ABSTRACT

A molecular diffusion experiment was conducted with the goal of determining the diffusion coefficient of acetone into air. For this experiment, acetone was placed in a capillary tube and was allowed to diffuse into non-diffusing air that was passed over the test tube at the temperature of 40oC. The temperature is kept constant and air stream is passed over the top of the tube to ensure that the partial pressure of the vapor is transferred from the surface of the liquid to be air stream by molecular diffusion. The initial reading and every 2 minutes subsequent reading of the liquid acetone level are determined, and the experiment is conducted for 10 minutes. The experiment is repeated by changing temperature to 45 oC and50 oC. A graph of t/L-Lo against L-Lo is plotted and best fit of straight line and slope of the graph are obtained. The diffusivity of acetone at two different temperatures is determined through calculation. The diffusivity of acetone at temperature of 40 oC, 45 oC and 50 oC are 8.415 x 10-5 m2/s , 3.6006x 10-8 m2/s and 2.3980 x 10-8 m2/s respectively. Throughout the experiment, the diffusivity of acetone is determined to be higher at higher temperature. This fits the theory where temperature affects the diffusion rate. Several recommendation should be taken during operating this experiment to minimize the errors.

INTRODUCTION

Mass transport in a gas or liquid generally involves the flow of fluid (e.g. convection currents) although atoms also di use. Solids on the other hand, can support shear stresses and ffhence do not flow except by di usion involving the jumping of atoms on a fixed network of ffsites. Diffusion can be divided into two types which are diffusion in a uniform concentration gradient and diffusion in a non-uniform concentration. Uniform concentration obeys Fick’s first law where the constant of proportionality is called the di usion coe cient in mff ffi 2s−1. Fick’s first law applies to steady state flux in a uniform concentration gradient. The diffusion in non-uniform concentration gradients obeys Fick’s second law of di usion with assuming that the di usivity ff ffis independent of the concentration.

Molecular diffusion is the transfer or movement of individual molecules through a fluid by random molecular movements . In the diffusion process, the molecules of interest flow from regions of high concentration to low concentration. Molecular diffusion can occur in both directions with the system.

The diffusion mechanism happen when the particles near each other at the corner of glass. Then, as time goes by, the particles will “move randomly around” in the water, which by means diffuse. Then, the particles will distribute randomly and uniformly in the water. The diffusion will still continue to occur but there is no net flux. The magnitude of this flux depends on both the magnitude of the concentration gradient and on the diffusive properties of the soil, as represented by the diffusion coefficient, D.

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This machine used for this experiment is to determine the gas diffusion coefficient by evaporation from a liquid surface for acetone-air system. In the case of study, acetone diffuses through non-diffusing air, which is passed over the top of the test tube containing the acetone. The air is allowed into the test tube, but does not diffuse into the acetone.

The diffusivity of the vapor of a volatile liquid in air can be determined by using Winklemann’s method. In which liquid was contained in a narrow diameter vertical tube, maintained at a constant temperature, and air stream passed through over the top of the tube. All these are to ensure that the vapour partial pressure was been transferred from the surface of the liquid to the air stream by molecular diffusion.

OBJECTIVES

There are two objectives that are needed to be achieved while conducting this experiment.

The objectives are as follows:

To determine the diffusivity of the vapour of acetone

To study the effect of different temperatures on the diffusivity

THEORY

The Armfield apparatus consists 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 surface 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/air meniscus within the capillary.CERa Gaseous Diffusion Coefficients Apparatus. The relation between the measured molar mass transfer rate (‘NA’ per unit area), the partial pressure gradient and the diffusion coefficient D is deduced from the one dimensional steady state version of Fick’s Law with bulk flow.The vapour of a volatile liquid in air diffusivity can be determined by using Winklemann’s method. In which liquid was contained in a narrow diameter vertical tube, maintained at a constant temperature and an air stream is passed through over the top of the tube. These are to ensure that the vapour partial pressure was been transferred from the liquid surface to the air stream by molecular diffusion.

