S T U D I E S I N VAPOR COMPOSITION, II.-(Coiztimed) BY H. R. CARVETH
Mechanical carriage of liquid particles In most work on vapor composition there has been ignored the question as to whether or not very small particles of the solution are carried over with the vapor. If such actually takes place, the velocity of distillation will be found to have a definite effect on the concentration of the distillate. Preliminary experiments made by Mr. V. H. Gottschalk confirm my own-no appreciable effect has been observed under our experimental conditions. Nore accurate experiments on this subject are necessary before the exact conditions for avoidance of this trouble may be determined. T h e study of the action of baffle plates and other engineeringsubjects is intimately connected with this topic. If it is possible to have distributed through a phase particles liquid or solid which by some physical property may be differentiated from other particles in the phase, it is necessary to examine such cases from the view point of theory. Recent work on the solution phase where colloids are present raises the question as to whether analogous cases for the vapor phase may not be found, i. e., where in a vapor phase there may be particles which are properly classified as liquid rather than vapor. Whether the effect on the properties will be as marked as on those of colloidal solutions is difficult to state ; the problem still remains open. Two components (one volatile), three phases - solid, liquid, vapor When in addition to a solution and a vapor phase there is present a second solution or a solid phase, the system is univariant. If one starts with a solution (at its own vapor pressure) and a great excess of the solid phases and passe, in the vapor of the volatile component a t atmospheric pressure, the system will tend to pass to the temperature at which three phases are i n equilib-
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rium at attnospheric pressure, and then to the tern-peratures a t which the two phases, vapor and unsaturated solution, exist under the same pressure. When steam was passed into a solution of calcium chloride mixed with a considerable amount of the solid, the temperature as indicated by the thermometer rose continually until, as in one experiment performed in a silvered vacuum tube, the boiling-point of 165" ( p = 744) was reached; after remaining at this point until the calcium chloride had all dissolved, the temperature fell, since the system was now striving toward the boiling-point of an infinitely dilute calcium chloride solution. T h e temperature rose, passed through a maximum and again fell; this, however, is not comparable to the other cases in this paper where the same phenomenon has been observed, because under the conditions chosen the range of temperature is not from the boiling-point of one substance to that of the other. Any one who has ever attempted to determine with accnracy the boiling-point of saturated salt solutions will appreciate the effect of varying amounts of the solid phase present. T h e method of vapor heating proposed i n this paper seems to offer a ready experimental method for such determinations. It will be found here, however, that the velocity of solution of some salts is very low and this may affect the observation, so that the actual maximum observed is not the highest temperature attainable, i. e., is not the true boiling-point of the solution. T h i s should be most readily reached by slow passage of the vapor and safeguarding from too great loss of heat. Readjustment between the phases takes place more and more slowly the greater the number of phases concerned. Some experiments on the variation in the boiling-point observable with saturated solutions were made for us by Mr. A. W. Browne. Making use of a saturated solution of ammonium sulphate, he found 1.65' (Beckmann) as the temperature at which the solid first started to appear. As more and more of the solid separated, the successive readings were 1.67, 1.70, 0.80,0.30, and 0 . 2 0 . When enough water had been added to form unsaturated solution, and the solution was evaporated until solid just appeared,
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the boiling-point (in a vessel of glass, nickel, or silver) rose to 1-68', showing that the change due to volatilization of ammonia could by no means account for the difference. Experiments repeated under many varying conditions show that potassium and sodium sulphates, chlorides and nitrates, behave like the ammonium sulphate -the presence of freshly precipitated solid phase lowers the apparent boiling-point of the solution. Further experiments by Mr. J. E. Root, whose results may later be published, confirm this fact. T h e regular Beckmann method has been used to determine the boiling-points of saturated solutions. but here again we have found the difficulty of the displacement of the zero reading with the velocity of heating. In work where one requires the true boiling-point for theoretical work, this Beckmann method will not do ; we resorted therefore to the method of vapor heating. For some time we made use of the apparatus shown i n Fig. I ; more