S Y N T H E T I C ANALYSIS I N T E R S A R Y SYSTEMS BY A. W. RROU'NE
In a recent article' Professor Bancroft has suggested a new method for analyzing the solid phase appearing in three coniponent systems without removing it from the mother-liquor. I n the following pages are described several experimental applications of this method to the analysis of the solid phase separating from aqueous solutions. T h e method may be applied in either of two ways : ( I ) as a direct method, and (2) as a zero method. In the first case, the solid phase under consideration is allowed to separate out in quantity, the composition of the original solutioii in terms of the three components having been previously determined by chemical analysis. Then, after the 3ppearance of the solid phase, the composition of the motherliquor is similarly determined. From the two series of values the composition of the solid phase may be computed ; either arithmetically, or by a graphical method involving the use of the triangular diagram. A simple illustration of the mode of applying the direct method is afforded by the case of an aqueous solution of sodium sulphate and sodium chloride. If the concentration of the former salt is sufficiently great and that of the latter sufficiently small, crystals of sodium sulphate with ten inolecules of water will appear on cooling the solution from say 33" to 21'. Now suppose that analysis of the solution prior to the appearance of the crystals shows the percentages of the three components, sodium sulphate, sodium chloride, and water, to be respectively a, b, and c ; and that analysis of the mother-liquor after the apJour. Phys. Cheni. 6, 178(1902). The same principle has been applied in an only slightly different form by Kentuer. Zeit. phys. Chem. 39,658 (1902). The first mention is to be found hidden away in a paper by Schreinemakers. Zeit. phys. Chem. 11, 81 (1893).
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288
pearance of the crystals shows the percentages to be a’, b’, and c’. Since no sodium chloride separates out, we may reduce the percentages, for purposes of comparison, to the basis h = 6’ = I. Then
a c b ,are the amounts of b
sodium sulphate and water, re-
a’ c‘ -are the amounts 6‘ ’ 6‘ in the mother-liquor. T h e excess of the amount of each component in the original solution over that in the mother-liquor is proportional to the amount of that component in the solid a a’ phase. Therefore - - 7represents the amount of sodium sulb b
spectively, in the original solution ; and
phate, and
c
--
b
c’
7the
b
-
amount of mater in the crystals.
The
quotients of these expressions, respectively, by M and M’, the molecular weights of sodium sulphate and water, represent the relative number of molecules of the two components present in the solid phase. And finally, by dividing the second quotient by the first, we obtain an expression ~~
M(c6’ - C ’ b ) a’b)
bl’(ab’-
for the number of molecules of water to one of sodium sulphate. This illustration deals with a solid phase in which only two of the three components are present. When all three components are present, the calculation of the final result from the analytical data may be accomplished in an equally simple way. In either event, however, the graphical method described below may be preferable because of its even greater simplicity. I n the second case, the composition of the mother-liquor in terms of the three components is determined, after some of the solid phase to be examined has appeared in the system. Then a considerable quantity of material supposedly identical in composition with the newly separated solid phase is added. After equilibrium has been re-established at the same temperature as before, the composition of the mother-liquor is again determined. If the composition is found to be the same in both
Synthetic Aizalysis in Tevizavy Systems
289
cases,-within the limits of experimental error - and has not been altered by the addition of the new matzrial, then the solid phase originally separating out is identical in composition with the substance added. Instead of determining the composition of the mother-liquor by analysis, we may measure some physical property which is a function of the concentrations of the components, such as the electrical conductivity, or the vapor tension of the solution for a given temperature, or the boiling-point for a given pressure. If the measurements made before and after the additions of the new material are the same, it is to be inferred that the substance added is of the same composition as the solid phase under exami n ation. As an illustration of the mode of applying the zero method may be taken the simple case of an aqueous solution of barium chloride and hydrochloric acid. Since any change in the percentages of the other two components would cause a change in the percentage of the hydrochloric acid (unless the change should be such that the sum of the percentages of the two components should remain constant), it is necessary to find the percentage of the acid only, by titration with standard alkali in order to obtain a fixed point of reference. This is done after a quantity of the solid phase has been allowed to separate out, and the system has been carefully brought to equilibriiim at a certain temperature, read to at least tenths of a degree. A considerable quantity of either the hydrated barium chloride or the anhydrous salt, together with an amount of water equivalent to the two molecules is now added. After equilibrium has been reached at the same temperature as before, the percentage of acid is again determined. If this percentage is found to be the same as that previously obtained, then the concetitration of the other two components must have remained unaltered except in the one above-mentioned case. Therefore the two compoEents barium chloride and water must be present in the solid phase in the same ratio as in the inaterial added ; i. e., in the ratio BaC12: 2H20.