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The derivation of equation to solve the objectives:

A) Rate of mass transfer, NA’

NA’ = D.(C A

L ) .( CTCBM )

Where; D is diffusivity (m2.s-1)

L is effective distance of mass transfer (mm)

CA is saturation concentration at interface (kmol.m-3)

CT is total molar concentration , CT = CA + CB (kmol.m-3)

CBM is log mean molecular concentration of vapour (kmol.m-3)

B) Evaporation of liquid

From (A) equation, consider the evaporation of liquid

NA’ = (❑L

M ) .( dLd t )Therefore,

D.(C A

L ) .( CTCBM )= (❑L

M ) .( dLd t )

Where; L is density of liquid (kg/m3)

M is molecular weight (kg/kmol)

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C) L-Lo at t=0

By integrating and substitute L=Lo at t=0

L2-Lo2 = t .( 2.M .D❑L

) .(C A .CTCBM )

So,

(L-Lo).(L-Lo+2Lo) = t .( 2.M .D❑L

) .(C A .CTCBM )

Otherwise,

( tL−Lo ) = ( ❑L

2.M .D ) .( CBMCA .CT )(L-Lo)+( ❑L

M . D ) .( CBMC A .CT )(Lo)

Where; L-Lo is the value differences of liquid level ,L – liquid level initial,Lo (mm)

t is time (min)

*Note that Lo and L cannot be measured accurately except for L-Lo can be measured accurately

by vernier on microscope.

D) Slope of graph (s.m-2), s

s = ( ❑L

2.M .D ) .( CBMCA .CT )

E) Diffusivity (m2.s-1), D

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D = ( ❑L .CBM2. s . M .C A .CT )

F) Saturation concentration at interface (kmol.m-3), CA

CA = ( PvPa ) .CT

G) Total molar concentration (kmol.m-3), CT

CT = ( 122.4kmol ) .(Tabs¿ )

H) Log mean molecular concentration of vapour (kmol.m-3),CBM

CB1 = CT

CB2 = ( Pa−PvPa ) .CT

CBM = (CB1−CB2

ln [CB1

CB2

] )

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APPARATUS

Figure 1.0: The Gas diffusion Apparatus

Figure 1.1: The ‘T’ shaped capillary tube with the air pump tube connected

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Figure 1.2 : Observing and measuring the meniscus level of acetone inside the capillary tube

APPARATUS

1. Gas Diffusion Apparatus

2. Acetone

3. Water bath

4. Microscope

5. Capillary tube

6. Syringe

7. Stop watch

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PROCEDURE

1. The distillate water was filled into the water bath until 35mm of the capillary tube was

obtained.

2. The capillary tube is then filled with acetone until the height is approximately 35mm with

use syringe.

3. The air pump tube is filled into the capillary tube until it had fully covered the entire

upper side of the capillary tube then the capillary tube is inserted into the water bath.

4. The vertical height of the microscope was then adjusted until the capillary tube was

visible.

5. If the capillary tube was not visible, the distance from the object lens was adjusted to the

tank until the meniscus of the acetone inside the capillary tube was clearer and if

necessary the position of the viewing lens in or out the microscope body can be adjusted.

6. When the capillary tube was viewed, the image of the meniscus will be upside down so

that the bottom of the meniscus of acetone would be at the top of image.

7. When the meniscus of the acetone has been determined, the sliding vernier scale should

be aligned with a suitable graduation on the fixed scale.

8. The air pump and the water bath heater are turned on.

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9. The initial value of the acetone inside the capillary was observed and recorded.

10. The temperature was set to 40 0C and a steady temperature was obtained.

11. The level of the acetone inside the capillary was recorded for every 2 minutes. The

experiment was then repeated at 2 different temperatures of 45 0C and 50 0C.

RESULTS

Temperature : 40oC

Lo : 55.04 mm

Time,

t (min)

Reading on vernier of

time,

L (mm)

Liquid level,

L-Lo (mm)

tL−Lo , (minmm )

0 55.04 0 0

2 55.04 0 0

4 57.06 2.02 1.9802

6 58.07 3.03 1.9802

8 60.09 5.05 1.5842

10 61.10 12.06 0.8292

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0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

f(x) = 0.0435684592174136 x + 0.901387157290353R² = 0.0455183358883988

Graph of t/L-Lo against L-Lo

yLinear (y)

L-Lo

t/L-

Lo

Temperature : 45oC

Lo : 58.07 mm

Time,

t (min)

Reading on vernier of

time,

L (mm)

Liquid level,

L-Lo (mm)

tL−Lo , (minmm )