recently this has been modified as indicated in Fig. 5, the object being to avoid expensive breakage and to allow of better control. T h e modification consists in making the apparatus in two pieces instead of one as was previously done. T h e lower end of the vapor heater passes through the cork of a joo cc distilling flask. T h e cork alsc carries a thermometer and a two-way stopcock, which serves either as a safety valve or as a means of adding more solvent. Into the inner tube was put pure salt, or saturated solution ; into the distilling flask a solution of the same salt saturated at its boiling-point. T h e vapor from the latter passes into the inner vessel. In the case of ammonium sulphate, fifteen successive readings made over an interval of one and a half hours showed a maxiniuni deviwith an increase in barometric presation from I . 53" to 1.5jo, sure of I mm. I n this case electric heating was also employed a t the same time that steam was being passed, but this was found not to be absolutely necessary, the extra supply of heat really serving to compensate for radiation loss. Concentration by superheated vapor That, by passiag in the vapor at a higher temperature, the
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solution may be concentrated very appreciably has been demonstrated in the case where vapor from a very concentrated calcium chloride solution was passed into a solution of magnesium sulphate. The apparatus employed is shown in Fig. 5. T h e amount of
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Fig. 5
effective work which can be performed depends on the differences of temperature and on the specific heat of the vapor. In this specific case the difference in temperatures of the vapors above the two solutions was about 20°, the specific heat of water vapor
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about 0.39 ; as a consequence, one gram of water vapor given off by the chloride solution would: if no heat loss took place while it was being transferred, carry with it from the boiling solution in the inner tube more of the solvent by giving to it about 8 calories per gram of vapor passed in, thus concentrating the solution in the inner tube. T h e more effective the protection from radiation losses, the more efficient must be the concentration. T h e application of this method would be a useless waste of time were it not that it is the only one which has been tried in this laboratory by which it has been found possible to determine with any degree of accuracy the boiling-point of a saturated solution, I t obviates the danger of superheating present in all work where glass vessels are heated over a free flame, does away with filling material and avoids the effects due to the presence of a solid phase. T h e readings are easily made, the maximum being chosen as the boiling-point, because it is coincident with the appearance of the solid phase which i n this case where transparent vessels are employed is easily observable. While for very exact work it may not be allowable to consider this maximum temperature as the true boiling-point, because supersaturation may be present, nevertheless the probable error may be obtained by comparing the result with that obtained by the converse method of solution. If so desired the very simple device of using a trap allows of the return to the outer boiling flask of the volatile component froni the inner tube, thus making the concentrator perfectly automatic and allowing of excellent control. I n this connection it might be mentioned that the very ingenious apparatus devised by Beckmann' may be applied to the method of determining vapor compositions by the boiling-point method employed by the author' for rough determinations. It is certain. however, that a vapor heater provided with a boiling vessel and trap will be far less fragile and just as serviceable as the new Beckmann type whether the apparatus be used for molecular weight or for vapor composition work. Zeit. phys. Chem. 40, 145 (1902). Jour. Phys. Chem. 3, 193 (1899).
Of course one may employ steam more highly superheated i n order to obtain more rapid evaporation if such is desirable. I n such a case as this, superheated steam is passed into the outer jacket of the apparatus shown in Fig. I , thence into the inner tube. Care must of course be taken not to have the water at such a temperature as to produce decomposition prodiicts. (In cases where calcium chloride solution is employed, i t must not be forgotten that at' its boiling temperature this solution gives off small amounts of hydrochloric acid.) I t is of course not necessary that the vapor of the solvent be used- any indifferent gas highly heated is also effective. I n technical practice the superheated gas or vapor is frequently passed over, but rarely through the solution being concentrated. I n the laboratory the method may be employed i n increasing the velocity of evaporation where material of construction is expensive, e. g., i n the volatilization of hydrofluoric acid from beakers which may not be heated externally. T h e extension of the method to the determination of physical constants is readily conceivable.
