(Kinetics of Sucrose Crystallization)
SUCROSE=SALTSOLUTIONS ANDREW VAN HOOK AND D. SHIELDS The activity theory of sucrose crystallization developed in the preceding paper is applied to the crystallization in the presence of electrolytes and nonelectrolyte impurities. Interionic theory indicates a maximum in the salt effect
and a common denominator in terms of the ionic strength to explain the effects of different valence type electrolytes. Molasses-forming constituent* are accounted for in a semiempirical way.
ALTS generally reduce the velocity of crystallization of pure
amount of salt present and should be stronger for the highervalence electrolytes. Should ,5 be positive, the salt effect would likewise be positive (this case corresponds with a reduction in solubility and attendant increase in activity coefficient, since in saturated solutions Gorution = Golid = constant = r m ) . With an irregular value of B either maxima or minima are expected for the velocity ratio curves. All of these effects have been observed (a, 4, 8,9, f I , IS, 16, 19, 81) but unfortunately much of the data is not amenable to a quantitative test. Ilucharenko (fa) supplies some data on the velocity of crystallization of sucrose in the presence of calcium oxide, calcium chloride, and sodium carbonate. It is only the last which is suited for the present analysis since the solid phase crystallizing in the first cases is not specified. Table I, from Kucharenko's results, presents the results of computations of the effect of sodium carbonate on the velocity of crystallization of sucrose at 50' C. The constancy of ,5 (percentage basis) is not too good, and the concentration range is small; but there is a suggestion of a value of the order of 0.2-0.4. Reduced to ionic strength dimensions, the lower value becomes:
S
sucrose solutions (8,6,9). In terms of the preceding analysis this reduction in velocity may be interpreted as a consequence of the effect of electrolyte on the activity of the nonelectrolyte (salt effect), Direct experimental information is not available to test this suggestion; therefore we shall assume the applicability of the reasonable equation (IO, 89): log
Ilmuorom
= BP
where p = constant of proportionality
This type of equation was first derived by Debye and McAulay (7)) and Scatchard (90) to describe the effect of electrolytes on nonelectrolyte activity, and was validated by the experimental work of Belton (a). Coupled with the result that log ?morae = bm for the Bucrose concentration effect alone, for sucrose-salt solutions log
Y
-
bm
+
+ Br -
(a asstd.), then becomes for The velocity equation, Vel. pure sucrose and sucrose-salt solutions, respectively: =i
+ ko &.,a.= koa = korm = komebm (Vel.).uorWe+ .nit
+ k&
-td.
= kom ebm
+ @#
Since the saturated solutions in both cases are in equilibrium with the same solid phase, it is possible to eliminate the term k . t d . from these equations by taking the difference. However the result, (Vel.).uol.ne
-
+
5
komebm(l-J'p)
(VeI.).uorw -o.19,, log (Vel.).uarw Compared to the generalized result of Figure 1, log (k;at/k;,or,) = -0.057~~it is surprising that the constants evaluate within a ratio of 3, in view of the wide differences in the velocity data used. In Figure 1 the data of Amagasa are represented in the coordinates suggested by the above equation; except for sodium sulfate, which Amagasa mentions &s being unusual, the result is gratifying. The general trend seems to be a linear curve, represented by log (k;.~t/k.~-) = - 0.057~, which falls off at higher salt concentrations. Similar results were obtained with sodium sulfate at high concentrations in this investigation. It was o b served that this salt does not follow the usual additive rule for ~
is not particularly advantageous, and the
ratio
ia preferred, for it accounts directly and qualitatively for the observed effects of salts upon the crystallization velocity of sucrose. If kaGh.td.is ignored relative to the velocity faaton, this equation reduces to P
Br
usually negative, and therefore a decelerating effect of salts is expected. This reduction should be proportional to the @ is
d 1
1.6
$0.6
a
-Y
0.4
-
a
Q
-
V
0
v
e
1
I
I
I
1.0
2.0
8.0
Ionic strength
1
Effect of Electrolytes on Velocity Constant at 30' C.,According to Amagasa (2) 0 NaCl; 0 KCl; A YaKOI; V KzCOI; d VazWhr b N ~ C I H I O0 Z~ KC:HtOl.
Figure 1.