0 58.07 0 0

2 58.09 0.02 100.0000

4 58.10 0.03 133.3333

6 58.10 0.03 200.0000

8 59.05 0.98 8.1633

10 59.05 0.98 10.2041

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0 0.2 0.4 0.6 0.8 1 1.20

50

100

150

200

250

f(x) = − 100.519104441191 x + 109.459945510005R² = 0.365966144195981

Graph of t/L-Lo against L-Lo

yLinear (y)

L-Lo

t/L-

Lo

Temperature : 50oC

Lo : 59.08 mm

Time,

t (min)

Reading on vernier of

time,

L (mm)

Liquid level,

L-Lo (mm)

tL−Lo , (minmm )

0 59.08 0 0

2 60.09 1.01 1.9802

4 61.10 2.02 1.9802

6 59.07 -0.01 -600.0000

8 60.08 1.00 8.0000

10 61.09 2.01 4.9751

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-0.5 0 0.5 1 1.5 2 2.5

-700

-600

-500

-400

-300

-200

-100

0

100

f(x) = 150.955086814278 x − 248.887278915016R² = 0.30644127309145

Graph of t/L-Lo against L-Lo

yLinear (y)

L-Lo

t/L-

Lo

SAMPLE CALCULATION

Calculation for 40°C

Liquid level, L-Lo = 55.04 – 55.04

= 0.00 mm

tL−Lo

= 20

= 0 min/mm

Plot the graph of t

L−Lo against L-Lo.

From the graph plotted,

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Slope of the graph, s = 0.043min/mm2

= 0.043minmm2 ×

60 s1min

×10002mm2

1m

= 2.58x 106 s/m2

Molecular weight, M (kg/mol)

Molecular weight of acetone = 58.08 g/mol

= 58.08 kg/kmol

Total molar concentration, CT (kmol/m3)

CT=( 1kmolVol )¿

= ( 122.4 )( 273

273+40 ) = 0.0389 kmol/m3

Logarithmic mean molecular concentration of vapour, CBm (kmol/m3)

CB1 = CT

CB1 = 0.0389 kmol/m3

CB2=(Pa−PvPa )CT

CB2=101.3−56

101.3×0.0389

= 0.0174 kmol/m3

CBm=(CB1−CB2 )

ln(CB1)(CB2)

= (0.0389−0.0174)

ln0.03890.0174

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= 0.0267 kmol/m3

Saturation concentration at interface, CA

CA = ( PvPa )CT= ( 56

101.3 )0.0389

= 0.0215 kmol/m3

Diffusivity, D (m2/s)

ρL = 790 kg/m3

D = ( ρLCBm)

s (2MC ACT )

= (790

kg

m3 )(0.0267kmol

m3 )

(2.58 x 106 sm2 ) (2 )(58.08

kgkmol )(0.0215

kmolm3 )(0.0389

kmolm3 )

= 8.415 x 10 -5 m 2 /s

Repeat the calculation for temperature 45°C and 50°C.

For 45°C, the diffusivity,

D = -3.6006x 10 -8 m 2 /s

For 50°C, the diffusivity,

D = 2.3980 x 10 -8 m 2 /s

DISCUSSION

Gas diffusion refers to one of mass transport process whereby molecules of interest flow from regions of high concentration to low concentration. Through this experiment of gas

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diffusion, we have to determine the diffusivity of the vapour and study the effect of temperature on the diffusivity. This experiment procedure was performed using the gaseous diffusivity apparatus. The diffusion of acetone which is a volatile liquid into another gas (in this experiment is air) can be conveniently studied by confining a small sample of acetone in a narrow vertical tube while maintaining a constant temperature of water bath, and observing its rate of evaporation into a stream of air passed across the top of the tube. This method is known as Winklemann’s method.

The procedures were repeated three times by varying the temperature at 40°C ,45°C and 50°C and the level of the acetone inside the capillary tube was recorded for every 2 minutes. Note that the temperature we specified should not be more than the boiling point of the fluid. Acetone liquid has a lower boiling point which is 56°C, therefore the temperature set up should less than that temperature or otherwise the acetone will be vaporised into the atmosphere instead.

