Gaseous Diffusion Coefficient

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 the vapour of a volatile liquid which is acetone. Acetone was filled by !mm of height of the vertical tube in the T"tube and then was  placed on the constant temperature at #! ℃

of the water bath. The T"tube 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 !minute for % hours. ho urs. The The diff diffus usiv ivit ity y was was dete determ rmin ined ed by calcul calculat ated ed the the tabul tabulat ated ed data data.. The The grap graph h was was s represented on t&d' against d' and the slope values is !.()*# mm2 . The partial pressure of  the acetone was calculated by using Antoine equation which is +(.) k,a. The result of diffusivity 2 mm acetone at temperature #! ℃  is to ##.%). s The hypothesis was accepted which is the level of the acetone will decrease by passing 2  R time but the plotted graph shows  is !.-)+ 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 no t constant values.

1

Table of Contents

Abstract Table of /ontent (.! 0ntroduction %.! 1b2ectives .! Theory .! 3escription of Apparatus #.! Experimental ,rocedure -.! 4esults and 3iscussions

( %    * +

-.( 4esults

+

-.% 3iscussions *.! 5ample /alculations +.! /onclusions and 4ecommendations

(! (( (

+.( /onclusions

(

+.% 4ecommendations ).! 4eferences (!.! Appendices

( ( (

2

1.0 INTRODUCTION

6aseous 6aseous diffusion diffusion coefficient coefficient apparatus apparatus involves involves diffusion diffusion with a flow of laboratory laboratory equipm equipment ent that that has been been design designed ed to allow allow measur measureme ement nt of molecul molecular ar diffus diffusivi ivitie ties. s. This This appa apparat ratus us is suit suitabl ablee to dete determ rmin inee the the diff diffus usio ion n coef coeffi fici cien ents ts of vapo vapour ur in air$ air$ whic which h methodologically measures the rate of evaporation of a liquid through a stagnant layer into a flowing air stream which air is provided to pass stream to remove vapour. The apparatus also comes with an air pump$ a travelling microscope with accurate focus ad2ustment 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. 1ne 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 Winklemann7s method 8(9$ 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 liquid to the air stream stream by molecul molecular ar diffus diffusion ion.. The molecul molecular ar diffu diffusiv sivity ity$$ 3$ is a kineti kineticc  parameter associated with static and dynamic conditions of a process 8%9. All the complexity and ungainliness of many calculations indeed$ conn ected 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 Winkelmann7s method which could be obtained from evaporation rate. The evaporation rate obtained is to measure diffusivity of liquid acetone to the air. 'evel of acetone is

3

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 fluid contain containing ing two or more more compone components nts exist existss a concent concentrat ration ion gradie gradient nt has a tendency tendency to flow in such direction direction for each constituent constituent as to reduce the concentration concentration gradient. The flow occurs is called the mass transfer$ which could take place either in both gas or liquid  phase and simultaneously 8(9. The diffusion of vapour A from its liquid into another gas : 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 : passed across the top of the tube. ;or simple instructional  purposes$ gas : is air and vapour A is an organic solvent such as acetone or methyl alcohol 89. An evaporated liquid in a narrow vertical tube at constant temperature is where mass transfer takes place. 0t 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 The rela relati tion on betw betwee een n the the meas measur ured ed mola molarr mass mass tran transf sfer er rate rate <= A per unit unit area> area>$$ ʹ

the partial pressure gradient and the diffusion coefficient$ 3 is deduced based on the following?

 N '  A = D

( )( ) C  A

C T 

 L

C Bm

s Where$ 3

@ 3iffusivity < m

2

/ ¿¿

4

kmol ¿

/A

@ 5at 5atur urat atio ion n con conce cent ntra rati tion on at inte interf rfac acee

'

@ Effective distance of mass transfer

m

3

¿ ¿

kmol

¿

/:m @ 'ogarithmic mean molecular concentration of vapour

kmol ¿

/T

m

@ Total Total molar concentration

3

¿ ¿

/onsidering the evaporation of the liquid

 N '  A = D

Where$

( )( )  ρ L

dL  M  dt 

 ρ L

3

@ density of liquid < kg / m

>

kmol B @ molecular weight < kg / ¿¿

Thus$

( )( ) ( ) ( )  ρ L

C  A dL = D  M  dt   L

C T 

C Bm

0ntegrating and putting ' @ '! at t @ !

5

m

3

¿ ¿

2

2

 L − L0=

( )( ) 2 MD

C  A C T 

 ρ L

C Bm

t 

'! and ' cannot be measured accurately accurately but '"'! can be measured accurately accurately using the vernier  calipers on the microscope?

