edted bv
tested demonstrcitions
Experimental Procedure An overhead diagram of the experimental setup, as well as an idealized trial, is illustrated in Figure 1. Aclean, dry 3 112 in. Petri dish was placed on a sheet of graph paper. (This facilitated measurement of distances.) Thirty milliliters of deionized water was poured into the Petri dish and allowed to settle for about 3 min. The temperature of the water was not adjusted but measured as 2 2 "C. ~ Apiece of each of the combination of soluble salts.. avoroximatelv .. 3-4 mm (-118) in. size, was dropped simultaneously on opposite sides of the dish. The use of forceps was found to he the most convenient method of introducing the solid salts. The initial positions of the solid salt pieces were noted. A timer was started and the time for the ions to meet a t an
A Liauid-Phase Diffusion Ex~eriment Thomas M. Nemetz and David W. Oalll Cleveland State University Cleveland, OH 44115
When a piece of absorbent material (i.e., cotton or felt) is dipped into concentrated HCI and another in concentrated NH?, t h e corresponding vapors emanating from these pieces can he reacted in the gas phase to make a cloud of NH4CI. When such samples are placed a t opposite ends of a glass tube, the distance each vapor diffuses can be measured easily. The kinetic theory of gases (and more specifically, Graham's Law of Diffusion) says that there is a correlation between the molecular weight of the vapor and distance t h e compounds will travel: line of precipitation heavier compounds will travel a shorter distance. This is the classic demonstration of diffusion of gases ( I ) . Even though this method of using gaseous HCI and NHa seems a n ideal example of diffusion, the vapors are offensive to the smell and even potentially hazardous. Further, for student e x p e r i m e n t a l purposes, long glass tubes are required, which can be cumbersome and may represent a n additional hazard. A less offensive techn i a u e b a s e d on vrecivitation of insbluble salts from'the liquid phase, while not as theoretically exact, might show the same qualitative results: that heavy ions move slower than less mastime = t sive ions. We have developed a n experiment in which soluble salts on opposite sides of a Petri dish diffuse through a layer of water and meet to form a n insoluble salt. The distance each ion travels can be measured and related to their masses. Several combinations of cations and anions have been found that produce similar and consistent results in forming an interface where the diffusing ions meet. Piece of soluble While meant a s a laboratory exercise, salt supplying this experiment also can be performed cation on a n overhead projector and/or in a TOPS-type exercise. A demonstration has been published that used a Petri dish to illustrate diffusion in liquids, but no quantification of the diffusion time = 0 phenomenon was presented (2).
-
'Author to whom correspondence should be addressed. 2Becausethe graph paper used was marked off in terms of inches, we used English-system measurements in t h i s exoeriment. Metric grapn pnoer ma) be am a& cornrnon y, and NO^'^ PIOV oe measdremenls 10 lllc nearest I I . meler We lnai*.lne eva a o r s for po nl ng ~~~~
244
~
Journal of Chemical Education
GEORGE L. GILBER; Denison University Granvlle. OH 43023
Piece of soluble anion
Petri dish, with 30mL water Figure 1. An overhead diagram of the Petri dish liquid-phase diffusionexperiment. The graph paper that is used to facilitate measurement of the distancesthe ions have traveled is not shown for better clarity. At time = 0 (lower diagram),two pieces of soiuble salt are carefullydropped on oooosite ends of the Petri dish. At some later time iuooer .. . . diaaram). " . a line of orecioitation is er aent D stancesare meas.reo as snonn Tne tc4re snows an oea zeo zone d8prec p won most re% '5 are r,ol as e e n o slr o.leo a lho~gnmany are s~rors ng , reg~lar
,
interface, a s determined by the formation of a curve of precipitate, was measured. The distance traveled hv each ion on a line directly connecting the two initial positions was measured to the finest measurement on the graph paper, here to the 1116th of a n inch.' Figure 1 also shows a dia~~
Table 1. Chemicals Used in the Liquid-Phase Diffusion Trials Cation Source
Anion Source
Precipitate (Color)
~
lead (11) acetate,
potassium iodide,
P ~ ( c ~ H ~ o ~ ) ~ . ~ HK1~ o
lead (11) iodide, Pblz (yellow)
nitrate, Mg(N03)2'6H20
sodium phosphate, Na3POw12H20
magnesium phosphate, Mgs(P043(white)
