Ben Clifford and E. I. Ochiai University of British Columbia Vancouver. BC V6T 1W5 Canada
A Practical and Convenient Diffusion Apparatus
I
An undergraduate physical chemistry experiment
In establishing in our undergraduate physical chemistry lahoratorv an exoeriment to determine the diffusion coefficients of aqueous solutions of sucrose and potassium dichro-Solvent column, mate we develoned a simnle economic diffusion annaratus .. volume = V which is especi~llyconvenient for student use. The basic method, described hv Linder. Nassimheni. Polson, and Rogers (I), follows the free boundary method of polson. ~ ~ d e r classroom conditions we encountered several practical prob-Interface, lems in the use of the l'olson apparatus. A glass nppnratus, ronstructerl from a Y-shaped stopcock barrel iitted with a area = A \'-bore Teflon@stopcork, was designed to nllow investigation of these prohlrms hy simple observntion o i the diilusiau of colored sdutions. and thiscell was itself found to he uartiru-Solution column, larly useful in a student experiment. The experimental initial conc. = nroblems and their solutions are discussed and the anoaratus .. and procedures for two experiments are described, the first to determine the diffusion coefficient of aaueous sucrose soI~nionsusing the neu, unit, and the second t~ find the difiuiion Figure 1. Diffusion of solute horn a column of solution into a column of solvent coeii~cientfor aaucous K?Cr,O- solutions. The latttr exneracross an initially sharp interface. imeut has been ~uccessfuflyised in the classroom.
M
Co
Principle of Method In this experiment a column of solution contained in the bore of a stopcock is aligned with a column of solvent contained in a neck of the stopcock harrel. After a time.. t.. there is a net one dimensional diffusion of m moles of solute from the solution into the solvent. I t has been shown (1)that the diffusion coefficient, D, is given by D=--m2 r co2A2 t
(1)
where co is the ori&al solute concentration in the solution and A is thi area of the interface between the columns. For eqn. (1) to be valid i t is necessary that the solute concentration remain zero at the top of the solvent column and q a t the bottom of the solution column for the duration of the run. The cross-sectional size and shape of the columns should be uniform so that the diffusion is one dimensional. If the solvent column plus diffused solute is of volume, V, and is mixed to -eive a uniform solution of solute concentration. c, then m = cV
(2)
L-
w b r o s s stop
handle (position I I ' shooe. . . V bo stopcock A potterr l h o n d l e iposition 2) x
Figure 2. The stopcock type diffusionapparatus.
and eqn. (1) becomes
In practice it is often convenient to start the diffusion run with a small volume in the solvent column which is diluted tovolume V after diffusion. In this case c (eqn. 3) is the concentration of the final diluted solution. Apparatus The diffusion cell is constructed from a Springham Interflon stopcock (Yshape, V hore pattern, 2 mm hore). Stopcocks with ground glass barrels are unsatisfactory because of seepage problems. The three necks are carefully checked to find the one which best aligns with one end of the stopcock bore, thus defining neck A (Fig. 2). The selected end of the stopcock bore is then alignment-drilled to a depth of 7-8 mm with the largest drill bit which will fit through neck A and the size of the hit, approximately 4 mm diameter, is noted. With the stopcock 678 I Journal of Chemical Education
installed in the barrel and the enlarged bore aligned with neck A. the remaining closed neck becomes neck C (Fie. 2),~and is . h i n t parallel to neck A. A 1mm straight bore Interflon stopcock is installed on the third neck. Necks A and C are reinforced with a clamp on which is fitted a brass stop positioned so as to facilitate the precise alignment of the enlareed stopcock bore with the bore of neck A. This stop can be constructed with a screw adiustment. T h r diffusion of solute from the sdurion contained in the sropcock h e to the sol\,ent in neck A is in arrordnnce with eqn. 131 pro\.idrd the hore through neck A into the stopcock is uniform in shape and area over the prncticat difiusion distanres. Whereas in a P111sontypecell the interfacesare planar and thr houndarv areas are simply the cross-sectional areas ut the cavities. the interface defined tw the stonrurk bore is slightly curved. If the bore diameter, b, is small compared with
-
~~~
with Teflon' tuhing is used to mix and transfer the liquid from neek A along with two small rinsings of water, making a total volume of about 1 ml, to an accurately weighed 25-ml Erlenmeyer flask. Neck A is then recharzed with about 2 cm of water in oreoaration for the
Figure 3. Detail of stopmk A definingthe surfacearea of the bwe as an ellipse with minor axis, b. and major axis 2.