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November, 1944
INDUSTRIAL A N D ENGINEERING CHEMISTRY
refractive index and also promotes more inversion than do other Sl3lts. A more critical test of the interpretation suggested would be the use of data designed specifically according to the prominent features of the theory. Thus the crystalliiation velocity of sucrose in the presence of polyvalent ions above the 1-2 type studied by Amagasa should be decisive in approving or rejecting the foregoing analysis, as would more revealing information about the constant term.
limiting value is inserted in Figure 2, and there seems to be rough conformity. However, at a not unreasonable value of lo-' for the ion radius, a, the net value of the bracketed term becomes negative and increasingly so a t higher concentrations. Hence the complete log y s - ~curve should exhibit a maximum and steadily decreasing slope thereafter. This first feature is exhibited by sodium acetate in Figure 1, and the second feature is displayed by all the salts reported except sodium sulfate. This same equation accounts qualitatively for the effect of salts on the solubility of sucrose. Since the same solid phase of the same activity occurs in all cases in equilibrium with the various saturated solutions, and since y &st increases and then decreases, the solubility should exhibit a reciprocal behavior of passing through a minimum. This is true for the majority of =Its for which data are available (8, 16). The results of Amagasa (8) were extended, especially with higher-valence type salts and a t low concentrations, and are given graphically in Figure 2. Most of the results were obtained a t an initial sucrose supersaturation of 1.15; although additional values a t other concentrations confirm the indication of the above equation that the salt effect should be independent of the nonelectrolyte concentration. The refractive index was ascertained to be additive in the case of added salt as reported by Amagrtsa (8), with sodium sulfate the only exception as already noted. Trivalent cations seemed to promote discoloration which, however, could be minimized by rapid cooling after solution. The nature of the coefficients in the dielectric constant equaas C2 a&*), was determined by a remtion, DO= D(l nance method. As reported by Akerlof (f), it was found that the addition of sucrose to water decreased the dielectric constant, and the effect continued regularly into the supersaturated region up to a coefficient of 1.2. A value for aa, of approximately 0.21 was realized a t this concentration. A t any definite sugar concentration the addition of electrolyte (NaCI, KCl, N&COa, NaCpHaOz, and NalSO, wcre observed) increased the dielectric
THEORY OF SALT EFFECT
According to the Debye-Huckel theory an aqueous electrolytenonelectrolyte solution may be described thermodynamically by the equation ( I 7):
where the function F, is the difference in free energy between the actual and the ideal solution; D and DOare the dielectric constants of solution and pure solvent, respectively, and are to be interrelated by the equation, Do
-
D(1
+ a2Ct + uaCd
Subscripts 2 and 3 refer to the electrolyte and sucrose concentrations, respectively. Concentrations C are given as in moles per liter, and C = n/u. b is an average ionic radius usually of the order of 10-6 cm. If the electrolyte is composed of Y+ positive ions of valence z+ and Y- negative ions of valence t, the quantities v and ware defined by the equations: y
Y+
+
1049
+ + +
v-
For the case of interest,
is the ionic strength, e is the unit electronic charge, 1 / ~is the effective diameter of the ion atmosphere, and z is a function of a and a, the effective finite diameter of the ion. Since b F , / h k?' In ya, the above equation gives the following result: p
-
1.6
-
Q 0.8 m
> 0.6
2.0
3.0
i
I
I
9'
d
*,-
1.0
.e
1.0
-
a -
d
d
x
D
P
-
d
.
4
0
YO
A;.
L
0.4
Experimentally ar is a positive quantity; hence the net sign and size of the total coefficient depends on the relative magnitudes of b, K, and +all positive quantities. I n the limiting case the second term under the brackets reduces to zero, and the equation becomes:
b
I
I
e
Upon inserting usual values for the various items in the coefficient, and using the value of a: = 0.21 at SO = 1.2 from ap-
proximate dielectric constant measurements, the value of the coefficient in Brigg's loparithmia terms becomes 0.60. This
0.1
0.2
0.8
0.4
0.6
Figure 2. Effect of Electrolytes on Velocity Constant a t 30' C., According to Van Hook arid Shields (Semilog Scale) 0 NaCl 4 0 KNOai A MgSOq V NarPO4i 0 Na2-4: D (NH&SG$ X d u m oitratei KaFe(CNh and KtFe(CN)s.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 36, No. 11
Figures 3 and 4 approve the suggestion that a semilogarithmic plot is superior to Cartesian coordinates for representing data in a linear manner. The values for these plots are taken from Figure 4 of Nees and Hungerford's paper (18)' and the purities are represented directly without conversion to a molal basie. At any fixed purity the approximate equation suggests that the ratio of intercepts should be in the ratio of the velocities of pure sucrose solutions. The ratios are 3.5 a t the left-hand side of the c w e and 2 a t the less pure side; the ratio for pure solutions is 2.3 (16). Additional observations (14, 22) confirm in a qualitative way the general features of this activity interpretation of crystallization from molasses.
