3.5 Two bulbs are connected by a tube, 0.002 m in diameter and 0.20 m in length. Initially bulb 1 contains argon, and bulb 2 con- tains xenon. The pressure and temperature are maintained at 1 atm and 105°C, at which the diffusivity is 0.180 cm²/s. At time t = 0, diffusion is allowed to occur between the two bulbs. At a later time, the argon mole fraction in the gas at end 1 of the tube is 0.75, and 0.20 at the other end. Determine at the later time: (a) The rates and directions of mass transfer of argon and xenon (b) The transport velocity of each species (c) The molar average velocity of the mixture

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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I am trying to do A, B, C this is what i got 

To determine the rates and directions of mass transfer of argon and xenon, we can use Fick's law of diffusion.

Using Fick's law for argon (A)

Where, JA is is the molar flux of Argon (mass transfer rate per unit area)

C is total concentration 

∆z is difference in position along the length of the tube.

xA1 is the mole fraction of argon in bulb 1 at later time 

xA2 is the mole fraction of argon in bulb 2 at later time

 

 

3.5 Two bulbs are connected by a tube, 0.002 m in diameter and
0.20 m in length. Initially bulb 1 contains argon, and bulb 2 con-
tains xenon. The pressure and temperature are maintained at 1 atm
and 105°C, at which the diffusivity is 0.180 cm²/s. At time t = 0,
diffusion is allowed to occur between the two bulbs. At a later time,
the argon mole fraction in the gas at end 1 of the tube is 0.75, and
0.20 at the other end. Determine at the later time:
(a) The rates and directions of mass transfer of argon and xenon
(b) The transport velocity of each species
(c) The molar average velocity of the mixture
Transcribed Image Text:3.5 Two bulbs are connected by a tube, 0.002 m in diameter and 0.20 m in length. Initially bulb 1 contains argon, and bulb 2 con- tains xenon. The pressure and temperature are maintained at 1 atm and 105°C, at which the diffusivity is 0.180 cm²/s. At time t = 0, diffusion is allowed to occur between the two bulbs. At a later time, the argon mole fraction in the gas at end 1 of the tube is 0.75, and 0.20 at the other end. Determine at the later time: (a) The rates and directions of mass transfer of argon and xenon (b) The transport velocity of each species (c) The molar average velocity of the mixture
B)
A)
Vargon
C
VAmass = (VA-mass) difussion
na
A * C *
=
Vargon
Argon
JAwill be constant throughout length
2.2 * 10-8 3.2 10-4 (0.180)
0.0314
Vargon =
Vxenon
Argon
-10
Argon = 0.66 @ 10cm,
2.212 * 10-³
=
=
0.34
-2.2 *
0.0314(3) (2 10-4) Argon
2.212 * 10-³
10-3
Xxenon
*
2.2 * 10-³
=
P
1
Rt 82.6(378)
C) Molar average velocity is Xxenon * Vxenon +Xargon Vargon
-(Argon - 0.75)
so 0.34
=
= 3.31 * 10-3
= = 3.2 *
cm
S
10-³ cm
S
-6.64*
10-4 mol
cm³
- & JA
=
CDAB
ΔΖ
(0.34)(-6.64 10-³) + 0.66(3.31 * 10-³) = 0
Transcribed Image Text:B) A) Vargon C VAmass = (VA-mass) difussion na A * C * = Vargon Argon JAwill be constant throughout length 2.2 * 10-8 3.2 10-4 (0.180) 0.0314 Vargon = Vxenon Argon -10 Argon = 0.66 @ 10cm, 2.212 * 10-³ = = 0.34 -2.2 * 0.0314(3) (2 10-4) Argon 2.212 * 10-³ 10-3 Xxenon * 2.2 * 10-³ = P 1 Rt 82.6(378) C) Molar average velocity is Xxenon * Vxenon +Xargon Vargon -(Argon - 0.75) so 0.34 = = 3.31 * 10-3 = = 3.2 * cm S 10-³ cm S -6.64* 10-4 mol cm³ - & JA = CDAB ΔΖ (0.34)(-6.64 10-³) + 0.66(3.31 * 10-³) = 0
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