(b)
(a)
Figure 4. The orientations of the stopcock type cell and bare positions used in preparation for a diffusion run. t h e stoncock diameter.. d . (i.e.. . .bld . 5 0.2). . , i t is within exnerimental limits of accuracy t o consider t h e houndary area, A, t o h e t h e cross-sectional area of t h e bore. For larger bores. if t h e solution and solvent have similar densitiesso t h a t t h e interfacial curvature does not change during a run, t h e interface is better approximated as a n ellipse with minor axis equal t o b and major axis equal t o the arc section, Z, subtended b y t h e bore, of t h e circumference, C, of t h e stopcock crosssection through t h e center of t h e hore (the effect of t h e stopcock taper is insignificant). T h u s from Fig. (3)
to he used, 5 times if the solution is changed. Sucrose analysis is by a modification of methods described by Wilson and Wilson (21, namely oxidation by excess acid solution of KzCrz07, but in this case the excess is determined colorimetrically rather than by titration. 1.00 ml of 2.00 X 10V M K2Cr207is added to the sucrose solution in the weighed flask followed by 1 ml of concentrated HB04. It is convenient to use automatic plunger type dispensers for these additions. The solution is heated just to boiling for 20 min, cooled to room temperature, then diluted with water to a finalsolution weightof 6.OOg (-5 ml). Dilution is hyweight because the procedure involves heating, and since the final volume required to give a reasonable absorbance reading is rather small, transfer, after heating, of the solution to a volumetric container is not too convenient. As the densities of all finally prepared samples are virtually identical there is no problem in diluting gravimetrically. The absorbance of the solution is measured at 352 mp against a blank of 1ml of concentrated H2S04 diluted to 6.00 g with water. The absorbance* of similarly treated I-ml samples of 0,20,40,60, and 80pg/ml sucrose are determined. Since analysis is by weighing, a calibration line of absorbance against weight of sucrose is prepared (assume the original sample solution densities to be eousl to that ofwaterl. This analvsis is suitable concentration. A 3-4 hr experiment using the stopcock type cell consists of foul
no sample treatment. After completion of each run, the contents of neck A are mixed and transferred directly toa 10-mlvolumetrie flask along with 2 or 3 rinsings. The solution is made to the mark and the absorbance is read colorimetrically at 352 mp using a water b1ank.A calibration curve of absorbance versus [KzCrz07]is prepared from readings measured on 2,4,8, 12, 16, and 20 X M KzCrz07. The procedure has been cheeked with a set of ten runs using0.2M K2Crz07 diffused far times between 300 and 2500 see. Results and Discussion
...
....
T h e area of the interfacial area is therefore
Experimental Procedure
To prepare the stopcock type unit for a diffusion run, in this ease with 10 g/l sucrose solution, the cell is first held as in Fig. (4a) and necks A and B are filled with water. The apparatus is rocked hack and forth to remove all air bubbles from the bores. A pipet, fitted with 10 crn of 1mm Teflon' tubing to prevent seratchingof the stopcocks is helpful in removing bubbles. Stopcock B is closed, the apparatus is heldasin Fig. (4b),then stopcock B isopened until all but about 2 cm of water is drained from neck A. Use the pipet to fill neck C with water. With this cell position maintained, stopcock A is rotated to position 1shown in Fig. (2) and stopcock B is used to drain the water from neck C almost to stopcock A. Neck C is filled with 10gfi aqueous sucrose which is then also drained almost to stopcock A. This flushing procedure is repeated at least 5 times to replace all the water in the bore of stopcock A withsucrose solution. The apparatusis then held as in Fig. (2) and the solution level in neck C is adjusted to about the same height as the water in neck A. The unit is then hung by neek Afor 15 min in a 2 5 T constant temperature bath such that the water level in the bath is above the liquid levels in necks A and C. The eauilibration unit is turned off during the diffusion run to minimize vilwation. Since the experiment r i done at Li°C, the temperdure will n method, that of Hodne - and Hofreiter (31,was not t h e m i i n problem.' A typical r u n using 10.00 gll sucrose diffused for 850 s a t 25'C ";ing a n appar&us with a 4.2 m m hore diameter gives an absorbance of 0.352 using the previously described sucrose analysis. Inrerpolation from the calihration plot gives a diffused surruse weight ut'5.23 X IU-!. g. With the boundary area considered t o he t h e cross-section bf t h e hore, eqn. ( l j g i v e s a value of D of 5.27 X 10-lo m2 s-I while using eqn. (6) to determine t h e interfacial area a s a n ellime (d = 13.2 m m ) eives avalue of D of 5.09 X 10-lo m2 s-I. ~ f m i l a 58.84 h ~ gfi (0.2M ) K2Cr207diffused for 1309 s i n a n apparatus with a 4.0 m m hare (d = 13.2 mm) gives a n absorbance reading of 0.712 for t h e diffused dichromate made u p t o a final volume of 10 ml. Interpolation from the calihration curve gives c = 5.88 X g/l KzCr207. Equation (3) i n this case gives D = 1.47 X m2 s-I with t h e houndary considered a s a n ellipse. T h e average diffusion coefficient a t 25°C of aqueous sucrose (10 gfi) from data ohtained with the stopcock type apparatus is 5.2 X 10-'0 m2 s-' with a standard deviation over t e n trials of 0.2 X 10-In m2 s-'. This value considers the boundary area, A, a s a n ellipse given by eqn. (6) whereas approximating A a s Volume 57, Number 9, September 1980 1 679
