Multicomponent Gas Diffusion and Adsorption in With Matlab Code
Gas Diffusion
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Transcript of Gas Diffusion
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ABSTRACT
The objectives of this experiment are to determine the diffusivity of the vapour of acetone as
well as to study the effect of temperature on the diffusivity. In this experiment, the main
apparatus used is Gaseous Diffusion Apparatus [Model: CER-A (ARMFIELD)]. This
experiment was conducted by using two set of temperatures, 45 ᴼC and 55 ᴼC as the
manipulating variable. For each temperature, the reading of the vernier scale was recorded at
every 5-minutes interval until the time reached 45 minutes. Before the reading was taken, the
vertical height of the microscope was adjusted until it was visible that the meniscus of the
capillary tube was set at the origin. At the end of the experiment, gas diffusivity of the of the
vapour of acetone was calculated along with 2 graphs being plotted for a clearer observations
of the experiment. The diffusivity of the vapour of acetone obtained at temperature 45 ᴼC and
55 ᴼC are 6.12 x 10−6 m2/s and 2.266 x 10−6 m2/s respectively. This shows that as temperature
increase, the diffusivity of the vapor of acetone decreases. However, this result deviates from
the theotrical results based on the principle of gas diffusion in which the diffusivity has to
increase when temperature increases.
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INTRODUCTIONS
Figure 1 : Gas Diffusion Apparatus
Gaseous diffusivity or gas dispersion apparatus which involves diffusion with
bulk flow is one of the items of laboratory equipment that have been designed to allow
measurement of molecular diffusivities and also to make the students become more
familiar with the basic notions of mass transfer theory. This apparatus is a bench mounted
apparatus for the determination of diffusion coefficients of a vapour in air, which uses the
method of measuring the rate of evaporation of a liquid through a stagnant layer into a
flowing air stream, comprising a precision bore capillary tube, which may be filled from a
syringe and the top of which means are provided to pass air (or an inert gas) stream to remove
vapour. The apparatus also comprise an air pump, a travelling microscope with accurate focus
adjustment and mounted for vertical axis movement against a Vernier scale and a
thermostatically controlled water bath, in which to place the capillary tube, capable
of accurate temperature control.
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The experimental capabilities of this apparatus are direct measurement of mass
transfer rates in the absence convective effects, use of a gas laws to calculate concentrations
differences in terms of partial pressures, use of Fick’s Law to measure diffusion coefficients
in the presence of a stationary gas, measurement of the effect of temperature on diffusion
coefficients and gaining familiarity with the use of laboratory instruments to achieve accurate
measurements of data required for industrial process design.
The diffusivity of the vapour of a volatile liquid in air can be conveniently
determined by Winklemann’s method in which liquid is contained in a narrow diameter
vertical tube, maintained at a constant temperature, and an air stream is passed over the top of
the tube to ensure the partial pressure of the vapour is transferred from the surface of the
liquid to the air stream by molecular diffusion. The molecular diffusivity, D, is a kinetic
parameter associated with static and dynamic conditions of a process. All the complexity and
unwieldiness of many calculations is, indeed, connected with the determination of this
quantity.
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OBJECTIVES
To :
(a) Determine the diffusivity of the vapour of acetone.
(b) Study the effect of temperature on the diffusivity.
THEORY
The diffusion of vapour A from a volatile liquid into another gas B can be conveniently
studied by confining a small sample of the liquid in a narrow vertical tube and observing its
rate of evaporation into a stream of gas B passed across the top of the tube. Normally, for
simple instructional purposes, gas B is air and vapour A is an organic solvent such as acetone
or methyl alcohol.
The apparatus consist essentially of a glass capillary tube placed in a transparent-sided
temperature controlled water bath. A horizontal glass tube is fixed to the upper end of the
capillary tube and air is blown through this by a small air pump included within the unit. This
arrangement allows the maintenance of a partial pressure difference within the capillary
tube between the evaporating liquid surfaces and the flowing air stream. A travelling
microscope, with sliding vernier scale, is mounted on a rigid stand alongside the thermostatic
bath and is used to measure the rate of fall of the solvent or air meniscus within the capillary.
