Justin kina Natlonal University of Lesotho P 0 Roma Lesotho. Afrlca
A Spectrophotometric Method for Measuring Diffusion Coefficients
Although diffusion is a phenomenon that plays an impor-
tant role in many physical, chemical, and biological processes, simple quantitative experiments on diffusion coefficients a t undereraduate level are not readilv available. Recentlv. ~ o s k o v i t and s Derewlany ( I ) reported a n elegant method which the diffusion coefficient of Co(H20)62+ ions through a membrane was determined using absorbance for measurement of concentrations. Other methods for determining diffusion coefficients based on the ahsorption of radiation by solutes have been described ( 2 4 , and in all cases, special designs of apparatus were required for the source of light and its detection. I n this paper, we describe a simple method for measuring diffusion coefficients using a spectrophotometer and a colorimeter with their normal accessories. The diffusion coefficients for KN03, AgN03, LiN03, and CoC126HzO in water a t 25°C were determined and the values are in eood aereement with those calculated from ionic cunductances at infinite dilution. The diffusion coeffirient of CoCIAH.>O - at 31°C was determined also.
in
Experimental A DB-G Beckman soectronhotometer in double and sin& beam modes doperation was used iur measuring the atrawlmwrs uf the *elutions. I'smp. n -harp pencil. R reference line wa< drawn un the ~ n m n dglnrs side of n I em quartz snmple cell along the edge of the partition dividing the sample and reference cell compartmentsof the spectrophotometer. Four horizontal lines were then drawn at 2 mm intervals parallel to and below the reference line. The temperature of the sample and reference compartments was kept at 25.0 i 0.2°C by circulating water from an external thermastat bath. Three milliliters of distilled water were pipetted into each of the sample and reference cells which were then placed in the appropriate compartments of the spectraphotometer and allowed to stand for at least 1 hr so as to attain thermal and mechanical equilibrium. The maximum absorption wavelength (304 nm for KNOs,AgN03, and LiN03; and 510 nm for CoC1~6Hz0)was then set on the spectrophotometer and then a cqstal of the salt was dropped into the sample cell. The crystals sank to the botton of the cell without dissolving aonreciahlv. At selected intervals of time. ahsorhancesat 5 different .. Iewls were rec~rd~d. These readings were ~ t k hy m slding rhr a,mqde wll uy, ur dew nnd aligning the pencilled yraduatimsnn rheground c h s r ~ i d with e thetopedgeun thepartition betuemtheanmplcand reference compartments. At the end of the experiment an absorbance value A, was recorded from a homogeneous solution resulting from the mixing of the contents of the sample cell. For CoC126Hz0similar experiments were also carried out using a Corningarnodel253 colorimeter at 31°C. The colorimeter did not have a temperature control accessory and the temperatures were measured at the ends of the
0
0.50
100
1.50
2.00
2.50
3.00
xz A graph of inA versus 9 for KN03
0 t = 330mln O
t=610min
t = 770 min
Table 1. Data on KNO. used lor Plotting a Graph of lnA versus XZ lor KNOo t = 330 mln
9
A
t = 610min InA
A
InA
f = 770 mln A
InA
aa = intercspt: a, = slope: P = coeflicientof determination The experimental conditions approximate to those of a reflection boundary1 for an amount of diffusing substance deposited a t a time t = 0,in the plane x = 0. Hence a t t = 0, x = 0, c = co; hut for all values of x > 0, c = 0. For these conditions, it has been shown (6) that
runs.
Results and Discussion Typical data for measurements on KNOs are given in Tahle 1. The center of the beam for thesample compnrtment was 1.50 cm f n m the inside of the bottom of the cell when it was standine a t the base of the holder. hence the maximum value of the monitoring distance x from the plane where the diffusion began was 1.50 cm. The displacement of the cellupward was limited to 8 mm because greater displacements showed anomalies in the matching of the cells. Using a crystal of KMnOd, it can be demonstrated that the permanganate color first spreads out as a thin layer at the bottom of the cell before diffus~onbegins thus approximating to the boundary conditions. This condition applies as long as the Beer-Lamhert Law is obeyed. 676 I Journal of Chemical Education
The diffusion coefficient may then he obtained by plotting, for a given time, a graph of In c versus x2 which gives a straight line whose slope equals (4Dt)-l. Since absorbance A, is directly proportional to the concentration2, a plot of 1nA versus x would also give a slope which equals (4Dt)-1. The figure shows such plots for KN03 using the data in Tahle 1. These plots can he done on a Hewlett HP-25 using a curve-fitting linear regression program which would also give a value for the coefficient of the determination. Tables 2 and 3 summarize the results of five runs each for KN03 and AgN03. The A, values for KN03, with the exception of the last one, show that the amounts of the salt used in the experiments did not differ greatly. For AgN03, however, there was a relatively wide variation in the A, values. T h e higher the A was, the lower the diffusion coefficient was which is in agreement with the generally known trend hetween the
Table 2.