( )( )

 L− L ) ( L  L− L +2 L )= ( L 0

0

0

2 MD

C  A C T 

 ρ L

C Bm

t 

Where$ t@ time Where  s are the slopes of the graph t&<'"' !> against '"'! then

s=

( )( ) ρ L

C Bm

2 MD

C  A C T 

1r$

 D=

ρ L C Bm 2 M

C  A C T  s

.0 DESCRI!TION O" A!!ARATUS

0n this experiment of gaseous diffusion$ apparatus that was used shown in figure ( which was the 51'TE 51'TECD CD 6aseous 6aseous 3iffusion 3iffusion /oefficient /oefficient Apparatus Apparatus and a telescope telescope with sliding venier scale. This model of apparatus consists of water bath$ 4T3 temperature sensor$ air   pump$ heater$ level leve l switch and capillary tube or known as t"tube and a valve.;irstly$ the water   bath or known as water tank is used for fill in water for heating process in order for acetone aceton e and 6

water go through diffusion process. =ext$ the 4T3 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 t" tube 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 t" tube in order to maintain the pressure difference between the evaporating of water surface and the flowing of air stream. 'evel 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 compone nt is telescope. Telescope Telescope with sliding vernier scale is used to measure the acetone level.

;igure ( 3iagram for gaseous diffusion coefficient apparatus 7

#.0 E$!ERI%ENTA& E$!ERI%ENTA& !ROCEDURE

(.

The The water water bat bath h was fil fille led d with with wat water er to to appro approxi xim matel ately y %!mm %!mm from from the the top top of the the wate water  r   bath.

%.

The The mai main n pow power er on the the con contr trol ol pane panell the then n was was swit switch ched ed on. on.

.

The tem temp perature co contr ntroll oller wa was se set to to #! #! ℃  and heater was switched on.

.

Temper mperat atur uree of of the the heat heater er was was rema remain ined ed cons consta tant nt at #!

#.

The The capil capilla lary ry tub tubee known known as t"t t"tub ubee was was fill filled ed with with abo about ut ! ! mm dept depth h of acet aceton one. e. The The

℃

.

acetone was filled in the t"tube using a dropper. -.

The The t"tub t"tubee was caut cautio ious usly ly inse insert rted ed thro throug ugh h right right in in the fitt fittin ing g on top of the the wate waterr bath bath cover with gentle tighten.

*.

Thro Throug ugh h the the teles elesco cope pe with with sli sliding ding verni vernier er scal scale$ e$ the the init nitial ial level evel of acet aceton onee was was observed. This was done to ensure the acetone level can be observed using the telescope. The initial acetone level was recorded.

+.

The The end end of the the t"t t"tub ubee was was conn connec ecte ted d to the the tub tubee of the the air air pump pump and and the the air air pum pump p was was switched on. At the same time the stopwatch was started.

).

Afte Afterr ! min minut utes es$$ the the air air pump pump was was swi switc tched hed off off.. Ther Theree were were no no conde condens nsat atio ion n occu occurr rred ed in in the t"tube$ the level of acetone was observed using the telescope and the reading on the scale of telescope was recorded.

(!. (!.

The The ste steps ps * to to ) was was repe repeat ated ed at ! minu minute tess inte interv rval als. s.

8

'.0 RESU&TS AND DISCUSSIONS '.1 RESU&TS

3 iffusion Table 1( 4esults for 6aseous 3iffusion Time

Time

'evel of Acetone







! ! -! )! (%!

! ( .+  .# . * .%

'"

L0 , dL

t&d'

! (.+# %.)# .# #.+#

#).%# #*.! #-.! #.)! #.!

! !.)* (.%%! (.%( (.%(

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

")*+,e 2(4esults on t&d' against d'

9

7

s :ased upon the graph above$ it has stated that the slope value is !.()*#

2

mm

 and from the

2

mm result given$ the value obtained for gas diffusivity is equal to ##.%)s

. While for the

 partial pressure of Acetone$ using Antoine equation$ it is best to use the table in the appendix append ix as reference and so the answer is +(.) k,a after conversion.

10

'.2 DISCUSSIONS

3iffusion is known as spreading out from one substance to another. 0t occurs when there is any difference in concentration gradient. =ormally$ 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. eating caused the particles to act way faster and collide with each other in a not oriented path. 0f this happened in the experiment$ it is easier to evaporate$ resulting in an increase of rate of diffusion. 3iscuss the trend of the graph. :ased on the results obtained$ the graph of t&d' against d' is  plotted. ;rom the graph it can be observed that the trend of the graph is directly proportional. The

s equation used to get the slope is y @ mx F c and the value of the slope is !.()*#

2

mm

while

2

mm the diffusivity value is ##.%)s

. The significance of correlation  R

2

 is !.-)+ which is

lesser than expected. :oth 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. :ut for the concentration$ an increase in concentration$ it will take a longer time for the diffusion because more particles are there in the solvent.

11

:efore the experiment started$ the temperature controller has been set up only at #! ℃ . This

is because the boiling point of Acetone is at #- ℃ . 5ay that the temperature went beyond that temperature diffusion will still happen but in a higher rate of diffusion. This is because Acetone is a substa substance nce that volatiGe volatiGe easily easily.. The molecul molecular ar attrac attractio tion n of the partic particles les in Acetone Acetone if  temperature exceeds more than #- ℃  become unstable thus making it easier to evaporate.

