Gaseous Diffusion Coefficient 4n5c2s

ABSTRACT Experiment was all about to determine the gas diffusion coefficient of acetone by using the established Winkelmann`s method. This experiment was based on mass transfer theory where by determine the diffusivity of the vapour of a volatile liquid which is acetone. Acetone was filled by 30mm of height of the vertical tube in the T-tube and then was placed on the constant temperature at 50 ℃ of the water bath. The T-tube was connected to air pump for allowed the gas diffuses to the free moving air. To obtained the diffusivity of the acetone, a telescope was setup to measured the level of acetone. The level of acetone was recorded for interval of 30minute for 2 hours. The diffusivity was determined by calculated the tabulated data. The graph was s represented on t/dL against dL and the slope values is 0.1975 mm2 . The partial pressure of the acetone was calculated by using Antoine equation which is 81.9 kPa. The result of diffusivity mm2 ℃ acetone at temperature 50 is to 553.296 s . The hypothesis was accepted which is the level of the acetone will decrease by ing 2 time but the plotted graph shows R is 0.6948 which lower than expected value. There were a few factors that affected the values which is human error when take the reading from the telescope and the controlled temperature was not constant values.

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Table of Contents

Abstract Table of Content 1.0 Introduction 2.0 Objectives 3.0 Theory 4.0 Description of Apparatus 5.0 Experimental Procedure 6.0 Results and Discussions

1 2 3 3 4 6 7 8

6.1 Results

8

6.2 Discussions 7.0 Sample Calculations 8.0 Conclusions and Recommendations

10 11 13

8.1 Conclusions

13

8.2 Recommendations 9.0 References 10.0 Appendices

14 14 14

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1.0 INTRODUCTION Gaseous diffusion coefficient apparatus involves diffusion with a flow of laboratory equipment that has been designed to allow measurement of molecular diffusivities. This apparatus is suitable to determine the diffusion coefficients of vapour in air, which methodologically measures the rate of evaporation of a liquid through a stagnant layer into a flowing air stream which air is provided to stream to remove vapour. The apparatus also comes with an air pump, a travelling microscope with accurate focus adjustment which mounted for vertical axis moving against a vernier scale and a thermostatically controlled water bath, which is to place the capillary tube, capable to give a very accurate temperature control. One of the experimental capabilities of this apparatus is direct measurement of mass transfer rates in the absence convective effects. The diffusivity of the vapour of a volatile liquid in air can be conveniently determined by Winklemann’s method [1], in which liquid is contained in a narrow diameter vertical tube, maintained at a constant temperature, and an air stream is ed 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 [2]. All the complexity and ungainliness of many calculations indeed, connected with the determination of this quantity. 2.0 OBJECTIVES The experiment conducted is aimed to determine the gas diffusion coefficient of acetone by using established Winkelmann’s method which could be obtained from evaporation rate. The evaporation rate obtained is to measure diffusivity of liquid acetone to the air. Level of acetone is

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measured to plot the evaporation due to time, the changes are to show the diffusion and evaporation of acetone occurs at controlled temperature. 3.0 THEORY A fluid containing two or more components exists a concentration gradient has a tendency to flow in such direction for each constituent as to reduce the concentration gradient. The flow occurs is called the mass transfer, which could take place either in both gas or liquid phase and simultaneously [1]. The diffusion of vapour A from its liquid into another gas B can be easily 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 ed across the top of the tube. For simple instructional purposes, gas B is air and vapour A is an organic solvent such as acetone or methyl alcohol [3]. An evaporated liquid in a narrow vertical tube at constant temperature is where mass transfer takes place. It happens to be from the surface by molecular diffusion. Winkelmann has established this technique to calculate the diffusivity of vapour of the volatile liquid. Evaporation rate that had been monitored which is the level drop of liquid surface with concentration gradient knowledge, the diffusivity can be obtained. The relation between the measured molar mass transfer rate (NʹA per unit area), the partial pressure gradient and the diffusion coefficient, D is deduced based on the following;

N ' A =D

Where, D

CA L

CT C Bm

( )( ) s = Diffusivity ( m2 /¿¿

4

CA

kmol ¿ 3 = Saturation concentration at interface m ¿ ¿

L

= Effective distance of mass transfer (m)

kmol ¿ 3 m CBm = Logarithmic mean molecular concentration of vapour ¿ ¿ kmol ¿ 3 = Total molar concentration m ¿ ¿

CT

Considering the evaporation of the liquid:

N ' A =D

Where,

( ρM )( dLdt )

ρL

L

3 = density of liquid ( kg /m )

kmol M = molecular weight ( kg /¿¿

Thus, ρL M

CA dL =D dt L

CT C Bm

( )( ) ( )( ) Integrating and putting L = L0 at t = 0:

5

2

2

L −L0=

C A CT

t ( 2 MD ρ )( C ) L

Bm

L0 and L cannot be measured accurately but L-L 0 can be measured accurately using the vernier calipers on the microscope;

( L−L0 ) ( L−L0 +2 L0 )=

(

2 MD ρL

)(

CA CT t CBm

)

Where, t= time (s) Where s are the slopes of the graph t/(L-L0) against L-L0 then:

s=

ρ ( 2 MD )( CC C ) L

Bm

A

T

Or,

D=

ρ L C Bm 2 M CA CT s

4.0 DESCRIPTION OF APPARATUS In this experiment of gaseous diffusion, apparatus that was used shown in figure 1 which was the SOLTEQ® Gaseous Diffusion Coefficient Apparatus (Model: BP 10) and a telescope with sliding venier scale. This model of apparatus consists of water bath, RTD temperature sensor, air pump, heater, level switch and capillary tube or known as t-tube and a valve.Firstly, the water bath or known as water tank is used for fill in water for heating process in order for acetone and 6

water go through diffusion process. Next, the RTD temperature sensor is used for detecting the heating temperature of the heater. The heater is used in this experiment to heat up the water in the water bath. The other component is capillary tube or called t-tube because of its shape. This ttube placed on top of the water bath and where the diffusion of gaseous is going to take place. The other component in this model is air pump. Air pump is used for drowning air through the ttube in order to maintain the pressure difference between the evaporating of water surface and the flowing of air stream. Level switch act as a detector to detect the level or the height of water in the water bath. The valve connected below the water bath is used to allow the water flow out from the water bath. The last component is telescope. Telescope with sliding vernier scale is used to measure the acetone level.

Figure 1: Diagram for gaseous diffusion coefficient apparatus (Model: BP 10) 7

5.0 EXPERIMENTAL PROCEDURE 1.

The water bath was filled with water to approximately 20mm from the top of the water bath.

2.

The main power on the control then was switched on.

3.

The temperature controller was set to 50 ℃ and heater was switched on.

4.

Temperature of the heater was remained constant at 50 ℃ .

5.

The capillary tube known as t-tube was filled with about 30 mm depth of acetone. The acetone was filled in the t-tube using a dropper.

6.

The t-tube was cautiously inserted through right in the fitting on top of the water bath cover with gentle tighten.

7.

Through the telescope with sliding vernier scale, the initial level of acetone was observed. This was done to ensure the acetone level can be observed using the telescope. The initial acetone level was recorded.

8.

The end of the t-tube was connected to the tube of the air pump and the air pump was switched on. At the same time the stopwatch was started.

9.

After 30 minutes, the air pump was switched off. There were no condensation occurred in the t-tube, the level of acetone was observed using the telescope and the reading on the scale of telescope was recorded.

10.

The steps 7 to 9 was repeated at 30 minutes intervals. 8

6.0 RESULTS AND DISCUSSIONS 6.1 RESULTS Table 1: Results for Gaseous Diffusion Time

Time

Level of Acetone

(min)

(ks)

(mm)

0 30 60 90 120

0 1.8 3.6 5.4 7.2

59.25 57.40 56.30 54.90 53.40

L-

L0 ,dL (mm) 0 1.85 2.95 4.35 5.85

t/dL (ks/mm) 0 0.973 1.220 1.241 1.231

Chart Title 1.4

f(x) = 0.2x + 0.34 R² = 0.69

1.2 1 0.8 t/dL 0.6

Linear ()

0.4 0.2 0 0

1

2

3

4

5

6

dL

Figure 2:Results on t/dL against dL

9

7

Based upon the graph above, it has stated that the slope value is 0.1975

s mm2

and from the

mm2 result given, the value obtained for gas diffusivity is equal to 553.296 s . While for the partial pressure of Acetone, using Antoine equation, it is best to use the table in the appendix as reference and so the answer is 81.9 kPa after conversion.

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6.2 DISCUSSIONS Diffusion is known as spreading out from one substance to another. It occurs when there is any difference in concentration gradient. Normally, diffusion took place from higher concentration to a lower concentration. That is what happened during the experiment. Acetone has the higher concentration while air has lower thus acetone diffuse into the air. Another factor that affects diffusion is heat. Heating caused the particles to act way faster and collide with each other in a not oriented path. If this happened in the experiment, it is easier to evaporate, resulting in an increase of rate of diffusion. Discuss the trend of the graph. Based on the results obtained, the graph of t/dL against dL is plotted. From the graph it can be observed that the trend of the graph is directly proportional. The

equation used to get the slope is y = mx + c and the value of the slope is 0.1975

mm2 the diffusivity value is 553.296 s . The significance of correlation

s mm2 while

R2 is 0.6948 which is

lesser than expected. Both partial pressure and concentration will give an effect on the rate of diffusion. When the partial pressure increases, it is easier for the solvent to evaporate. This is because pressure affects the movement of the molecular particles in the solvent. But for the concentration, an increase in concentration, it will take a longer time for the diffusion because more particles are there in the solvent.