TABLE 11. EFFECTOF CARAMEL ON VELOCITY OF CRYSTALLIZATION O F SUCROSE
30
Figure 3.
40
35 Impurities, per cent
Relative Velocity a t aupersatn. Coefficient of: 1.01 1.02 1.03 1.04 0.88 0.90 0.91 0.90 0.79 0.73 0.64 0.67 0.76 0.60 0.37 0.60
Effect of Molasses Impurities on Crystallization of Sucrose (Semilog Scale)
xs
-
1.wr os0
-
1.04
constant but not quite linearly. Precise measurements were not made and the limit of measurement with the apparatus used was only to a value of AD = 20 and a salt concentration of p = 0.05 (KC1). MOLASSES CRYSTALLIZATION
The complete description of intensive properties of any solution is given by the Gibbs-Duhem equation,
cni
dps
= 0
f
which reveals that We would be able to compute the activity of sucrose in any solution if we had the values of the activities of all other components of the solution. Lacking this information for the molasses constituents of an impure sirup we can only extend the previous equations in agreeable directions. A first suggestion is log y * bm
+ h + BM
where M is the molality of the nonsugars and B , as 8, is unand doubtedly negative in contrast to positive b. The terms BM are tantamount to an interpretation (6) based on the formation of a sucrose-electrolyte-nonsucrosecomplex.
TABLE I. EFFECTO F SODIUM CARBONATE ON CRYSTALLIZATION VELOCITY OF SUCROSE Coefficient 1.02 1.03 1.04 1.05
2% salt 0.27 0.20 0.19 0.18
8, Percentage Basis 1% salt 0 . 6 % salt 0.38 0.47 0.27 0.35 0.25 0.32 0.31 0.24
Again no suitable data are available to test this equation quantitatively. Upon reduction, as before, the result, log (Vel.impure/ Vel.,,,) p. B M , indicates that the effect on velocity of a nonelectrolyte impurity should be exponential in terms of its concentration, and that the relative effect will be greater a t lower supersaturations. Table 11, assembled from Kucharenko's data (I@, confkms'this suggestion in a qualitative way.
30
35 Impurities, per cent
40
Figure 4. Effect of Molasses Impurities on Crystallization of Sucrose(Cartesian Coordinates) X So
-
1.011
0 So
-
1.04
Several series of experiments (Figures 5 and 6) were performed in which the initial sirup was, in most cases, a t a concentration of SO= 1.08. As observed in the case of added electrolyte and according to theory, experiments at different sucrose concentrations reveal the same relative lowering of the velocity by equimolal amounts of impurities. The dextrose curve is just about half the displacement of the invert sugar curve; on a weight basis the two become identical on account of the 1/2ratio of molecular weights. Since the invert sugar used was an equimolal mixture of dextrose and levulose, the results for levulose would have to be the same as for dextrose. The caramel was made by heating sucrose a t 200" C. under vacumn until 60% of the initial weight was lost, leaching with hot methyl alcohol, and evaporating the clarified water solution. A molecular weight corresponding to the formula of saccharan, C I Z H ~ Owas ~ , employed for expressing molalities (6). Ammonia, phenol, aniline, and ethyl alcdhol fall approximately on a common c w e , out to about 2M with apparently a diminishing effect a t still higher concentrations. All of these substances have a depressing effect on the solubility of sucrose in water a t the concentrations used (19, 16) and therefore should ha9e a contrary accelerating effect on the basis of any straightforward supersaturation theory of reaction velocity. Amagasa (2) finds similarly that solubility cannot be completely
INDUSTRIAL A N D ENGINEERING CHEMISTRY
November, 1944
correlated with velocity effects, although the pattern found in the preceding paper with electrolytes follows that demanded by salting-out theory. I n general, salts (noncomplex formers) have an initial depressing effect on the solubility of sucrose in water, changing to increasing solubility at higher concentrations (2,26). This leads to the maximum observed in the velocity ratio curvea. I n most of the mixtures investigated, the refractive indices were additive in terms of the concentrations of constituents of the solution. For working purposes a linear calibration curve was drawn between the refractive index and the supersaturation coefficients in terms of the sucrose and water constituents. I n aeveral cases the linear additive rule was confirmed by a complete series of synthetic mixtures. Only in the case of sodium sulfate, aniline, and gum acacia was the rule found to be unreliable. The de Whalley rule for invert sugar mixtures did not apply at the high concentrations used (24). 2
1061
for these substances, and only in the case of ammonia was an amount found sufficient to indicate appreciable adsorption; 4.7% of the original ammonia (4 M) was found on the crystals. The behavior of the majority in this way would seem to eliminate the possibility that the diminished velocity is the result of an impeding adsorbed layer; possibly this does occur with ammonia. 1.0 r I
6
1.