The relation between the measured molar mass transfer rate (N’A per unit area), the partial
pressure gradient and the diffusion coefficient, D is deduced based on the following;
……………………….……….. Equation [1]
Where D = Diffusivity (m2/s)
CA = Saturation concentration at interface (kmol/ m3)
L = Effective distance of mass transfer (mm)
CBm = Logarithmic mean molecular concentration of vapour (kmol/ m3)
CT = Total molar concentration = CA + CBm (kmol/ m3)
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N’A = D {CA/L}{CT/CBM}
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Considering the evaporation of the liquid:
……………………. Equation [2]
Where ρ is the density of liquid
Thus,
………………. Equation [3]
Integrating and putting L - Lo at t = 0
…………… Equation [4]
Lo and L cannot be measured accurately but L-Lo can be measured accurately using
thevernier on the microscope
…. Equation [5]
Or
where:
M = molecular weight (kg/mol)
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N’A = {ρL/M}{dL/dt}
{ρL/M}{dL/dt} = D {CA/L}{CT/CBM}
L2 – L20 = {2DM/ρL}{(CA×CT)/CBm}t
(L – L0)(L-L0+2L0) = {2DM/ ρL}{(CA×CT)/CBm}t
t/(L-L0) = { ρL/2MD}{ CBm/( CA×CT)}(L-L0) + {(ρL × CBm)/( CA×CT×MD)}L0
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t = time(s)
where
s are the slopes of a graph t/(L-L0) against L - Lo then:
……………. Equation [6]
……..……….. Equation [7]
APPARATUS
1) TR 14 Membrane Test Unit apparatus.
2) 500 mL beakers.
3) Electronic balance.
4) Capillary tube
5) Gloves
6) Ruler
MATERIALS
1) Acetone
2) Sodium Chloride
3) Water
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s = (ρL × CBm)/( CA×CT×2MD)
D = (ρL × CBm)/( CA×CT×2sM)
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PROCEDURE
1. The capillary tube is partially filled with acetone to a depth of approximately 33.03mm.
The top nut was removed from metal fitting.
2. Carefully, the capillary tube was inserted through the rubber ring, inside the metal nut
until the top of the tube rests on the top of the nut.
3. Gently the assembly is screwed onto the top plate, with the ‘T’ piece normal to the
microscope. The flexible air tube was connected to one end of the ‘T’ piece. The object
lens is adjusted to within 20-30 mm from the tank.
4. The vertical height of the microscope was adjusted until the capillary tube is visible.
When the meniscus has been determined, the vernier scale should be aligned with a
suitable graduation on the fixed scale.
5. Then, the air pump was switched on.
6. The level inside the capillary tube was recorded.
7. The temperature controlled water bath was switched on and a steady temperature was
obtained.
8. The reading was taken every 5 minutes for 10 times. The experiment was done at
temperature 45°C and repeat step by using temperature at 55°C and initial length
acetone at 38.04mm.
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RESULTS
Temperature: 45 ºC
Initial length: 33.03 mm
Time (ks) Reading scale (mm) (L - Lo) (mm) tL−Lo
(ks/mm)
0.3 34.04 1.01 0.290.6 36.06 3.03 0.190.9 38.08 5.05 0.181.2 40.10 7.07 0.171.5 33.02 0.00 1.501.8 35.04 2.01 0.892.1 36.05 3.02 0.692.4 38.07 5.04 0.482.7 40.09 7.06 0.38
Temperature: 55 ºC
Initial length: 38.04 mm
Time (min) Reading scale (mm) (L - Lo) (mm) tL−Lo
(ks/mm)
0.3 34.03 4.01 0.070.6 40.09 2.05 0.290.9 35.03 3.01 0.291.2 41.09 3.05 0.391.5 37.04 1.00 1.501.8 43.10 5.06 0.362.1 39.05 1.01 2.082.4 36.01 2.03 1.182.7 41.06 3.02 0.89
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CALCULATIONS
5min x 60 s
1min ÷1000 = 0.3ks
Temperature: 45 ºC
1.01 3.03 5.05 7.07 0 2.01 3.02 5.04 7.060
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Graph of t/(L−Lo) versus (L - Lo )
(L - Lo )
t/(L
−Lo)
Density of acetone, ρ = 790 kg/m3
Gas constant, R = 8.314Jmol
. K
Molecular weight of acetone = 58.08kgmol
Vapor pressure, Pv = 56 kN/m3
Slope, s = 0.036 ks /mm2 = 3.6 x 107 s/m2
Assume standard conditions (P = 101.32 kN/m2, V=22.4 m3, T = 273 K)
Tempereature, Ta = 45 ᴼC = 318 K
CT = (1/V )(T / Ta )
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= (1/22.4)(273/318)
= 0.0383 kmol/m3
CB1 = CT = 0.0383 kmol/m3
To find CB2 :
CB2 = (Pa – Pv / Pa)CT
= (101.32-56/ 101.32) 0.0383
= 0.0171 kmol/m3
To find CBM :
CBM = (CB1-CB2)/ln (CB1/CB2)
= (0.0383 – 0.0171)/ln (0.0383/0.0171)
= 0.0263
To find Ca :
Ca = (Pv/Pa)CT
= (56/101.32) 0.0383
= 0.0212 kmol/m3
To find diffusivity,D :
D = (790x0.0263)/(0.0212x0.0383x2x3.6x107x58.08)
D = 6.12 x 10−6 m2/s
Temperature :55 ºC
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D = (ρL × CBm)/( CA×CT×2sM)
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4.01 2.05 3.01 3.05 1 5.06 1.01 2.03 3.020
