T H E VISCOSITY OF SUPERSATURATED SOLUTIONS. I BY I. K . TAIMNI
It is well known that solutions of most substances can be cooled below their saturation point without crystallization, provided due precautions are taken to prevent the inoculation of the solution with the minutest crystal of the solid present in the solution. But if the process of cooling is continued, a temperature is reached a t which the solid phase makes its appearance even though the solution has been protected from introduction of germ crystals from outside. This phenomenon is known as the spontaneous crystallization of supersaturated solutions. H. -4.Miers and Florence Isaac’ examined supersaturated solutions of some salts like sodium nitrate and sodium chlorate and showed that, corrcsponding to every concentration of the salt, there was a definite temperature, a t which spontaneous crystallization took place. The line joining the temperatures at which solutions of different concentrations crystallized out spontaneously was found to be approximately parallel to the solubility curve of the salt and was called the “supersolubility curve.” An examination of the refrative index of the solutions showed that, as each solution was progressively cooled, its refractive index continued to increase, but, a t a certain temperature below the solubility temperature, its value reached a maximum and then began to fall. If the solutions was allowed to cool at rest in presence of growing crystals, this fall was gradual; but if it was stirred during the process of cooling, the fall in the value of the refractive index was abrupt and was followed by a shower of crystals. When the values of the temperatures a t which the maximum refractive index was attained were plotted against the concentrations of the solutions, a curve identical with the “supersolubility curve” was obtained. The sudden fall in the value of the refractive index was attributed by hliers to the sudden weakening of the solution as a result of the spontaneous formation of a large number of crystal nuclei in the solution which rapidly grow in size and produce the shower of crystals referred to above. It, therefore, follows from the work of hliers that a definite change takes place a t the temperature of spontaneous crystallization, a temperature at which the solution passes from the “metastable” into the “labile” state. A number of investigators have examined various physical properties of supersaturated solutions with a view to find out whether the solutions undergo some sudden change a t the solubility temperature, a change which will manifest itself by the curve-representing the physical property in question-showing a break a t the saturation point. Thus C. Heimz examined the electric conductivity and showed that none of the salt solutions examined exhibited J. Chem. SOC.,891,413(1906). Ann. Physik Chem., (3) 27, 673 (18863
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any sudden change in their specific resistance as they passed into the supersaturated condition. W. W. J. Nicol’ examined the specific viscosity of solutions of some salts a few degrees below the solubility temperature, and found that the viscosity curves are perfectly regular a t the saturation point, there is nothing to indicate any change in the constitution of the solutions as they pass from the unsaturated into the supersaturated condition. h similar result was obtained by K. Bindel2 who examined the specific gravities, specific heats, and heats of solution of supersaturated salt solutions. From the above investigations it is evident that a solution which is progressively cooled undergoes no sudden change in passing through the solubility temperature. lliers was the first to demonstrate the existence of a second definite critical point in the condition of a cooling solution. The first critical point is, of course, the solubility temperature a t which the solution passes from the unsaturated into the “metastable” region, a region in which the introduction of 3, crystal from outside is necessary to start the process of crystallization. The second critical point is the “supersolubility” temperature a t which the solution passes from the “metastable” into the “labile” region, a region in which crystals begin to form and grow spontaneously in the supersaturated solution. While the curves representing various physical properties remain perfectly regular in passing through the solubility temperature, Miers found that the refractive index curves of solutions passed through maxima at their respective supersolubility temperatures. It was, therefore, expected that an examination of other physical properties of supersaturated solutions might reveal similar irregularities in the curves representing those properties. A physical property suitable for an investigation of this kind is viscosity. The present investigation was undertaken with a view to measure the viscosity of supersaturated solutions. It will be seen that the viscosity curves, as far ns they have been traced, remain quite regular. We are, therefore, justified in concluding that the viscosity of a solution undergoes no sudden change below the saturation temperature. The viscosity measurements were made by means of an apparatus devised by Scarpa3 and used by F. D. Farrow4 for measuring the viscosity of soap solutions. I t was necessary to introduce certain modifications in this apparatus to prevent the inoculation of the supersaturated solutions with germ crystals carried by dust particles or formed at the margin of the solution through evaporation of the solvent. The method consists in measuring tho time tl, taken in drawing up, by suction, a fixed volume of the solution through a capillary tube, and the time tz which this volume of the solution takes in flowing out through the capillary tube under the action of gravity. J Chem SOC.,51, 389 (1887). Ann. Physik Chem., (3) 40, 370 (1890). 3 Gam., 40, 271 (1920). 4 J. Chem SOC.,101, 347 (1912).