A.. 0.212
Time in min 225 420
Dlnusion Coefflclent of KNOt at 25'
D X lo5 cm2 see-'
3
1.88 1.81
Mean D X lo5 cmZSBC-'
1.00 0.98
Table 4. A Comparison of Experimental D Values from the Present Work Compared with Do Values Calculated from Llmitlng Conductances Limiting Conductances
1.85
Do X
(8)
loS
A-a
Salt KN03
73.50 71.44
1.93
AgNOa
61.92 71.44
1.77
LiNO*
38.69 71.44
1.34
CoCI2(6H20)
55
1.28
76.34
. . ."
C&12(6H20)
x lo5
DO..
1.88 0.07 1.57 0.08 1.4 i 0.1 1.29 0.10 1.36 i 0.08
+ +
T 25'C 25% 25%
Number of runs 5 (14 readings). 5 (10 readings). 3 (9
reading^)^ 25% 31%
3 (11 readings)' 2(6 readings)=
~eckmanspec~ophotamete.in double beam mode
Table 3.
DlHusion Coefflclents of AgNOs at 25' Mean
AP 0.300 0.324
0.456 0.575 0.789
Time in mm
D X lo5 cm2 set-'
P
300 360 360 540 1320 1080 300 540 420 1140
1.71 1.68 1.61 1.51 1.69 1.57 1.54 1.49 1.45 1.48
0.99 0.99 0.99 1.00 1.00 100 0.99 0.99 1.00 1.00
DX lo5 emZsecC 1.70
1.60 1.57 1.52 1.47
concentrations of the diffusing material and the diffusion coefficients. The diffusion coefficient for a strong electrolyte a t infinite dilution may he calculated using the formula (7)
....
-.
where T is the absolute temperature, ul and v 2 the numbers of cations and anions ti.om the dissolution of one molecule of the elertr(~lrte,z l the cationic charge, and XI and X, the equivalent Eation and anion limiting conductances. Tahle 4 shows the experimental D values from the present work and Dnvalues as calculated from limitine conductance. The experiiental D for AgN03 is relatively lowdue to the low D values for solution where lareer of the salt were " auantities . used as is indicated by the A, values in the Tahle 3. As expected the diffusion coefficient for CoC1~6H20at 31°C was higher than that at 25%.
Errors and Assumptions
In our calculations, D was assumed to be independent of concentration since eqn. (1) strictly applies under conditions where D is inde~endentof concentration. Considerinc! the A ~ N O e x ~p e r i m k s , however, where there is a markediariation in A, hence variations of values of co a t x = 0, it is evident that D varies with concentration. There are two likely sources of error; namely, initial disturbances due to the dropping of the crystals and convective effects due to the size of the cells. The sliding of the sample cell up and down caused no significant disturbances. Conclusions
The method described gives D values that are close to those calculated from ~imitin~conductances within experimental error. The simplicity of the equipment used as well as the technique is such that the method would he suitable for undergraduate laboratory projects for ionic substances with suitable ahsorhances and possibly demonstration experiments. A major disadvantage as a demonstration experiment is the time scale (6-40hr) required for the readings. Literature Cited (1) Moskovits. M. and nerewlany, L.,Edueafion in C h m i s t w 15 (1978). (2) Euersulo, W. G.and Doughuy. E. W.. J. Chem Phys. 41.663 11937). W. G.. Kindsvater, H. and Peteten, J. D., J. Cham. Phya.. 46. 370 (3)
M.,
Irll,
4 1 Hsm.s\. \ V and xpph$n\. 11 H. U...4cer Phlr Trurn.? b :Ill 19'18 :,. DFP.~L.\I,J ('HI.'V FIJI 1 ' I(..-* 1169 U' .I ."Pl,,~..n.(.t,em.~try." lBrtnl.-llnll. Inr EudleuodCIIII. U.1. 1911 w LI .r l i ~ ~ t' R.."I ~ ~( i d~ II 3 oucn.H h .rhp ~ h >1 hridl.l.t,) 7 IIA,,,~II. Publishing Carp. New York, 1958. 18) Gesser. HymanD.,"Descriptivo Prineip1osofChemistry:The C. V. Mosby Company,
~"d
.
Saint Louis. 1914.
Volume 57, Number 9, September 1980 1 877
~ ~ t ~ ~ .
