ACETONE DIFFUSION THROUGH AIR
1
Contents
• • • • • • • • • •
Introduction Theory Experimental Apparatus Experimental Method Results "iscussion Conclusions Re%erences 'ist o% (ym)ols Appendices
3 4-5 6 7 -! #$ ## #& #3 14
Introduction 2
A molecular di%%usion experiment *as set up+ *ith se,eral aims These *ere to illustrate the theory o% mass trans%er+ to calculate the di%%usi,ity o% acetone throu.h air+ to examine the in%luence o% temperature on the di%%usi,ity and %inally to compare the results o)tained *ith those o)tained *ith di%%erent experimental methods The %lo* o% mass in a li/uid or .as .enerally in,ol,es the %lo* o% %luid throu.h a material0 solids ho*e,er can support shear stresses and hence mass is trans%erred )y di%%usion "i%%usion can )e descri)ed as either di%%usion in a uni%orm concentration or di%%usion in a non-uni%orm concentration 1ni%orm concentration o)eys 2ics %irst la*+ *here the constant o% proportionality is no*n as the di%%usion coe%%icient 2ics %irst la* applies to a steady state %lux in a uni%orm concentration .radient "i%%usion in a non-uni%orm concentration .radient o)eys 2ics second la* o% di%%usion+ *ith the assumption that di%%usi,ity is independent o% the concentration
3
Theory The %lux o% acetone molecules can )e calculated %rom 2ics 'a* throu.h a sta.nant layer o% air molecules *hich are non-di%%usin.+ this .i,es the e/uation
In the case o% this experiment+ acetone is di%%usin. throu.h the air+ ho*e,er air is not di%%usin. )ac into the acetone The cross-sectional area throu.h *hich the di%%usion occurs is constant alon. the len.th o% the tu)e throu.hout the experiment This allo*s the %lux to )e calculated The air passin. o,er the top o% the tu)e has no acetone+ hence P A 2 is ero P A 1
can )e calculated %or any .i,en *ater temperature+ usin. ,apour pressure
data %or acetone %rom this the rate o% di%%usion is also calculated %rom the rate o% e,aporation+ as sho*n in E/uation &
4
E/uatin. and inte.ratin. these t*o e/uations .i,e E/uation 3 as %ollo*s
2rom this+ the di%%usi,ity o% acetone in air can )e %ound )y plottin. a .raph o% z f − z o 2
2
a.ainst
t r
and tain. the .radient %rom the strai.ht lines plotted 8ith
this in%ormation+ the relationship )et*een temperature and di%%usi,ity in the .as state can )e seen
2uler+ et al de,eloped the relationship )et*een the total pressure+ a)solute temperature and di%%usi,ity This is sho*n )elo*
2rom this+ it can )e seen that the di%%usi,ity should )e proportional to the a)solute temperature raised to the po*er o% #75
5
Experimental Apparatus
The apparatus *as set up as %ollo*s
Figure 1: Schematic of experimental set up
6
Figure 2: Photograph of experimental set up
Experimental Method The am)ient pressure o% the room *as taen prior to the experiment commencin. The air pump *as set up to initiate a .entle air %lo* throu.h the T-piece The *ater )ath *as %illed *ith *ater at the re/uired temperature %or run #+ this *as then %ollo*ed )y the test tu)e )ein. %illed to the hi.hest .raduation *ith acetone+ so as to match the le,el o% *ater in the )ath The T-piece *as then reattached and the experiment could commence The .raduation le,el o% li/uid meniscus *as read e,ery & minutes %or &$ minutes 9nce this *as completed+ the same procedure *as carried out *ith di%%erin. temperatures %or di%%erent runs+ *ith the acetone )ein. replenished each time