.
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A. W. Browne
I t is not necessary that the new material added shall have the exact coniposition of the solid phase under consideration, else the zero method would be of valueonly as ameans of confirming data otherwise obtained. Different known amounts of one or more of the components known or supposed to be present in the solid phase may be successively added, the effect of each addition upon the composition of the solution being determined by one of the above-mentioned ways after. the system had come to equilibrium. For example, if a salt is known to crystallize from solution with a number of molecules of water, the number may be readily ascertained by adding, to a system containing a quantity of the solid phase in question, a portion of the anhydrous salt, together with an amount of water eqnivalent to one or more molecules. If it is found, after a sufficient time has elapsed for the hydration of the anhydrous salt added, that the composition of the solution is not the same as it was before the addition of any new material, then another water equivalent is added. This process is repeated until the solution is brought back to its original composition, T h e total number of water equivalents added is then equal to the number of molecules of water of crystallization. There are numerous possibilities regarding the composition of a solid phase appearing in a three-component system. Among the simplest of these are the following. T h e phase may be (I) a pure component, (2) a binary compound of components, (3) a binary solid solution, (4) a ternary compound, (5) a ternary solid solution, (6) a solid soltition of one component in a compound of the other two, (7) a solid solution of two binary compounds, and (8) a solid solution of two ternary compounds. A s actually occurring instances of the forgoing we have, under proper conditions : ( I ) potassium chloride separating from the system potassium chloride, hydrochloric acid and water ; (2) sodium sulphate with ten molecules of water from the system sodium sulphate, sodium chloride and water; ( 3 ) a solid solution of potassiuni sulphate and ammoniuni sulphate from the system potassium sulphate, ammonium sulphate and water ; (4)
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291
a hydrated ferric chloride with hydrochloric acid of crystallization from the system ferric chloride, hydrochloric acid and water ; ( 5 ) a solid solution of potassium nitrate, sodiuni nitrate and silver nitrate froin the system potassium nitrate, sodium nitrate and silver nitrate (6) a solid solution of hydrated ferric chloride and ainnioniuni chloride from the syate n ferric chloride, ainnioniuin chloride and water; and (7) a solid solution of the heptahydrates of zinc sulphate and ferrous sulphate from the system zinc sulphate, ferrous sulphate and water. A wellauthenticated instance of the eighth case is not at hand. T h e method in either of its f o r m may be applied to the above and to all other cases in which a solid phase separates from a three-compouent system. Since the application in any case is fairly typical, it has been thought sufficient for tlie purposes of the present paper to consider cases coining under the first three heads only. ;I
Experimental work (I.) T h e solid phase is a pure component. T h e system studied was potassium chloride, hydrochloric acid and water. T h e zero method was employed. A saturated solution of potassium chloride in presence of hydrochloric acid was inade by placing about 150 grams of the " C. P,') salt, 2 2 5 grains of water, and 60 grams of concentrated hydrochloric acid in a flask fitted with a stopper provided with a perforation for the thermometer. T h e flask was gently warmed and then allowed to stand for 45 minutes, being frequently shaken to facilitate the establishment of equilibrium. T h e proportions of the cotiiponents had been chosen with a view to having the salt present in considerable excess. Two samples were now pipetted off froiii the clear solution at the temperature 22.3') and weighed. T h e amount of hydrochloric acid present was deterinined by titration with half-normal sodium hydroxide solution, with methyl orange as indicator. After introducing about I 50 grams of additional potassium 011 the basis of the fact that potassium and sodium nitrates, and sodium and silver nitrates, respectively, form solid solutions.
