at constant temperature and pressure. Gases A and B are assumed to be ideal.
Transcribed Image Text:z = 22
5. Consider the diffusion system shown on the right. Liquid A is evaporating into gas B,
and we imagine that there is some device which maintains the liquid level at z = z1. Right
at the liquid-gas interface the gas-phase concentration of A, expressed as mole fraction,
is XA1. We further assume that the solubility of B in liquid A is negligible. At the top of
the tube (at z = z2) a stream of gas mixture A-B of concentration XA2 flows past slowly;
thereby the mole fraction of A at the top of the column is maintained at XA2. The entire
NAL:+
Az
system is presumed to be held at constant temperature and pressure. Gases A and B are
NAl:
assumed to be ideal.
z = Z1
By performing a mass balance over an incremental column height Az, at steady state:
dN Az =0
dz
where NAz is the molar flux of A with respect to a fixed axis z. The molar flux NAz is equivalent to the following
expression:
dx
dz
XA
where c is the molar density of the solution, and DaB is the mass diffusivity of A to B. For ideal gas mixtures at
constant temperature and pressure, c and DAB can be assumed to be constant. By solving the differential
equation above, show that
1-x
1-XA
1-X42
1-x
or
1-x 42
1-X 1
1-x A1
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