Two components, three phases - liquid, liquid, vapor , A few experiments have been made with liquids which are not thoroughly miscible even at the boiling-point. Chloroform, which was slightly impure, was passed into boiling water contained in the inner tube. T h e teniperatrire fell in about twenty seconds to 57.9" ( p = 743.8) and then rose slowly. O n passing the mixed vapors of water and chloroform into boiling water the temperature had fallen at the end of two and one-half minutes to 58.4" ( p = 751.7). In this case the impurities had a very marked effect. With benzene in the inner tube and water in the outer, the benzene had evaporated completely before the thermometer became constant. With positions reversed, the final mixture in the inner tube boiled at 68.85" ( p = 745.2). Nauniann gives the value of 68.8" at p = 741.5. T h e best conditions for observing the minimum correspond to those in the case of solid, solution and vapor, where the vapor
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from the system is passed into the same system held in the inner tube. This allows of a far inore speedy readjustment of all condition factors, and is the one which should be used i n all work where quantitative measurements are being made. Two components - four phases Starting with any invariant system, the mere increase of the volume of vapor will bring no change in the system. If, however, the vapor is capable of supplying heat, the change will be toward a univariant and then toward a divariant system. Among such caqes would have to be considered the cryohydric, eutectic and inversion points -(I) d i d solvent, solute, solution and vapor; (2) two solids, solution and vapor ; (3) one solid, two solutions and vapor. When but one of the cornponents is volatile, the phenomena as observed (e. g., constancy of temperature condition factors at invariant point) should be the same as those observable in simple heating or cooling work. When both compounds are volatile, the case is merely an extension of the threephase system offering little more of interest. Vapor pressures by differential methods If into the outer vessel one puts always the system with the higher vapor pressure and into the inner that with the lower vapor pressure, and keeps the apparatus at constant temperature a bubble of vapor may not pass through the solution unless the driving pressure is equal to the external pressure plus the column of solution in the inner tube. Equilibrium is present when the bubble does not pass through. T h e method then offers a variation for the demonstration of differences of vapor pressures at constant temperature as well as differences in temperature at constant pressure; it is tiot, however, of such great practical service as the latter. What constitutes a component ? T h e definition of a component is always given by reference to the number of limitations imposed on the possible number of constituents, every new condition lessening the number of components by one ; e. g., if one has the four possible constituents, K, Na, NO3 and C1, with only one limitation- that K - S a =
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+
NO3 C1 for every phase, the number of components is three.’ With a one-phase system the degree of variance cannot be told without imposing certain conditions : in‘ other words, phase separation is most intimately associated with the definition of a component. On the other hand, 2 7 it is found iiz separation work that certaiiz limitations are present, the coinponency as weZ2 as the variaizce may be discovered. If the phase has been separated and a further readjustment takes place with measurable velocity in that or some other phase in equilibrium with it, it is known that equilibrium has not been reached, that possibly there is some change in the components of the system, and hence that the variance is not constant. While making any kind of measurement in a phase, e. g., the determination of any condition factor, it is frequently found that the element of time has to be very carefully considered, T h e unwritten opinion of chemists seems to be that when such a change takes place in a one-phase system, there is present some change - physical or chemical. As an instance, one might take the case of methyl alcohol and acetic acid. When mixed in equivalent parts, the solution is homogeneous and the physical properties definite, but after a time, the physical and chemical properties have changed, the velocity of change depending upon the ‘temperature and other controllable factors. Among the properties whose change is most readily measurable is the ,vapor pressure. I n this particular instance the boiling temperature will fall as time passes. If the boiling-point changes with the time, it is certain that some rearrangement has taken place in the solution, -in ordinary indefinite langnage, some physical os chemical change ; the initial conditions were not those of equilibrium. Velocity of readjustment T h e velocity with which readjustment takes place now appears in a new light-,as an indicator of rearrangement in the solution phase itself. When benzene was passed into alcohol, os water into the solution of a non-volatile salt, the readjustment I
Cf. Phase Rule, p.
226.
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took place with great rapidity. T h e chemical or physical constants or condition factors did not vary with the time, - e. g., if the liquid in the inner tube was taken out and boiled for a long interval, there was no change observable on bringing i t back to its initial condition. This would not be the case if one passed methyl alcohol into acetic acid or vice-versa, or mixed and boiled the two materials. T h e study of velocity variations may indicate therefore whether one is dealing with a system in a state of equilibrium or not. An article by Christiansen on the boiling-points of mixtures of chloral and waterTshowed that by his method of determining boiling-points, h e could not reproduce the results, nor did h e offer a n explanation for the peculiar behavior. Other observers have studied the dissociation of chloral hydrate, obtaining contradictory results which Ostwald' records without offering explanation. Attracted by the difficulties of the subject, we attempted by means of the vapor heating method to rediscover the minimum which Christiansen had found. It was found that starting with chloral and water one minimum could be found very strongly marked, but that-the whole course of the curve was very uncertain, maxima and minima occurring in great numbers, but not reproducible at the same temperature. T h i s was probably due to the fact that in our endeavors to use small amounts of material, every operation changed the history of the chloral-water mixtures. T h e thermometer readings are not given as no attention was a t that time paid to the thermal treatment of the mixture and reproduction is therefore impossible. T h i s now indicated very clearly that in the solution some readjustment was taking place and that some new factor, probably the formation of chloral hydrate, was exercising an influence. I n such a case while one might, by referring to separation by crystallization or distillation, decide arbitrarily that the number of independent components was two, it is still conceivable that if the reaction velocity could be decreased the sys'Jour. Phys. Chem. 3, $35 (1899). Ostwald. Lehrbuch, I, 201 (1891).
