Download - Chap 1(a) molecular-diffusion_in_gas(2)
![Page 1: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/1.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Principles of Mass TransferCHAPTER 1CHAPTER 1Molecular Diffusion in Molecular Diffusion in GasesGases
1
![Page 2: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/2.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Topic Outcomes
2
It is expected that student will be able to: Apply the diffusivity coefficient of molecular
diffusion in gases. Solve mathematical solution of molecular diffusion
in gases.
![Page 3: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/3.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
CONTENTS
Mass Transfer
Molecular Diffusion Convective Mass Transfer
Gases Liquid Solid
3
![Page 4: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/4.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
4
![Page 5: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/5.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Introduction
5
![Page 6: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/6.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
6
![Page 7: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/7.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Equimolar Counter diffussion in Gases
7
![Page 8: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/8.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Molecular Diffusion in Gases
Equimolar Counter diffussion in Gases
8
![Page 9: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/9.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
9
![Page 10: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/10.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
For a binary gas mixture of A and B, the diffusivity coefficient DAB=DBA
10
![Page 11: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/11.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
11
![Page 12: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/12.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Problem 6.1-1 (pg 452) Diffusion of Methane Through Helium
A gas of CH4 and He is contained in a tube at 101.32 kPa pressure and 298 K. At one point the partial pressure of methane is pA1 = 60.79 kPa, and at a point 0.02 m distance away, pA2 = 20.26 kPa. If the total pressure is constant throughout the tube, calculate the flux of CH4 (methane) at steady state for equimolar counter diffusion.
12
![Page 13: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/13.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Example 6.2-1 (pg 415) Equimolar Counterdiffusion
o Ammonia gas (A) is diffusing through a uniform tube 0.10 m long containing N2 gas (B) at 1.0132 x 105 Pa pressure and 298 K. At point 1, pA1 = 1.013 x 104 Pa , and at point 2, pA2 = 0.507 x 104 Pa. The diffusivity DAB = 0.230 x 10-4 m2/s.
1. 1. Calculate the flux J*A at steady state
2. 2. Repeat for J*B
13
Numerical value
Units
82.057 cm3.atm/kg mol . K
82.057x 10-3 m3.atm/kg mol . K
8314.34 J/kg mol . K
8314.34 m3 .Pa / kg mol .K
8314.34 kg . m2/s2 . kg mol.K
o.7302 ft3.atm/lb mol.0R
![Page 14: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/14.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
14
![Page 15: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/15.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMPProblem 6.2-1 (pg 452) Equimolar Counterdiffusion of a Binary Gas Mixture
• Helium and nitrogen gas are contained in a conduit 5 mm in diameter and 0.1 m long at 298 K and a uniform constant pressure of 1.0 atm abs. The partial pressure of He at one end of the tube is 0.060 atm and the other end is 0.020 atm. Calculate the following for steady-state equimolar counterdiffusion:
1. Flux of He in kg mol/s.m2
1. 2. Flux of N2
2. 3. Partial pressure of He at a point 0.05 m from either end.
15
![Page 16: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/16.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
16
![Page 17: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/17.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
17
Solution: DAB = 0.687 x 10-4 m2/s (Table 6.2-1) z2-z1 = 0.1m pA1 = 0.060 atm pA2 = 0.020 atm R = 82.06 x 10-3 cm3.atm/g mol.K (Table A.1-1) a) Eqn. (6.1-13)
12
2A1AABAZ
*
zzRT
ppDJ
010.029810x06.82
02.006.010x687.0J
3
4
AZ*
2
6AZ
*
m.s
kgmol10x124.1J
b) 2
6AZ
*
m.s
kgmol10x124.1J
![Page 18: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/18.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Diffusion of Gases A and B Plus Convection (General Case) (pg 416)
18
Convection is the concerted, collective movement of ensembles of molecules within fluids (e.g., liquids, gases)
![Page 19: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/19.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
19
![Page 20: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/20.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
20
For equimolar counterdiffussion, NA=-NB , then NA=J*A=-NB=-J*B
Eq 6.17
![Page 21: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/21.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
‘A’ Diffusing Through Stagnant, Nondiffusing ‘B’
(Special Case)
21
![Page 22: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/22.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
22
![Page 23: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/23.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
23
![Page 24: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/24.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
24
![Page 25: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/25.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Example 6.2-2 (pg 419) Diffusion of Water Through Stagnant, Nondiffusing Air
Water in the bottom of a narrow metal tube is held at a constant temperature of 20oC. The total pressure of air (assumed dry) is1.0 atm and the temperature is 20oC. Water evaporates and diffuses through the air in the tube, and the diffusion path z2 – z1 is 0.1524 m (0.5 ft) long. The diagram is similar to Fig 6.2-2a. Calculate the rate of evaporation at steady state in lb mol/hr.ft2 and kg mol/s.m2. The diffusivity of water vapor at 20oC and 1 atm pressure is 0.250x10-4 m2/s. Assume that the system is isothermal.