a0
100
Molassss oonstrtuent, grama/lOO gram water
Figure 6. Effect of Molasses Constituent on Velocity Constant A composite run was performed in which the contaminants W invert sugar. Areduction were 2 M sodium chloride and 2 i to 0.30 was computed from the inof log (Vel.impun/Vel.pure) dividual results; that observed was 0.27, confirming the equation:
i
‘ci
,B
0.
f
The results in Figure 6 are for blended mixtures of pure sucrose, water, and a cooking molassw which ww arbitrarily assumed to contain 50% of molasses constituent, 30% sucrose, and 20yo water. This arbitrary assumption probably accounta for the deviations in the early part of the curve.
1
LITERATURE CITED
(1) Akerlof, J . Am. Chem. SOC.,54, 4133 (1932). (2) Amagasa and Nishiaawa, J . Chem. SOC.Id., Japan, 39, Suppl. 0.0
I 1.0
I
I
I
2.0 Molakty
8.0
4.0
Figure 5. Effect of Nonelectrolytes onvelocity Constant Oinvertmuear; bdextnmm; 0 ammonia; A hand; Vnnillne; d ethyl alcohol; X oaramaT
The effects of colloids me of interest and, perhaps, of practical significance. Since such materials have little effect on the activity of solutes, it follows, according to the present activity interpretation and the inference that viscosity is not a ratedetermining factor, that colloids should have little effect on the rate of crystallhation of sucrose. A sirup was made up in which the amount of gum acacia was approximately one sixth the amount of sucrose which, with the water present, was equivalent to a coefficient of 1.08. The viscosity of this sirup, by the rising bubble method, was approximstely twenty-five times that of pure sirup of the same sucrose-water ratio. The velocity of crystallhation observed was practically the same (99%) as that of pure sirup. Similarly it was observed that amounts of starch up to 6% of the weight of sucroee had no effect OR the velocity of crystallization of these seeded solutions. The crystals grown at a reduced rate in the presence of phenol, aniline, ammonia, acacia, and several electrolyta were tested
Binding 263 (1936). (3) Belton, PTOC.Leeda Phil. Lit. Soc., Sci. Sect., 4, 178 (1932). (4) Birkett, Intern. S w a r J., 38, 12 (1936). (6) Browne, C. A., and Zerban, F. W., Handbook of Sugar Analysis, 3rd ed., 1941. (6) Clamen, H., Centr. Zuckerind., 50, 97 (1942). (7) Debye, P., and McAulay, J., Physik. Z., 26, 22 (1925). (8) Dedek, J., Chimie & Mu&&, Spedd no., 563 (May, 1927). (9) Dubourg, J., and Saunier, R., Bull. doc. chcm., 6 , 1196 (1939). (10) Groaa, P., Chem. Rev.,13, 91 (1923). (11) Hruby and Kaajanov, &&tu CukTouaT., 56, 345 (1931). (12) Jackson, R.F.,and Silsbee, C. G., Bur. Standards, Tech. Papm 259,277(1924). (13) Kaurnetaov, A. F.,Suer. bdge, 45,9 (1926). (14)Krasil’ehohikovand Tsap, Khim. Referat. Zhur., 1940,No. 10-11. 120; Chum. Aba., 37,1021 (1943). (16) Kucharenko, I. A., Plantar Swar Mfr., 75, May-June, 1928. (16) Landolt and B6rnstein, Physikalkch-Chemkohe Tabellen. (17) MacDougal, “Thermodynamics”, 3rd ed., 1939. (18) Neea, A. R.,and Hungerford, E. H., IND. ENQ.CIIIM.. 28, 893 (1936). (19) ganders, IC., Chimie & indwtrie, Special No., 1147 (June,
isas).
(20) Scatchard, !&ana. Famday SOC.,23,454 (1927). (21) Simiru, J . SOC.Trop. Am. Taihoku Imp. Univ., 10, 420 (1938). (22) Smolenski and Zelsneny, Gas. Cukrownicta, 74, 303 (1934). (23) Taylor, H. S., “Treatise on Physical Chemistry”, 2nd ed., 1982. (24) Zerban, F. W., J . Aasoc. O&kZ d g r . Chem., 26, 143 (1943); ACS meeting, Cleveland, 1944.
PI%~~ODNTED before the Division of Sugar Chemistry and Technology at the 106th and the 107th Meeting of the AMERIOAN CEEMICA~ EOCIETY, nt Pittsburgh, Pa., and Cleveland, Ohio, respectively.