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H. R. Carvetk
tein might on the same grounds be regarded as a three-component, water, chloral, and the compound. A case exactly analogous to the above was discovered by Nr. V. H. Gottschalk while studying the system acetic anhydride and water. T h e curves obtained by the vapor heating method showed singular points at different temperatures according to the manner in which they were obtained. When conductivity was employed as the analytical agent, further examination showed that this was because the reaction velocity even a t the boilingpoint is low. T h i s system may be regarded therefore not as a two but as a three-component system. T h e bearing of this on the occurrence of more than one singular point in the boiling-point curve of a system is obvious. T h e curve for one component A and the compound AB might show a maximum, a minimum, or might be normal ; the compound AB with the component B might also be abnbrmal or normal. Passing therefore from A to B and examining the boiling-points of mixtures in equilibrium, one might have numerous combinations, two minima and one maximum, two maxima and one minimum, etc. If more than one compound were formed, the number of singular points might be increased indefinitely. If compounds niay be formed and the measurement of the boiling temperature be made before equilibrium has been reached, the boiling curve for this instable condition may give one much information in regard to the formation or decomposition of compounds. At present the only one case of a two-component system which seems to show both a maximum and a minimum is the fluid pair, sulphur dioxide and methyl chloride,' which however has not been examined from this point of view. W i t h the facts above k7zowq oize nazd insist that i?z the future work the $rst step i ~ zthe exainization o f any biizary system is a n attempt io discouev iizdicntion of change. Among typical cases of systems which are apparently twoCaubet.
Coniptes rendus,
131,
108 (1900).
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component, but are not truly such, may be cited: sulphur trioxide and water, chloral and alcohol, acetone and chloroform, carbon and sulphur. T h e compound may show a boiling-point lying higher or lower than either component or else intermediate thereto. In cases such as sulphur and chlorine one may have a series of compounds which may be isolated by resorting to different methods of separation, distillation alone not being a t all conclusive since the compound may dissociate in the vapor. I n such cases it is absolutely impossible to state what the number of components present may actually be, in order to foresee what may be observed under supposed circumstances. I n examining such a case, however, care must be taken to ensure the presence of equilibrium conditions. Doubtless many of the peculiar relations found i n phase separation by freezing, crystallization, etc., will later be traced back to the formation of compounds. Three components - one volatile, two non-volatile I n this case the vapor is of constant composition. T h e study of the temperature changes with varying concentration may be followed very readily by means of the method of vapor heating. Unsaturated solutions may be carried to saturation by means of the superheated vapor, or molecular weight determinations may be carried out in the same solutions. T h i s subject will in a subsequent paper be discussed in regard to its bearing on fractional crystallization. T h e cases in three-component work which are of interest are those subject to easy control, i. e., univariant and divariant. One is also interested in the passage toward those, but until a trivariant is reached, the temperature changes in passing upward mean absolutely nothing. Three-components, not reacting - two volatile Given three components of which A and B are, and C is not, volatile, i t is possible to learn much about the vapor compositions from a study of the boiling-point relations of saturated solutions. If one starts with a saturated solution of C in A a t the boiling-point and passes i n B as vapor, the thermom-
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etre indicates readings tending toward the temperature of ebullition of the saturated solution of C in R. T h e boiling curve as observed may be either normal or present a maximum or minimum. When the three-phase system changing from A and C to B and C shows a normal curve, we are always dealing with a bivariant system, the relation of A to B in the solution being different from what it is i n the vapor. If three phases are present at the maximum or minimum, we know that we are really dealing with a univariant system because the removal of the vapor is done at definite temperature under definite pressure, and hence the concentration is determined. I n other words, with an abnormal curve, the relation of A to B is at a definite point the same in the vapor as in the solution. T h e various types which may be observed under this heading are : (I) T h e binary pair of volatile components gives a normal curve, while the same system with a third component added to saturation may show a normal or abnormal curve. ( 2 ) T h e binary pair may give a curve with maximum or minimum, while the ternary system may be either normal or abnormal. I n such systems rhe conditions which we wish to examine relate to the effect of the third non-volatile component on the concentration and temperature changes, on the vapor composition, and on the behavior on fractional distillation. I n the case where a binary pair giving a normal curve still gives a normal curve with a ternary system, it has been found that with the latter the boiling curve lies higher, and that the curve of vapor composition is displaced toward the side i n which the non-volatile component is least soluble. T h i s holds just as well in the case of unsaturated as with saturated solutions.. T h e addition of the third component will therefore hinder the work of fractional dephlegmation if the substance added is more soluble in the more volatile and help if it is more soluble Miller. Jour. Phys. Cheni.