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Results
Run Water Bath Temperature( Deg C) Time (Mins) $ & 4 6 #$ #& #4 #6 # &$
(#"$2 % #$2) 8
1
2
3
35 Distance bel! tp " tube (m) $$45 $$5$ $$55 $$55 $$56 $$57 $$5 $$5 $$5 $$5 $$5!
45
50
$$3$ $$35 $$36 $$3 $$3! $$4$ $$45 $$4 $$5$ $$5# $$5&
$$5$ $$55 $$57 $$57 $$5 $$5! $$6$ $$6# $$6# $$6& $$64
$ & 4 6 #$ #& #4 #6 # &$
9
$$$ $ $$$ $ $$$ # $$$ # $$$ # $$$ # $$$ # $$$ # $$$ # $$$ # $$$ #
$$$$
$$$$
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$$$#
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$$$&
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$$$&
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Graph of zf^2 - zo^2 VS T 0.002 f(x) = 0x + 0 0.002
zf^2 - zo^2
f(x) f(x) = = 0x 0x + +0 0
0.001 0.001 0.000
0
5
10
15
20
*00+%05 3$ 75$# 3&&6& &5!E-$4
,*00+%05 3# 75$# 5$!55 #34E-$4
25
T
&ra'ient " lt -bslute Temperature (.) Ttal /stem ressure (mmg) apur pressure " acetne at liui' sur"ace (mmg) Di""usiit " -cetne in air (m$2s)
10
,*00+%052 3&3 75$# 6##67 !E-$5
"iscussion The aim o% this experiment *as to calculate the di%%usi,ity o% acetone throu.h air+ to examine the in%luence o% temperature on the di%%usi,ity and %inally to compare the results o)tained *ith those o)tained *ith di%%erent experimental methods The results o)tained %or the di%%usi,ity o% acetone in air experimentally+ )y usin. the .radient o% the .raph+ are ,ery close to those o)tained )y calculation usin. the e/uations mentioned pre,iously This *ould su..est the experiment *as a success As *ell as this+ the in%luence on temperature on the di%%usi,ity has )een pro,en as sho*n in the results the results *ere as expected in the hypothesis 2inally+ the results o)tained experimentally %or the di%%usi,ity o% acetone in air+ are a.ain ,ery close to those o)tained experimentally usin. other methods This a.ain *ould su..est the experiment *as a success "espite the apparent success o% the experiment+ there *ere se,eral sources o% error in this experiment "ue to the practical set up o% the test tu)e in the *ater )ath+ it *as ,ery di%%icult to measure the meniscus le,el accurately i% this experiment *ere to )e repeated+ a .raduated test tu)e *ould )e used as this *ould ensure .reater accuracy in measurin. the meniscus le,el 2urthermore+ the assumption *as made that the temperature remained constant *hilst the experiment *as )ein. carried out this+ ho*e,er+ is unliely to )e true i% this experiment *ere to )e repeated a method o% ensurin. the temperature *as ept constant *ould )e explored
Conclusion 11
To conclude+ this experiment can )e considered a success %or the a%orementioned reasons The di%%usi,ity determined experimentally *as ,ery similar to that o)tained )y calculation usin. di%%erent methods As *ell as this the e%%ect o% temperature on di%%usi,ity *as pro,en to )e as hypothesised The sli.ht di%%erence in )et*een experimental and calculation can partly )e attri)uted to the sources o% error mentioned pre,iously the inaccuracy in measurin. due to the e/uipment used+ as *ell as the %act that the temperature o% the *ater )ath did not remain constant throu.hout the experiment I% this experiment *ere to )e repeated a .raduated test tu)e *ould )e used and a method o% eepin. the *ater temperature constant *ould )e explored+ in order to ensure .reater accuracy
Re%erences 12
Incropera+ 2:+ ": "e8itt ;#!!6<+ Fundamentals of Heat and Mass Transfer + =ohn 8iley > (ons+ :a.es 46$+ 5&-6#& ;#!!6< (innott+ R and To*ler+ ? ;&$#$< Coulson and Richardson's Chemical engineering Amsterdam Else,ier :a.es 634-65$ Maloney+ = ;&$$< Perry's chemical engineers' handbook @e* Bor Mc?ra*-Dill
'ist o% (ym)ols 13
Appendices 14
-ppen'i6 1 7 /ample Calculatins
All calculations are )ased on results %rom Run #
•
•
Total System Pressure =1001 mbar= 1001∗0.750062 =750.81 mmHg Vapour Pressure of Acetone at Liquid Surface@ 35 ℃ via interpolation
200 +
•
( 400 −200 ) ( 35−22.7 )=322.62 mmHg ( 39.5 −22.7 )
Diffusivity of Acetone ∈ air =¿
0.001=1200 Da
Da=
15
0.31 1200
[(
2∗58.07∗100099.8 791∗8314.5 ∗08
=2.58 X 10− m / s 4
2
)( ln
100099.8
100099.8 −43012.47
)]