0.5
1
1.5
2
2.5
Graph of t/(L−Lo) versus (L - Lo )
(L - Lo )
t/(L
−Lo)
Density of acetone, ρ = 790 kg/m3
Gas constant, R = 8.314Jmol
. K
Molecular weight of acetone = 58.08kgmol
Vapor pressure, Pv = 56 kN/m3
Slope, s = 0.1 ks /mm2 = 1.0 x 108 s/m2
Assume standard conditions (P = 101.32 kN/m2, V=22.4 m3, T = 273 K)
Tempereature, Ta = 55 ᴼC = 328 K
CT = (1/V )(T / Ta )
= (1/22.4)(273/328)
= 0.0372 kmol/m3
CB1 = CT = 0.0372 kmol/m3
To find CB2 :
CB2 = (Pa – Pv / Pa)CT
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= (101.32-56/ 101.32) 0.0372
= 0.0166 kmol/m3
To find CBM :
CBM = (CB1-CB2)/ln (CB1/CB2)
= (0.0372 - 0.0166)/ln (0.0372/0.0166)
= 0.02553
To find Ca :
Ca = (Pv/Pa)CT
= (56/101.32) 0.0372
= 0.0206 kmol/m3
To find diffusivity,D :
D = (790x0.02553)/(0.0206x0.0372x2x1.0 x 108 x58.08)
D = 2.266 x 10−6 m2/s
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D = (ρL × CBm)/( CA×CT×2sM)
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DISCUSSIONS
This experiment was conducted to obtain the gas diffusion coefficient and its relationship with
the change in temperature. The manipulating variable involved is the temperature and the
responding variable was the level inside the capillary tube, L which was taken every 0.3 ks
until 2.7 ks was reached. This experiment was carried out at two different temperatures which
are at 45 ᴼC and 55 ᴼC with respect to gas diffusivity. Alongside, gas diffusivity of vapour
acetone is also calculated.
Based on the two graphs of t
Lo−L against Lo – L that had been plotted, the gradient or also
known as the slopes were calculated. The data collected however shown to deviate variedly,
due to the present of errors.. A linear graph was not able to be obtained and thus to overcome
this problem the slopes was calculated taking from two points relative to the line obtained.
Next, the diffusivity of vapour acetone at different temperature was being calculated. It was
based on the data collected for T = 45 ᴼC, D equivalent to 6.12 x 10−6 m2/s while at T = 55
ᴼC, D was found to be 2.266 x 10−6 m2/s. The result has proven that as the temperature
increase, the diffusivity decreases. However, according to the principle of gas diffusion from
this experiment, supposedly the diffusivity of vapor acetone increases with increasing
temperature.
Diffusion is the movement of molecules from area of high concentration to area of
lower concentration and this is increased with increasing temperature which means
when the temperature increase the diffusion will also rising up. In the other word, when
temperature is higher, then the rate of diffusion would probably increase caused by
increasing kinetic activity of the solution. However, due to this inaccuracy, values for
gas diffusivity calculated using equation above may not explain correctly the definition of gas
diffusion.
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CONCLUSION
As a conclusion, the result for diffusivity coefficient at 45 °C is 6.12 x 10-6 m2/s and the
diffusivity coefficient at 55 °C is 2.266 x 10-6 m2/s. During the experiment, there are some
errors occur. To get accurate values of diffusivity, a few of recommendations step should be
taken. In this experiment, the results obtained are almost accurate even there are some errors
occur.
RECOMMENDATIONS
1. Some recommendations should be implements in this experiment. One of them is
insulating the glass container. It will maintain the temperature through the experiment
and the heat will not loss to the surrounding.
2. Next, the reading meter should be stabilized with the person who read the meter. The
person who read it should be at the same level to the meter to reduced parallax error.
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REFFERNCES
Journal of Physical and Chemical Reference Data. Gaseous Diffusion Coefficients.
Retrieved November 15, 2012 from http://jpcrd.aip.org/resource/1/jpcrbu/v1/i1/p3_s1?
isAuthorized=no
Gases: Graham’s Laws of Diffusion and Effusion. Graham’s Law. Retrieved
November 15, 2012 from
http://www.chem.tamu.edu/class/majors/tutorialnotefiles/graham.htm
Diffusion of Gases. Diffusion and Effusion. Retrieved November 16 2012 from
http://chem.salve.edu/chemistry/diffusion.asp
USEC. Gaseous Diffusion. RetrievedNovember 16, 2012 from
http://www.usec.com/gaseous-diffusion
Advancing the Chemical Sciences. Learn Chemistry: Diffusion of gases of ammonia
and hydrogen chloride. Retrieved November 16, 2012 from http://www.rsc.org/learn-
chemistry/wiki/TeacherExpt:Diffusion_of_gases_-_ammonia_and_hydrogen_chloride
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