potassium carbonate. K~C03.1.5H20
calcium carbonate, CaC03 (white)
set of salts were performed to sodium phosphate, calcium phosphate, check for consistency in time of Caz(P04)3(white) Ca(N03)~-4HzO Na3P04.12HzO diffusion and position of the interface. Most trials were comTable 2. Results of the Liquid-Phase DiffusionTrials plete in 3-6 min. After measureLents were taken. the solution in -~~~~ the Petri dish was properly disM. d+ Ions Distance of Ion Travel, inches' M. 6Hz0 posed of and then scrupulously dM+ M+ .6H20 Cation Anion cleaned in preparation for the next trial. 0.612 0.745 0.491 1.050 (f0.103) 2.138 (iO.218) Some hints for better perform- pb2' Iwere during the Mg2*+ ~ 0 1.833 4 ~(f0.036) 1.270 (f0.036) 1.433 3.908 1.533 course of this investigation. Having two people, one for each salt, ca2' + C03" 1.656 (i0.119) 1.390 (f0.116) 1.191 1.497 1.139 to count down together and then Ca2++ Pod* 1.792 (i0.072) 1.292 (i0.039) 1.387 2.369 1.371 simultaneouslv drop t h e each piece in place may he more convenient. Consistency of perform1.6 : ance (and, therefore, results) was established easily by use of forceps, so that the solid salt pieces were dropped a t the 1.4 same initial points in the Petri dish. As mentioned, the use of graph paper made for easier distance measurement. 1.2 Two small dots on the graph paper underneath where the Petri dish stands allows one to place the solid salt in about 1 the same position for every trial. Although most trials did not form a precipitate a s evenly a s indicated in Figure 1, many of them were surprisingly regular. The comhinations of solid soluble chemicals used and the O m 0.6 precipitate and the color formed a t the interface are listed \O in Table 1. + 0.4 Caution: Lead compounds are toxic and should be handled with care. Gloves should be worn when working with solid 0.2: lead compounds and solutions. Proper disposal procedures for lead should be followed. 0-. . , . , , I , . , 1 . . . 1 . ~ ~ r . ~ . I . . . I . ~ . I Results and Discussion 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 All four of the salt comhinations listed above gave consisdJd. tent results both in terms of the time it took for formation Figure 2. Plot of the inverse ratio of the solvated ion mass versus the of the precipitate, as well as the relative distances each ion ratio of the distances traveled. An x = y line is superimposed. in the precipitate traveled from its initial point. Tahle 2 shows the rHw distance data (including t h e standard depected that a heavier ion would diffuse the lesser distance, viations of the measured distances in the trials) as well as a simple inverse ratio was attempted. As indicated in the various relationships hetween these distances and the table, the ratio MfM+did not correlate very well with the masses of the ions. What should be pointed outfirst is the ratio dJd-, the ratio of the distances traveled by the posirelatively high precision of the distance results, despite tive and negative ion of the precipitate. the crudity of the experiment: the standard deviation is An ion does not travel in solution without a retinue, howabout 10% or less of the distance. in several cases less than ever; surrounding each dissolved ion is a sphere of solvent 3%. In these latter cases, the deviation approaches the molecules. Understanding the uncertainty in the assumplimit of the experiment, because for these trials the distion, we assumed that each aqueous ion moved along with tances were measured to the nearest 1/16. The point is a sphere of six water molecules. The ratios of the masses of that, despite the inherent simplicity of the procedure, these the ions plus six water molecules was determined and also diffusion results are reproducible. listed in Tahle 2. In spite of the naive model, the ratios Determining from first principles what relationship of (M_+6H~O)/(M++6HzOj are startlingly close to the ratios the masses of the ions would correlate to the distances dJd-. A plot of the two ratios is shown in Figure 2, along traveled is difficult; there is no kinetic theory of liquids with a n x = y line. t h a t provides a simple answer for liquids a s for gases. The aualitative results are obvious. There is a n inverse However, i t was felt that a naive approach was warranted, relationship between the ratio of the distances the ions mostly to determine if a simple relationship did exist hetravel in aqueous solution and the masses of the (hexa) tween ion masses and distances traveled. Because it is ex~~
~
~
~
~
~
+
s
zm +
.
-
2'
1
.