25
![Page 26: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/26.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
26
![Page 27: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/27.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Problem 6.2-3 (pg 453) Diffusion of A Through Stagnant B and Effect of Type of Boundary on Flux
Ammonia gas is diffusing through N2 under steady state conditions with N2 nondiffusing since it is insoluble in one boundary. The total pressure is 1.013 x 105 Pa and the temperature is 298 K. The partial pressure of NH3 at one point is 1.333 x 104 Pa, and at the other point 20 mm away it is 6.666 x 103 Pa. The DAB for the mixture at 1.013 X 105 Pa and 298 K is 2.30 x 10-5 m2/s.
a) calculate the flux of NH3 in kg mol/s.m2
b) do the same as (a) but assume that N2 also diffuses, both boundaries are permeable to both gases and the flux is equimolar counterdiffusion. In which case is the flux greater?
27
![Page 28: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/28.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Diffusion Through Cross Sectional Area (Sphere)
28
![Page 29: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/29.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
29
![Page 30: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/30.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
30
![Page 31: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/31.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Example 6.2-4 (pg 421) Evaporation of Naphthalene Sphere
A sphere of naphthalene having a radius of 2.0 mm is suspended in a large volume of still air at 318 K and 1.01325 x 105 Pa. The surface temperature of the naphthalene can be assumed to be at 318 K and its vapor pressure at 318 K is 0.555 mm Hg. The DAB of naphthalene in air at 318 K is 6.92 x 10-6 m2/s. Calculate the rate of evaporation of naphthalene from the surface.
31
![Page 32: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/32.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Problem 6.2-5 (pg 453) Mass Transfer from a Naphthalene Sphere to Air
Mass transfer is occurring from a sphere of naphthalene having radius of 10 mm. The sphere is in large volume of still air at 52.6°C and 1 atm abs pressure. The vapor pressure of naphthalene at 52.6°C is 1.0 mmHg. The diffusitivity of naphthalene in air at 0°C is 5.16 x 10-6 m2/s. Calculate the rate of evaporation of naphthalene from the surface in
kg mol/s.m2.
32
![Page 33: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/33.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Diffusion Coefficient for Gases
33
![Page 34: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/34.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
34
![Page 35: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/35.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
35
![Page 36: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/36.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
36
![Page 37: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/37.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Example 6.2-5 (pg 427) Estimation of Diffusivity of a Gas Mixture
• Normal butanol (A) is diffusing through air (B) at 1 atm abs. Using the Fuller et al. method, estimate the diffusivity DAB for the following temperatures and compare with the experimental data.
• Given MA (butanol) = 74.1 kg (mass)/kg mol,
• MB (air) = 29 kg (mass)/kg mol]
a) For 0oC.
b) For 25.9oC
c) For 0oC and 2.0 atm abs
37
![Page 38: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/38.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
38
![Page 39: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/39.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
Numerical value
Units
82.057 cm3.atm/kg mol . K
82.057 x 10-3 m3.atm/kg mol . K
8314.34 J/kg mol . K
8314.34 m3 .Pa / kg mol .K
8314.34 kg . m2/s2 . kg mol . K
o.7302 ft3.atm/lb mol.0R
Gas Law Constant R (pg 955)
![Page 40: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/40.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
40
![Page 41: Chap 1(a) molecular-diffusion_in_gas(2)](https://reader030.vdocuments.site/reader030/viewer/2022032620/55c69538bb61ebbd158b4625/html5/thumbnails/41.jpg)
2008/2009 II
BKF 2432: MASS TRANSFER FKKSA, UMP
41
TEST 1 EP 203