Based on the collection data, the ratio of the time to the different in height of acetone were calculated. Besides, graphs of the ratio against the difference in liquid level were also plotted in order to determine the slope. This slope was useful in order to calculate the diffusivity of the acetone. From the results of this experiment, the diffusivity of the vapour of acetone at 40°C,45°C and 50°C were determined which were 8.415 x 10-5 m2/s , 3.6006x 10-8 m2/s and 2.3980 x 10-8 m2/s respectively. It has also being analysed from the graphs that the slope with lower temperature was more stepper than slope of higher temperature hence causing the diffusivity of the acetone with higher temperature will have a higher value. Theoretically, the molecules of substance possess higher kinetic anergy and move more freely from the energy gained at higher temperature. Thus, this will increase the rate of diffusion into the gaseous area.

However, during conducting the experiment there were several experimental error or mistake occurred effecting slightly the result we obtained. The first one was during taking the reading of meniscus of acetone. The eye position should be parallel to the meniscus in order to get accurate precise measurement. While adjusting the meniscus, make sure the meniscus is located most nearer to the horizontal line before taking the reading from the vernier scale. On top of that, the interval time to get another reading is too short which is 2 minutes thus causing the result to be unchanged sometimes. Therefore, the experiment should be carried out in longer time to get better results.

The apparatus used in this experiment such as the capillary tube and syringe should be cleaned and rinsed with distilled water before using them in this experiment. When confining the acetone into the capillary tube, make sure there is no bubble formed. The temperature specified also must be constant through out the experiment.

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In carrying out the laboratory experiments, safety takes precendence over all other consideration. Proper clothing and laboratory helmet sould be wear all the time in the pilot plant laboratory. Gloves should be wear while handling the acetone.

CONCLUSION

This experiment was performed to determine the diffusivity of the vapour and to study the effect of temperature on the diffusivity. From the analysed data and calculated results the diffusivity of the vapour of acetone at 40 Nc ,45 Nc and 50 Nc were determined which were 8.415 x 10-5

m2/s , 3.6006x 10-8 m2/s and 2.3980 x 10-8 m2/s respectively. We can conclude that diffusivity of the acetone with higher temperature will have a higher value. Besides that, it has been theoretically proved that higher temperature causing the molecules of substance to gain higher kinetic energy and moves randomly and freely hence increasing the rate of diffusion. Finally, the experiment has accomplished us with the study of diffusivity coefficent and familiarity with the use of laboratory instruments to achieve accurate measurements of data required for industrial process design.

RECOMMENDATIONS

Before the acetone was pumped, make sure there was no air bubble inside the capillary tube

Use different capillary tube when start with different temperature The travelling microscope that attached to the vernier scale must be tightly installed and

stable The level of the travelling microscope also must be paralleled with the capillary tube Eye level also must be parallel to the meniscus level When adjusting the vernier scale, the position of the travelling microscope should not be

disturbed The method of recording the reading from the vernier scale must be correct

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REFERENCES

https://docs.google.com/viewer?a=v&q=cache:wO469vFMUXcJ:www.discoverarmfield.co.uk/ data/pdf_files/cer.pdf+&hl=en&gl=my&pid=bl&srcid=ADGEESiDEIAcYF_uM31f3C98IHGIjlrsNf9H6wdVnVK3FFAXCn7vmzW0zwsGUgMbAWAvdizPR0oYz9HN4K4p_X80xENZs4WhgOm08j-zsk_hALSPSDAoyqIdRPyV52pNI0W3qiu4TYMt&sig=AHIEtbTZyypIRmBSpWJCQM7Z_PvdvAIkgg&pli=1 accessed on 3rd APRIL 2012,01:40

http://www.scribd.com/doc/39000629/Gas-and-Electrolyte-Diffusion-Presentation accessed on 3rd APRIL 2012,20:45

http://www.discoverarmfield.co.uk/data/pdf_files/cer.pdf accessed on 3rd APRIL 2012,20:45

http://en.wikipedia.org/wiki/Fick's_laws_of_diffusion accessed on 3rd APRIL 2012,20:45

http://thesis.library.caltech.edu/1586/11/10Chapter2.pdf accessed on 3rd APRIL 2012,20:45

http://www.reference.com/motif/Science/does-temperature-effect-diffusion-rate accessed on 3rd APRIL 2012,20:45

http://www.studyzones.com/questionzone/answer/73267x1565/How-does-temperature- affect-the-rate-of-diffusionaccessed on 3rd APRIL 2012,20:45

APPENDICES

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