I,
633 (1897). Gaus. Zeit. anorg. Chem. Zeit. phys. Chem. 40, 84 (1902).
25, 236 (1901).Abegg und Riesenfeld
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in the less volatile. For an example of the latter, the addition of sodium chloride to an acetone-water mixture helps i n the separation by distillation, the sodium chloride being more soluble i n water. T h e addition of a non-volatile organic body soluble in acetone and insoluble in water would hinder the separation by distillation. When the binary pair giving the normal curve shows on the addition of a third component a niaximum or minimum, a very peculiar displacement of the vapor coinposition curve would be indicated whose cause or significance is not a t present fully understood. Peculiar solubility or reaction relations might lead to the discovery of such a case. If a maximum were present, fractional dephlegmation would give the more volatile over at first, the less volatile returning to the boiling flask. T h e indicated boiling-point in the flask might therefore rise, pass to a maximum and then fall again, in the course of a continued fractionation. In case a minimum were present the boiling-point might fall, pass through a minimum and then rise again. I n the case of direct distillation, the boiling-point would rise to the maximum or the boiling-points of the sattirated solutions of the components. I n such cases the use of direct distillation as a means of separation is very ineffective compared with fractionation methods. If the ternary system shows a normal curve while the binary is abnormal, the displacement in vapor composition produced by the addition of the third component is as marked as in the last case. On direct distillation, the boiling-point of the solution will rise continuously until the temperature remains constant where one is distilling over one pure component. Such a case may probably be obtained with calcium chloride, hydrochloric acid and water. T h e behavior on fractional dephlegination may be examined in this fashion. T h e vapor contains continuously varying amounts of A and €3 (two-component system) which are dephlegniated by other continuously varying solutions of A and B. T h e temperatures indicated by the distilling vapor may, therefore, rise, pass through a maximuin and then fall. If the normal curve shows a minimum, this mixture on fractionation
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distils over first of all and the boiling-point of the vapor rises continuously ; the boilingpoint of the solution itself may fall or may rise on fractionation. T h e last two problematical cases considered offer far less of interest than the case where a n abnormal binary curve remains abnormal in the ternary system. T h e displacement due to solubility effects is still present in this case. Direct distillation would of course result i n the boiling-point rising continuously to the maximum point of the ternary system where the solution and vapor contain the same relative amounts of A and B. Dephlegniation of the vapor would again mean the passage of solutions of A and B into other solutions of A and B with the concomitant changes in the temperatures and concentrations of solution and vapor. Dephlegmation in three-component work I t has already been seen that the fractioning column works by performing in one apparatus a very great number of fractionations. T h e question arises, can the displacement effected by t h e addition of a third component be increased by combining a number of fractionations into one more effectively than by the use of the fractioning column, working with a two-component the separation of system ? Taking a specific case, -would hydrochloric acid and water by distillation be more effective if i n addition to solid calcium chloride in the still, one put solid anhydrous salt in the still-head ? Would the still-head itself be more effective than one containing glass beads alone? This case has not been tested. Experiments made with alcohol-water mixtures with lime in the still-head showed very little improvement over glass beads, the experimental conditions being exactly alike. I n freeing carbon bisulphide froni water, the use of lime in the column was very much more effectiTe. T h i s method is of course merely a variation of that emplojed frequently where for example the vapors are passed over metallic sodium as a dehydrating agent, only that in the latter case other decomposition products are formed. T h e method may be of ad-
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vantage in certain specific cases, but is probably of restricted usefulness. Dehydration by distillation T h e ordinary method of dehydrating aqueous salts in an exsiccator salts holding water of crystallization depends on the distillation of water vapor from a place of higher to lower pressure. This takes considerable time, and the question arose whether it could not be performed more rapidly by direct distillation. T h e salt chosen was ferric chloride holding twelve molecules of water. This was put into the inner tube of the apparatus (Fig. 5) and benzene vapor passed through i t ; the vapor issuing was condensed, and dropped through a calcium chloride tube back into the flask containing the boiling benzene. I n the first experiment, with roo grams of the salt, the amount of water lost in one hour was six grams, or about 15 percent of the total water content. I n the second run with I I O grams, the loss of water in two hours was 2 2 grams, or 50 per cent, the composition of the final mixture corresponding to the hexahydrate. I n the third experiment 64 grams of the pentahydrate lost 4 grams in forty-five minutes, or about 30 percent of the total water content. T h e substance which is to be used to carry over the water vapor depends on the stability of the salt. I n this case we were unable to detect a trace of hydrochloric acid carried over by 50 grams of benzene. While the method is very rapid, its use is suggested mainly for the cases where rapid work or large amounts of material a-e required. Three components - all volatile I n the case where the components are all miscible, the maximum number of phases being two, the system is trivariant ; too many variables have therefore to be fixed to study the system from the view point of vapor heating. Schreinemakers' is examining such cases from another standpoint. T h e effect of the third component on the displacement of the maxiniunr or mini tniim should prove very interesting ; for example, might .___
Zeit. phys. Chem. 36, 257, 413, 710 ; 37, 129 ; 38, (1902).