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Before the experiment started, the temperature controller has been set up only at 50 ℃ . This is because the boiling point of Acetone is at 56 ℃ . Say that the temperature went beyond that temperature diffusion will still happen but in a higher rate of diffusion. This is because Acetone is a substance that volatize easily. The molecular attraction of the particles in Acetone if temperature exceeds more than 56 ℃ become unstable thus making it easier to evaporate. That is a reason why the temperature was set up not beyond than 70 ℃ . During the experiment, there were few inconsistencies which affecting the results. First, there was a slightly human error when taking the reading of the Acetone level using the telescope. Secondly, though the temperature controller was set up at 50 ℃ ,

it did not constantly remain

at that temperature. Instead, there were changes of temperature that is about ± 0.2℃ .

7.0 SAMPLE CALCULATIONS 1. Molecular weight of Acetone:

M = 58.08

kg kmol

2. Temperature was converted to Kelvin, k

12

T=

1k (50 ℃ × 1℃ )+273 k=323 k

Pa

3. Pressure

is a atmospheric pressure:

101.3 kPa 4. Density of Acetone:

791.0

kg m3

5. Vapour Pressure was calculated by Antoine Equation:

Pa=10

A−

B C+T

Where A, B and C is a constant values for the acetone from -64 ℃ to 70 ℃ . A= 7.11714 B= 1210.595 C=229.664 7.11714 −

Pa=10

1210.595 229.664+ 50

= 614.3161 mmHg

Converted to kPa .

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614.3161 mmHg×

101.325 kPa 760 mmHg

= 81.9 kPa .

6. From the graph gradient: s Slope, s =0.1975 mm2

7. Total molar concentration,

CB2

(

×10−3

)

C Bm

kmol = 0.0377 m3

kmol ¿ ( m3

kmol = 0.0377 m3

CT

P a−Pv C ( ) T Pa

=

kmol 3 ) m

m3 × kPa 8.314 (323 K ) kg × mol × K

8. Logarithmic mean value,

=

(

101.3 kPa

P CT = RT =

CB1

CT

=

kPa−81.9 kPa ( 101.3101.3 ) kPa

kmol m3

Solve for

C Bm

14

0.0377

kmol m3

=

7.2199

C Bm

=

C B 1 −C B 2 C ln ⁡( B 1 ) C B2

0.0377−0.0072199 0.0377 =( ) = 0.01844 ln ⁡( ) 0.0072199

9. Saturation concentration at interface (

Pv CT = ( Pa )

CA

=

kmol m3

kmol ¿ 3 m

81.9 kPa kmol kmol 0.0377 =0.03048 ( 101.3 ) kPa m m 3

3

10. Diffusivity, D

ρ L C BM 2 M C A CT s

D =

) (791 mkg )(0.01844 kmol m kg kmol kmol s 2( 58.08 ) 0.03048 0.0377 (0.1975 ) ( )( ) mol m m m 3

=

3

3

3

=553.29581

2

2

mm s

8.0 CONCLUSIONS AND RECOMMENDATIONS 8.1 CONCLUSIONS As a conclusion, this experiment is to study the diffusivity of the gaseous based on theory of mass transfer using Winkelmann’s method. From the hypothesis is the level of acetone will decrease by ing time, can concluded that the hypothesis is accepted with represented the result table. From the graph plotted, the flowing air is significantly increase the diffusion 15

coefficient which slope is 0.1975

s 2 mm

and the

R2

is 0.6948. The value of

R2

is lower

than expected showed that there were a few inconsistencies which affected the result collected. The human error when reading the telescope and the controlled temperature were changed that is

about ± 0.2℃ . The diffusivity of the acetone was calculated is equal to 553.296

mm2 . s

In

addition, the temperature different in this experiment will affected the result because it will affected in molecules speed or kinetic energy. Therefore, the molecules movement is affected and diffusion is slightly disturbed. 8.2 RECOMMADATIONS 

The telescope reading must be only one person in the team to read because the eyes levels



of other team member are different to reduce the parallax errors. The temperature must constant so that always check the heater to temperature of water



bath. Make sure the air pump work properly and at constant velocity of air flow into the



capillary tube. Acetone is flammable substance so it need to handle carefully and should not be nearest to sources of heat.

9.0 REFERENCES (1)

Chemical Engineering Laboratory Manual, Semester June-October 2013.

(2)

Leonard B., Kinetic Theory of Gases, Mineola, New York: Dover

Publications Inc. 16

(3)

E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems, 2nd ed., Cambridge, United Kingdom: The Press Syndicate Of University Of Cambridge.

(4)

Landolt-Bornstein, Gases in Gases, Liquids and Their Mixtures, New York: Springer Berlin Heidelberg.

10.0 APPENDICES

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