-/ 1 Volume 72 Number 3 March 1995
245
solvated ions. As indicated by Figure 2, the relationship is not exact; a decent fit is found using a second-order polynomial, but over-fitting of the data is perhaps something to be avoided for such a simple exercise. But the results of the four combinations of salts used here are making a statement: the less massive ion travels a farther distance than the more massive ion, and a better quantitative understanding of this phenomenon is perceived when a solvation sphere is considered. This is equivalent to the results of the gas-phase diffusion experiment mentioned above, and is sufficient to serve a s a laboratory experiment in a general chemistm lab setting. The idea ofhiffusion has been studied theoretically; however, i t seems difficult to apply in this liquid-phase case. There are several generalizations of gaseous behavior described bv Fick's laws (3):they include, for concentration gradients:
where J;. is the flux of comoonent i in the r direction. the concentration gradient is &;i 62,and D is a proportionality constant called the diffusion coefficient. For diffusion in a n ideal solution, the force causing the diffusion is balanced by a frictional force proportional to the viscosity of the liquid; the diffusion coefficient can be derived as (3, 4)
where n is the viscositv of the liauid and r i s the radius of the sphkrical particle;ihe other iariables have their classic definitions. This expression of the diffusion coefficient does not, however, depend on the mass of the ion, which is one of the easiest variables to define for experimental systems like these. It is also the variable of interest for gasphase diffusion. Simple diffusion theory does not address specifically why heavier ions diffuse faster than less massive ions, although i t is thought that the qualitative relationship should be obvious. Conclusion We have developed a laboratory experiment to measure the diffusion of ions in the liquid phase and to show that the relative distances of diffusion are related qualitatively to the inverse of the mass of the solvated ion. For the instructional lab, this experiment promises to be less noxious than the gas-phase experiment, although less theoretically obvious. However, the reproducibility of the data and the conclusions one can derive from the data show that the point that 'heavier moves slower'can be predicted and proven using the liquid phase.
The "Magic" Flask Rubin r at ti no' and John J. Fortman Wright State University Dayton, OH 45435 Pirketta scharlin2 University of Turku SF 20500 Turku, Finland Often demonstrations of even elementary concepts, such as the color changes of various indicators or using the scientific method to predict the sequence of color changes in a series of beakers (the spectral order of colors), can catch the attention of more "sophisticated" students by using an unexoected "trick" or a n element of "maeic." Because effective lecturing involves a n element of theater, why not make use of s i m ~ l tricks e to intrigue a class? Of course. our goal i s not to mystify and we7'explain" how the trick worked either a t the time of use, or a t a later time, if you wish, to give students the opportunity to figure the trick out on their own. The "magic" flask demonstrations described in this paper are a lot of fun to do, and student response is quite gratifying. There are several kinds of "magic" vessels that can be purchased from magic suppliers that appear to be empty on first pour, but can be used to pour repeatedly liquids while going "empty" each time. The commercially available one we have is made from aluminum and cost $45 over 10 years ago. I t has approximately a 2-L capacity, but the design is such that i t is difficult to use and is not a good container for the dilute solution of NaOH we normally use. In this paper we will describe two versions that work well and some demonstrations that may be performed with them. Our elegant version was fabricated for us by a skilled glassblower out of a 2-L round-bottomed flask. The estimated cost would range from $50 to $100 depending on your glass-blower. The dimensions given in Figure 1 are not critical, but the data presented in the table refer to these dimensions. The inner tube is 43 mm i.d. and 25 cm long. The annular space is about 3 mm and the clearance between the inner tube and the flat bottom of the flask is 5-8 mm. Although the drawing shows a 6 x 12 mm slot at 'Author to whom correspondence should be addressed 'Visiting Associate Professor.
Acknowledgment Sunuort for this ~ r o i e c from t the State of Ohio Board of ~eg&t.s is acknowiedged. We thank the reviewers for some excellent suggestions in revisine . ... ..the manuscriot. This rrrojecr is tin rxr(nsion i,f the Honor; (;ener:~l ('hemistry Prom:im ;it Cl~vclnndStatr I:nivrrsitv. ;~drnmistcredb y John R. Luoma. Additional support from David G. ~ e h e m a n n and Robert L. R. Towns is appreciated.
-
Literature Cited 1. Alycn. H. N.: uutton. E E. Tested Dmo~trirnlionrin Chrmr.%
6th od. Journal of Chemical Education Press: Earton. PA, 1965. 2. Ref. 1 , p202There isapparentlyamicmrealeTOPSexp~~im~nt~AIy~~,Micro-Chcmistry P~ertcd-TOPS#I511 us in^ s Petri dish to d~monrfratediffusion. but wa have bcen unable to locab, the rrference for s~leciFicr.We thank Lhe reviewers for btinfing thlr to our attention. 3. Atkins, P.i'hysiml Ci>miist!:v;W. H. Freeman and Company: Snn Francisco. CA. Jobn Wiley and Sons: New 1990:Alberry. R. A : Silbey. R. W. Ph.ysIcnl Chem~r#ly: Ydk. NY 1992. 4. Laoffer M. A. J. Cheln. Edrrc. 1981. .58, 250.
Figure 1. The all-glass magic flask. Dimensions in millimeters
246
Journal of Chemical Education