the cross-sectional area of the bore gives 5.4 X 10-'0 m2 s-'. These results are in excellent agreement with the value for 1.001 1°1 surrose, ohtained by Gosting.and Morris (41.of5.148 X 10-10 m2 s-1. As diffusion coefficients vary as c2 (eqn. 3), particular attention should be paid to the analyses. Determination of c from the colorimetric evaluation of the dichromate remaining after reduction by sucrose gives concentration values with an average standard deviation of 0.7% while analysis by the method of Hodge and Hofreiter gives an average standard deviation of 3.7%. The absorbances of solutions treated by each of these methods decrease an average of 2% and 8%. resoectivelv. over a 16-hr Deriod. Ten trial; using the new cell give an average value of D for m2s-I with astandard 0.2 M K2Cr207a t 25% of 1.48 X deviation of 0.03 X 10-9 m2 s-'. The mean values of 125 runs carried out by students for both 0.1 M and 0.05 M K2Cr207 are 1.50 X m2 s-' with the average standard deviation within a set of runs being 0.25 X 10-9 m2 s-'. The results are m2 s-' a t in good agreement with coefficient of 1.47 X 25°C estimated for 0.05 M dichromate by exponential extrapolation of published values ( 5 )of D at 12'C and 18'C. Originally the stopcock type cell, being glass, was designed t o make possible observation of the diffusion of colored solutions so that some explanation could be found for the poor results we were obtaining with the Polson type cell. Runs performed in the new apparatus without temperature equilibration show significant mixing of the liquid columns by convection. This explains why most of the results we obtained with the Polson unit a t room tem~eraturewere rather hiah. Kquilibration, which is quite con\.enient hecause of the cell geumetry,eliminates the problem. It should benoted that with the stopcock type unit equilibration beiore a run issimplitied hy ihe fact that the e~lutionand the solvent rolumns are simultaneously open and free t o expand or contract. Another advantage of this unit is that before the start of a run any air bubbles which might subsequently affect the boundary area are easily seen and are removed with a plastic-tipped pipet. When data obtained in the undergraduate laboratory with the Polson type unit gave coefficients approaching zero it is probable that the greasing of the mating surfaces was faulty and allowed seepage from the liquid column interfaces. On a
a
680 1 Journal of Chemical Education
few occasions small scratches necessitated the major operation of re-milling the surfaces. Problems of leakage in the stopcock type apparatus have yet to he encountered. A drawhack of the stopcock t!ye apparatus is that sinre the l'eflonm is soft, the bore cannot be marhined tu the tolerances of the cavities in a steel unit. This uncertainty in the bore dimensions and hence the interfacial area can cause sienificant error in D which depends upon A-2. ~urthermore,since(a) the bore in stopcock A can be straight for no more than 78mm, (b) the cross-sectional area of the bore of neck A may vary somewhat with distance from the interface and (c) there is a slieht deviation from simole one-dimensional diffusion because of the interfacial curva&e, it is reasonable to suspect that the conditions necessary to the validity of eqn. (1)may not be met. However, as the values of D show no systematic trend with increasing diffusion times and distances. it is evident that these prohiems are not significant within the accuracy of the experiment. Hence, although there are practical limitations to the stopcock type diffusion cell, its simple construction and ODeration, its dependability under c l a s k m conditions, and i n the case of runs using colored solutions, its ca~ahilitvto allow observation of the phenomenon of diffusion;all make it particularly practical and instructive for use in an undergraduate experiment. Acknowledgment The assisrance of Mr. Steve Rak and Mr. Hill Henderson in the design and construction of the apparatus, and the assistance of Mr. Peter Borda in develonment of theirnalvticnl procedure is gratefully acknowledged. Literature Cited (1) Linder,P.W.,Na~simbeni,L.R..Polson.A.,andRodgem,A.L.,J.CHEM.EDUC.,53. ,en """ ,*o,c, \.".",. (21 Wilson. C. L., and Wilson, D.W.,"CompchhhhiiAn~IytiytiIChhmiitry~ V d nA,T%e Elxvier Publishing Company. 1964. p. 150. (31 Hodge, J. E.. and Hofreiter. B. T.. in "Methods in Carbohydrate Chemistry: vol. I, ArsrlnmirP....
" lR* .-.., -.
(41 Costing, L. J. sndMarria,M. S , J A m w Chem.Soe., 71,1998(19491. ( 5 ) "lnternetiod Critical Tables of Numerical Date, Physies, Chemistrys~dT ~ c h d ~ ~ ~ : 1st Ed., Vol. Y. McCraw-Hill. 69 (1924).