1
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I. K. TAIhfNI
Given constant conditions, the viscosity of any liquid, according to Scarpa, is proportional to the expression
tl t z (tsmeasured in seconds). tl tz
+
or where K is a constant which can be determined by calibrating the apparatus with water. The great advantage of this method over the ordinary method lies in the fact that it is not necessary to measure the density of the liquid. It is extremely di5cult to avoid the inoculation of a Supersaturated solution with germ crystals in the process of the density determination, and hence the ordinary method which requires a knowledge of the density of the solution a t each temperature is practically inaoplicable in the case of supersaturated solutions. The work of numerous investigators has shown that the crystallization of a supersaturated solution is brought out by germ crystals introduced from outside. Provided the vessel containing the solution has been properly cleaned and the substance has been completely dissolved, the inoculation of the solution with germ crystals can take place either through the dust particles suspended in the atmosphere, or through evaporation of the solvent and the consequent deposition of minute crystals a t the margin of the solution. Modifications were, therefore, introduced into Scarpa's apparatus to guard against the inoculation of the solutions in either of these ways, and it was thus found possible to cool the solutions far below their respective solubility temperatures. Of course, in some cases, crystallization took place, owing to the formation of a few nuclei in the solution itself, but even in such cases, the crystallization was so slow that it w&s possible to determine the viscosity of the solution at temperatures some degrees below the temperature of spontaneous crystallization. The viscometer and the accessory apparatus used are shown in Fig. I . A is a cylindrical glass vessel with a side tube F. The mouth of the vessel is fitted with a rubber stopper through which passes a glass tube G connected a t its lower end with a viscometer consisting of a bulb B to which a capillary tube C is attached. The glass tube G can be put into communication with the aspirator H and thus suction applied to fill the bulb of the viscometer with the solution contained in the vessel A. The suction exerted depends on the difference of water level in the aspirator H and the beaker placed underneath, and its value is measured by means of the water manometer M. Before connecting the aspirator H with the viscometer, the pressure is always brought to a constant value-30 cm-by adding to or withdrawing water from the beaker. The difference in the manometer reading before and after each reading of time is not greater than one millimeter and thus the pressure remains practically constant during the process of filling the viscometer bulb. The U-tubes D and E are connected with the two-way tap T which puts one or the other of the U-tubes into communication with the air continued in
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the aspirator S. The mouth of this aspirator is fitted with a rose for producing a fine spray of water. This spray removes all the dust particles from the air contained in the aspirator, and thus all the air coming into contact with the surface of the supersaturated solution is free from crystal germs, which if present will bring about the release of supersaturation even in the “metastable” region. It is not possible to purify the air by passing it through water as this would disturb the pressure. a
N 1
FIG.I Apparatus for measuring Viscosity of Supersaturated Solutions
When the solution is to be sucked up into the bulb of the viscometer, the tap T is turned so as to put the U-tube D into communication with the air in the aspirator S, the clip at P is closed, and suction applied by opening the clip at K. When the bulb is to be emptied the clip at K is closed, and both the U-tubes are simultaneously put into communication with the air in the aspirator S, by turning the tap T and opening the clip at P. Both the U-tubes contain a small quantity of water which serves to maintain a vapour pressure at the surface of the solution higher than the vapourpressure of the solution itself. This prevents any evaporation of the solvent from the surface of the solution and the consequent formation of minute crystals near the margin of the solution. Theoretically, water should distil from the U-tubes, into the solution and decrease its concentration but in practice the quantity of water so carried over is so small as to be negligible. The aspirator L and the wash-bottle N serve to pass a current of dust-free air through the whole apparatus when necessary. This sweeps away any dust particles that may be hanging in the air enclosed within the apparatus. After closing the clip a t Q, water is made to flow into the aspirator L from the tap J . The air in the upper part of the aspirator is forced out, and after being washed in the Wolff’s bottle N, is made to circulate through the whole apparatus and then ejected into the aspirator S. When the aspirator L becomes full with
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water, the clip a t Q is opened and water made to flow out through the opening near the bottom of the aspirator. Purified air from the aspirator S fills the aspirator L and can be circulated through the aspirator as before. The parts of the apparatus surrounded by a dotted line are enclosed in a gas-heated water thermostat with glass sides. For temperatures below the room temperature iced water was added from time to time as required. As solutions of widely different viscosity were investigated, it was necessary to use viscometers with capillary tubes of different radii. With a particular solution, that viscometer was used which made the time of flow convenient to measure. Three viscometers were used but as these were calibrated with water, it was not considered necessary to measure their essential dimenions. For convenience sake, values of the expression ( ” are plotted against (ti tz) temperature. The absolute viscosity is proportional to this expression and can be obtained by multiplying the expression by the “viscosity factor” given with each curve. The value of this “viscosity factor” was obtained by alibrating the particular viscometer used with water. As the value of the ex-
