SOME SIMPLE EXPERIMENTS DEALING' with RATES of SOLUTION GEORGE W. GLEESON Oregon State College, Corvallis, Oregon
T
HE purpose of the following is to describe briefly two simple, inexpensive, laboratory procedures dealing with the rate of solution of common salt. The significance of the experimental data can be obtained elsewhere (1,2, 3) and any discussion of the development of theory beyond that necessary for elemental treatment is omitted from this writing. It is con-
According to the Berthoud-Valeton Theory (4), the rate of solution of a crystalline substance depends upon rate of diffusion and a first order surface reaction. This fact can be most simply expressed as,
Where W is the weight of undissolved solute 0 is the time S is the surface area of the undissolved solute C, is the concentration of solute in solution a t saturation Ce is the concentration of solute in solution at time 0 K is a constant Equation 1 is for a second order process; however, by maintaining negligible concentration of solute in the solution, the diffusional resistance drops out and a first order process results wherein the rate of solution depends only upon the surface area of undissolved solute. Figure 1 shows the simple arrangement of apparatus for study of the first order process. A constant head is maintained by an overRow weir which is supported by a ring stand. The container is a common crock with bottom opening and overtlow, in which a laboratory tripod supports a 48-mesh screen. The
sidered that the experiments contain all of the essential elements desired in elementary laboratory instruction; namely, the procedures can be completed in less than three hours; the equipment and supplies are relatively inexpensive; no particular manipulative skill is necessary, and adequate treatment of the data in the form of a report or write-up calls for ingenuity and the application of some mathematical procedures. The last-mentioned element is too frequently omitted from the "cook b o o k type of experiment. Furthermore, the simplicity of the manipulation and the rather farreaching significance of the results are generally a surprise to students.
FIGURE 2.-SALT CUBESA ~ E RVARIOUS PERIODS OF SOLUT~ON
solvent (water) flows past the salt cubes on the screen a t a rate such that salt accumulation in the water is negligible. The ordinary tap water supply is usually of a uniformity of temperature sufficient to maintain essentially isothermal conditions.
187
The salt cubes are prepared by sawing one-inch cubes from a block of ordinary stock salt. With reasonable care, perfect cubes can be prepared. Six or more of these cubes are weighed and measured, and arranged on the screen in known order. The screen and contents are submerged and the time taken. At the end
Equation 4 indicates that a plot of W'h versus 9 should yield a straight line on ordinary coordinates with an intercept at-0 = 0 of C/3 and a slope of K f / 3 . Verification of this fact and a comparison of previously calculated results with the experimental results are the subject of discussion required in the student report. Table 1 and Figure 3 are included to illustrate the results which may be obtained by following the procedures described. Figure 4 illustrates the laboratory apparatus necessary when the second order process controls. A twoTABLE I EXPBPIXENTAL RBSVLTSPROM PDISI.OXDBRPBOCBSS ~irne-8
wcipkf-w
mi"u1.l
corn
0 10 20 30 40 50 60 70 80
32.0 25.1 18.2 14.6 8.8 7.0 4.03 2.68 1.35
equation 3WlJi = K'e equation simplifies to
n " 0
/
0
2
0
J
O
4
0
5
0
6
0
W
~
oa SOLUTION BY
OB
THE
+ C, fore - 0. C = 3(32)'1:
= 9.54 ao the
3.18 4- K"8.