That is a reason why the temperature was set up not beyond than *! ℃ .

3uring the experiment$ there were few inconsistencies which affecting the results. ;irst$ there was a slightly human error when taking the reading of the Acetone level using the telescope. 5econdly$ though the temperature controller was set up at #! ℃ ,  it did not constantly remain

at that temperature. 0nstead$ there were changes of temperature that is about ± 0.2 ℃ .

-.0 SA%!&E CA&CU&ATIONS CA&CU&ATIONS

(. Bolecular weight of o f Acetone

 B @ #+.!+

kg kmol

%. Temperature Temperature was converted to Helvin$ k 

12

T@

(

50 ℃ ×

1 k  1℃

 Pa

. ,ressure

)+

273 k =323 k 

 is a atmospheric pressure

(!(. kPa

. 3ensity of Acetone kg *)(.!

3

m

#. Iapour Iapour ,ressure was calculated by Antoine Equation

 A −

 Pa=10

B C + T 

Where A$ : and / is a constant values for the ace tone from "- ℃  to *! ℃ .

A@ *.((*( :@ (%(!.#)# /@%%).--

 Pa=10

7.11714 −

/onverted to

  1210.595 229.664+ 50

 @ -(.(-(

mmHg

kPa.

13

614.3161 mmHg×

 101.325 kPa 760 mmHg

 @ +(.) kPa .

-. ;rom the graph gradient s 5lope$ s @!.()*# mm2

*. Total molar concentration$

8.314

(

C T 

@

m

>

3

<

)

3

C Bm

kmol  <

m

3

5olve for

m

m

3

¿

@ !.!**

m

 Pa

>

3

C T 

@

(

101.3 kPa−81.9 kPa 101.3 kPa

−3 kmol

× 10

kmol

kmol

 P a− Pv

C B 2

 <

m ×kPa ( 323 K )  @ !.!** kg×mol×K 

+. 'ogarithmic mean value$

 @

kmol

101.3 kPa

P C T =  R T  @

C B 1

C T 

3

C Bm

14

)

kmol !.!**

m

3

@

*.%())

C B 1 −C B 2 C Bm

@

C B 1 ) ln ( C B 2

0.0377−0.0072199

@<

ln (

  0.0377 0.0072199

kmol ). 5aturation concentration at interface <

 P v

C  A

 @ <  P a >

C T 

 @

(

  81.9 kPa 101.3 kPa

m

)

3

kmol

)

> @ !.!(+

m

3

¿

0.0377

kmol 3

m

 kmol

=0.03048

m

3

(!. 3iffusivity$ 3

(

 ρ L C BM  3 @

2 M C  A C T s

 @

2 ( 58.08

kg ) mol

(

 kg

791

m

3

)

 kmol

(0.01844

 kmol

0.03048

m

3

)(

m

3

0.0377

)

kmol m

3

)

(0.1975

s m

2

)

 @##.%)#+(

2

mm s

.0 CONC&USIONS AND RECO%%ENDATIONS RECO%%ENDATIONS .1 CONC&USIONS

As a conclusion$ this experiment is to study the diffusivity of the gaseous based on theory of mass transfer using Winkelmann7s method. ;rom the hypothesis is the level of acetone will decrease by passing time$ can concluded that the hypothesis is accepted with represented the result result table. table. ;rom ;rom the graph graph plotte plotted$ d$ the flowin flowing g air is signif significa icantl ntly y increa increase se the diffus diffusion ion 15

s coefficient which slope is !.()*#

2

mm

 and the  R

2

 is !.-)+. The value of  R

2

 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

2

about ± 0.2 ℃ . The diffusivity of the acetone was calculated is equal to ##.%)-

mm . s

0n

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. .2 RECO%%ADATIONS RECO%%ADATIONS

•

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. Bake 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.

/.0 RE"ERENCES

<(> <(>

/hem /hemic ical al Engi Enginee neeri ring ng 'abor 'aborat atory ory Ban Banual ual$$ 5emes 5emeste terr June" June"1c 1cto tober ber %!( %!(..

(2)

Leonard B., Kine Kineti tic c Theo Theory ry of Gase Gases s, Mine Mineo oa, a, !e" !e" #or$% or$% &o'e &o'err

*iaion- n. 16

(3)

/. L. L .   --er, Diusi Diusion: on: Mass Mass Transfe ransferr in Fluid Fluid Syste Systems, ms, 2nd  ed., a*ri a*ride de,, nied nied indo indo% % e re-re-- ndi ndiae ae f ni'er ni'er-i -i  f  a*ride.

(4)

Lando:Born-ein, Gases in Gases, Liquids and Their Mixtures, !e"  #or$%  #or$% ;riner Berin Berin
10.0 /!&/

17