227
(1901) ; 39, 485
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benzene, added to water-alcohol mixtures, not displace the vapor composition very decidedly ? Even when a second liquid phase appears the syste~nwili in most cases be divariant. In connection with fractional distillation work, attention must be directed to one point - that it is perfectly feasible to separate by fractional distillation with steam or other inmiscible solvent. I n some cases the amount of liquid returned to the still may be too great, but this trouble is easily obviated. T h e relation between displacement in vapor composition and catalytic or solvent action may be illustrated by reference to the action of hydrochloric acid on methyl alcohol. When the acid vapor is passed in, a very small amount of methyl chloride is formed. T h e presence of zinc chloride - a dehydrating agent -increases the velocity of the reaction to a great extent. This is probably not due to solubility alone, but niight also be attributed to re-arrangement produced by the presence of the salt, e. g., formation of unstable compounds. I t may later be found that even where no new chemical product is formed, the addition of the third component exercises an effect not of solubility alone, but also of re-activity. I t follows naturally that the question of yield is influenced very decidedly by the displacements due to solubility effects. Multi-component systems Like all others these have first to be examined in regard to their reactivity. This determined, the same conditions hold which have been applied above in determining the significance of changing factors. Vapor heating method applied in other work T h e apparatus described in Figs. I or 5 may be applied in laboratory work for several purposes. I n the first place it is a serviceable form for the checking of thermometers at the boiling-points of various liquids. T h e method needs no further description. I t may also be used to find the purity of a volatile substance in exactly the same manner as is indicated by the thermometer placed at the head of a Hempel column. I n cases where the substance shows a maximum or niinimum boiling-
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point with another substance easily obtained in a pure state, the method may be employed to test the purity of the reagents because here we have another fixed point. T h i s was shown by experiments on chloroform and water (p. 326). It has also been used in this laboratory for the detection of volatik acids or bases given off by a boiling solution, the solution formed in the inner tube there reacting upon the reagent or else being withdrawn for testing afterward. I n this way it has been possible to easily detect ammonia and hydrochloric acid in the hydrolyzed solutions of various salts containing them, e. g., ammonium acetate, or SUIphate, zinc chloride, magnesium chloride, etc. For this work, the heating produced by the absorption militates somewhat against the use of the apparatus.
Summary I n this paper on applied Phase Rule work, it has been shown how by the examination of ,condition factors there have been discovered practical and simple experimental methods :(I) For the rapid determination of the general course of a boiling curve for mixtures of two volatile components ; ( 2 ) For the exact determination of vapor composition ; (3) For concentrating solutions and determining the exact boiling-points of solutions, saturated or unsaturated ; hence a modified apparatus for molecular weight determination by the vapor heating method. (4) For dehydration of salts and liquids ; (5) For the displacement of maximum or minimum boilingpoints, and the examination of this displacement. T h e study has shown the rational method for the avoidance of superheating ; has discussed the ideal form of dephlegmators, indicating their action; has described for the first time the method of continuous separation by distillation, and shown that economy of operation and purity of product go hand in hand ; has indicated the necessity of looking for velocity terms before undertaking any study involving the separation of phases ; and in general has shown how three- and multi-component systems
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may at times be referred back to systemsof a smaller number of coni ponents. To his students, especially Mr. Ira W. Derby, the writer wishes to express his thanks for hearty co-operation ; to Professor Bancroft for suggestion and kindly criticism he is deeply indebted. Cornell Universil'v