~
TXC-MINUTES FIGURE3.-RESULTS
Wl'"
wcilht-w"r cam 3.18 2.93 2.63 2.44 2.07 1.91 1.59 1.37 1.11
liter beaker contains the solvent, and a l'/z- to %inch salt cube as cut from a block of stock salt is the solute. The larger the salt cube in comparison to the amount
MEASUREMENT OF RATE FIRST ORDERPROCESS
of every ten-minute period, one cube is removed from the solution, roughly dried with paper toweling, and placed in a drying oven. E v e ~ ytime a cube is removed, the remaining cubes are rotated to rest on a new face, thus maintaining the approximate cubical shape by distribution of "stream lining." After all cubes have been removed and dried, they are again weighed and measured. (Drying a t llO°C. for forty minutes is sufficient.) Figure 2 illustrates the condition of ten cubes after solution as described above for periods of from ten to one hundred minutes. Returning to a consideration of equation 1, elimination of the concentration terms gives,
Since, for geometrical solids, the surface area is proportional to the weight to the two-thirds power @roof of this fact is left to the student) we may express equation 2 as,
Integration of equation 3 gives,
3wX
= K'8
+C
(4)
where Cis the constant of integration which may be obtained by substituting the weight of cube number one a t 0 time.
of solvent, the more definite will be the evidence of the effect of concentration upon the solution rate. Air agitation has been used in the past, but more satis-
factory results are obtained by mechanical agitation, since the air bubbles tend to cling to the basket. The procedure is to obtain the basket weight submerged, the weight and measurement* of the salt cube and, finally, the weight of the basket plus salt cube submerged a t zero time. The agitation is maintained a t a uniform rate and intermpted every five minutes in order to obtain the submerged weight of cube plus basket.
The weighing procedure is repeated a t five-minute intervals until sufficient data are available. Equation 1 is applicable for the second order process. C, is, of course, a constant as obtained from solubility tables, but Ce is a variable quantity and is evaluated as, Ce = WO- W Where Wo is the weight of the cube (unsubmerged) at 0 time. W is the weight of the cube (unsubmerged) a t any time. substitution of - for - and w z / a fnr S gives
wn w
dW = KrlV2/s(C.- Wo
F
ca
+ M')
The area under the curve (obtained by square counting, with a planimeter, or by weighing cut sections on a balance) gives the value of the left-hand side of the equation, and these values are plotted versus 0. Equa-
tion 6 indicates that the latter plot should be a straight line passing through the origin and having a slope of K'. Furthermore, if a plot of ?Vlaversus €Iis constructed, inspection will show that the second order process approximates the first order process a t the start when the concentration of salt in s6lution is small, and that the deviation from the first order process iucreases as the concentration gradient is diminished by the increase in concentration. Table 2 and Figures 5 and 6 are included to indicate the results that are obtained in class work according to TABLE 2 EX.BP~XBNT*L
RESULTS1
1 ~ SB-ND 0 ~
OEDBP
Weight of cube-& Wdghl u ~ i r -w : i v ~ i ~ u t zmewed r dissolvrd solved 8 . WaYCo-U') Tinzc
-s
sub-
z
PROCBSS
pv6
-
/
~
(5)
C, - Wo is a constant which can be designated by Co. Substituting this value and rearranging for integration between limits gives,
The left-hand side of equation 6 presents some difficulties; consequently, students are advised to integrate graphically by plotting 1
wyco - W')
versus e
the procedures described. It would probably be somewhat misleading not to call attention to the fact that as the concentration of the solution increases in the second order process, the buoyant effect on the cube
and basket is greater and the recorded loss in weight is due to the sum of the loss of weight of cube plus decrease in weight due t o increased buoyant effect. Applying suitable corrections presents the student with a difficulty that requires some thought to master. In conclusion, the writer believes the experiments as described offer an opportunity for mathematical
interpretation of results, information of real significance, and training in analyzing experimental data, that are seldom encountered using such inexpensive equipment and requiring such elemental laboratory technic. Furthermore, the students exhibit a lively interest in an experiment which combines the several elements of their training.
LITERATURE CITED
(1) HIXSONAND CROWLL, I d . Eng. C h . ,23, 923, 1002, 1160 (1931). (2) HEXSON AND TENNEY, PIOC. A . I. Ck. E., 31, 173 (1934). I d . Eng. Chcm.,25, 1196 (1933). (3) HIXSONAND WILKENS.
(4) J. C h . , Phys., 10, 625 (1912). See "Chemical engineers' handbook," McGraw-Hill Book Co.. Inc., New York City. 1934, p. 1474.