+
+
pression ( -L-.L ) varies to a slight extent with the height of the liquid in the (tl t 2 ) vessel A, the “viscosity factor” gives only approximately the absolute viscosity. The relative value of the viscosity for each solution is, however, cor-
+
rectly given by the expression ( ti'tz ) because the height of the solution re(tl t 2 ) mains constant throughout one series of experiments. I n carrying out an experiment, a solution of known concentration was prepared by introducing a weighed quantity of the substance into a small flask and adding a measured quantity of water. The mouth of the flask was closed with a rubber stopper which was made quite secure in its place by means of a piece of string. The flask was heated in boiling water till all the solid had gone into solution. The rubber stopper was then removed from the flask and the solution-still much above its solubility temperature was carefully transferred to the bottom of the vessel A with the help of a piece of glass tubing. The rubber stopper carrying the viscometer was carefully replaced, the whole apparatus was lowered well beneath the surface of water in the thermostat, and after adjusting the viscometer in a vertical position, the solution was allowed to attain the constant temperature of the thermostat. The times taken in the ascent and descent of the solution were measured by means of a stop watch, several readings being taken for each temperature. The times of ascent and descent of the solution are influenced by the temperature and the pressure, and experiments were therefore made to detcrmine roughly the extent to which a slight error in the measurement of these affected the time of ascent or descent. It was found that a difference of pressure of I cm altered the time of ascent by about one per cent. The error in the measurement of pressure which could a t most be . 5 mm, could not, therefore affect ~
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the time of descent by more than .057~. The effect of slight error in the measurement of temperature depended to a very great extent on the nature of the solution whose viscosity was being measured, but even in the case of those solutions whose viscosity was greatly affected by change of temperature, an alteration of .os0C did not affect the time of ascent or descent by more than .s%.
FIQ2. Viscosit of Sodium Sitrate Solutions I. Soirution contains 50% Salt 11. Solution contains 51% Salt Viscosity Factor 33 X 10-5
Solutions of six substances-sodium nitrate, sodium chlorate, copper sulphate, sodium thiosulphate, tartaric acid and cane sugar-were examined. Two solutions of different concentrations were investigated in the case of each substance, in order to obtain an approximate idea of the effect of change of concentration on the viscosity of the solution. Sodium Nitrate, Sodium Chlorate and Copper Sulphate The curves in Figs. z and 3, which are very much alike, show the change of viscosity with falling temperature for solutions of sodium nitrate and sodium chlorate. It will be seen that the curves remain quite regular in pass-
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I. K . TAIMNI
ing through the temperature of spontaneous crystallization as determined by Miers. It was not possible to measure the viscosity a t temperatures very much below the temperature of spontaneous crystallization, because, when the solutions were cooled a few degrees below this temperature, minute crystals began to appear in the solution and ultimately blocked the capillary tube. I n no case did the crystals make their appearance in the “metastable” region, but only after the solution had been cooled a few degrees below the tempera-
40 0’
T€MWR4 TUP€
20‘
40‘
FIQ.3 Viscosity of Sodium Chlorate Solutions I. Solution contains 53.4% Salt 11. Solution contains 54.4% Salt Viscosity Factor 33 X IO-^
ture of spontaneous crystaIlization. It follows, therefore, that the appearance of crystals was due to spontaneous formation of crystal nuclei in the solution itself and not to the introduction of germ crystals from outside. The curves in Fig. 4 for copper sulphate solutions are similar to those obtained for sodium nitrate and sodium chlorate, except that the solutions could be cooled much below the solubility temperature before crystals began to appear in the solution. While in the case of sodium nitrate and sodium chlorate solutions spontaneous crystallization took place roughly about I O degrees below the saturation temperature, in the case of copper sulphate solutions, the first crystal did not form until the temperature of the solution had been reduced 3oO-40~ below the saturation point. No definite supersolubility data were available, but the curves, as far as they could be traced remained perfectly regular.
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611
Sodium Thiosulphate, Tartaric Acid and Cane Sugar The curves for these substances are given in Figs. 5-7 and differ in some ways from the preceding curves. Not only is the initial viscosity very much greater than in the case of the preceding three substances, but it also increases very rapidly as the temperature is lowered. For example, the viscosity of 66y0 tartaric acid solution at 10' is almost double that a t zoo and the viscosity of 7 ~ cane 7 ~sugar solution at 16' is almost three times that a t 26'.
Viscosity of Copper Sulphate Solutions I. Solution contains 38.3% hydrated Salt 11. Solution cgntaim 35.1% hydrated Salt Viscosity Factor 33 X 10-6
Another peculiarity in the c a a of these substances is the divergence of the two curves representing two different concentrations of the same substance. This means that the differenceinviscosityof the twosolutions becomes greater and greater as the temperature is lowered. In the case of sodium thiosulphate solutions, the difference a t 60' is about 5 units and a t joabout 3 j units. In the case of tartaric acid solutions, the differznce a t 60" is about I O units and
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I . K . TAIMNI
a t IO' about 2 0 0 units. In the case of cane sugar, the difference a t 60' is about 2 0 units and a t 15' it reaches the remarkable value of about I350 units. Although solutions of these substances were cooled 30O-45' below their respective solubility temperatures, no sign of spontaneous crystallization was
TEMPERAru&
0'
20
40.
FIG. 5 Viscositv of Sodium Tbiosulphate Solutions I. " Solution contains 75% hydrated Salt 11. Solution contains 70% hydrated Salt Viscosity Factor 24 X IO-^
obtained. I n some cases, after finishing the viscosity measurements; the solutions were placed in a freezing mixture of ice and salt, but even then no crystallization took place. The present investigation was primarily undertaken with the object of finding out whether the viscosity curves of cooling solutions suffer any marked change in passing through their respective supersolubility temperatures. Supersolubility data were available only in the case of two substances, sodium nitrate and sodium chlorate. Viscosity curves for solutions of these substances show no break in passing through the supersolubility temperatures as
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613
determined by Miers. I n the case of the other four substances, supersolubility data were not available, but the viscosity curves remain quite regular even 30O-45~ below the saturation temperatures. Of these four substances, solutions of only one, namely copper sulphate, exhibited anything like the phenomenon of spontaneous crystallization
FIQ.6 Viscosity of Tartaric Acid I. Solution contains 61.2% Acid 11. Solution contains 66.6% Aicd Viscosity Factor 24 X IO-(
minute crystals making their appearance in the highly supersaturated solution a t sufficiently low temperatures. In the case of sodium thiosulphate, tartaric acid and cane sugar solutions, there was no sign of spontaneous crystallization. Either the solutions of these substances do not show the phenomenon of spontaneous crystallization at all, or the lowest temperatures reached were still above their supersolubility temperatures. This inability on the part of these highly supersaturated solutions to crystallize out spontaneously may be attributed to the high viscosity of the liquid, on account of which the nuclei
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I. K. TAIMNI
formed in the solution take a very long time to attain the size at which they become visible. This latter explanation does not, however, seem to be tenable, a t least in the case of sodium thiosulphate solutions, which in spite of being very viscous a t low temperatures, crystallized out immediately on inoculating the solutions with a minute crystal of the salt.
FIQ.7 Viscosity of Cane Sugar Solutions I. Solution cont+ns 75% Sugar 11. Solution contslns 70% Sugar Viscosity Factor 22 X 1 0 - 8
SU-lW Viscosities of supersaturated solutions of six substances-sodium nitrate, sodium chlorate, copper sulphate, sodium thiosulphate, tartaric acid, and cane sugar-have been determined by means of an apparatus devised by Scarpa, and modified by the author in a suitable manner for measuring the viscosity of a supersaturated solution. It has been shown that the viscosity curves, in the case of sodium (2) nitrate and sodium chlorate solutions remain quite regular not only in passing through the saturation temperature but also in passing through the temperatures of spontaneous crystallization as determined by Miers. The refractive index curves of these solutions, according to Miers, pass through maxima a t the temperatures of spontaneous crystallization. I n the (I)
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case of the other four substances examined, no ‘supersolubility’ data are available but the viscosity curves, as far as they could be traced, ( 3 0 O - 4 5 ~ below the saturation temperature) remained perfectly regular. ( 3 ) Out of the four substances, only one, via: copper sulphate, exhibited the phenomenon of spontaneous Crystallization a t sufficiently low temperatures. I n the case of sodium thiosulphate, tartaric acid and cane sugar solutions there was no sign of spontaneous crystallization even when the temperature was lowered 3 0 O - 4 5 ~ below the saturation temperature. I desire to express my thanks to Professor Donnan for his helpful criticism and valuable advice during the course of this investigation. T h e S i r William Ramsay LaboratoTien of Physical and Inorganic Chemistry, University College, London, December 19, 1927.