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No. of analysis
1
20.317 gr
Ia
b b
2a
-
Weight of sample
1 1
Weight of HC1 -
Percent HC1
11.338
1.4404 1. I335 0.8034
7.091 7.078
8.805
0.6231
7.078
16.016
7.086
1
Average pct. HC1
17.085
}7
082
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293
the crystals for every molecule of the anhydrous sodium sulphate was calculated. Results were as follows : Percentage composition of Component
Solution (by synthesis)
Mother-liquor (by analysis)
~
NaCl 2.14 3.05 2 I .07 Na,SO, 28.1j i H,O 69.72 75.88 Water of crystallization for Na2S04= 9.7 t 0.05 molecule. This result was not quite as satisfactory as had been hoped. T h e error niay have arisen from either or both of two sources: ( I ) incomplete hydration of the anhydrous sodium sulphate, caused perhaps by the formation of a protective coating of the hydrate upon the particles of the anhydrous salt; or (2) the presence of some impurity in either the sodium sulphate or the sodium chloride weighed out at the start. T o test whether or no the error arose from incomplete hydration, a second experiment was performed similar to the first in every respect except that extra precaution was taken to insure complete hydration. T h e anhydrous salt was very finely powdered, and sifted little by little into the flask containing the weighed amount of water. Bfter each small addition of the salt the flask was vigorously shaken, to prevent caking of the material during the process of hydration. Furthermore, such proportions of the components were chosen that the sodium sulphate was almost completely dissolved at a higher temperature. Analyses and calculations were made in the same way as before with the following results : ~
-
1
Component
Percentage composition of
I' I
'
I
Solution (by synthesis)
I
Mother-liquor ( b y analysis)
I
NaCl 11.70 I 14.96 Na,SO, 17.68 IO. 1 3 H,O 70.62 Water of crystallization for Na2S04= 9.7 5 0.05 molecule.
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T h e agreement between these two results obtained under conditions for which the probability of error as the result of incomplete hydration was widely different, eliminates the possible influence of that source, and points toward the alternative influenceof some iiiipurity in the salts used. Both of the salts were so-called C. P.” preparations, but had not been further pnrified by me. Care had been taken thoroughly to dehydrate the sodium chloride before weighing. Some little turbidity had been noticed in the solution, however, when the sodium sulphate was sifted into the flask, and trouble had not been taken to re. move the insoluble material with a view to introducing a correction. This impurity would have the effect of making the apparent concentration of the sodium sulphate in the original solution greater than the actual, and that of the water, since it was determined by difference, smaller than the actual concentration. T h u s the final result would be too small, as is illustrated in both experiments. In the third experiment, further trouble from this source was avoided by determining the composition of the original solution, as well as that of the mother-liquor, by analysis. T h e procedure in this case was as follows : About 41 grams of sodium chloride, 61 grams of anhydrous sodium sulphate and 50 grams of water were warmed, with frequent shaking, until all the salt went into solution. When the solution had cooled to about 34” it was given a thorough final shaking, to insure uniformity of composition. Four samples were now pipetted off: two into small weighed flasks, and two into weighed ‘(pigs” of the sort used in solubility work. T h e chlorine content of the first pair was determined as in the preceding experiments ; and in the second pair the amount of water was determined by evaporating the solution to dryness and heating the residue until the dehydration of the sodium sulphate was complete. From the results for chlorine the percentage of sodium chloride was calculated as before, and the percentage of sodium sulphate was found by difference. T h e remainder of the solution, cooled to about 2 I O , was
Synthetic ,4italysis in Terizary Systems
Component
Solution ( b y analysis)
2 95
Mother-liquor ( b y analysis)
NaCl 10.82 13.53 16.I I 9.12 Na,SO, 73.07 77.35 H,O Water of crystallization for Na2S0, = 10.0t 0.05 molecule. This satisfactory result shows that the purity of the salts had been rightly questioned. If the first two experiments were to be repeated, all difficulty such as here experienced could of course be avoided by dissolving the salt in water, and recrystallizing after the removal of extraneous insoluble material by filtration. (2) T h e system studied was barium chloride, hydrochloric acid and mater. T h e zero method was applied. About 500 grams of hydrated barium chloride, 50 grams of hydrochloric acid and 400 grams of water were placed in a stoppered Erlenmeyer flask provided with a thermometer, as in the precediiig experiments. T h e flask was slightly warmed and shaken vigorously to insure saturation of the solution, and then allowed to cool, 21.3' being the final temperature read from the thermometer after the system had reached equilibrium. T h e proportions of the three components had been so chosen that the salt was present in considerable excess at this temperature. As in the preceding case, by determining the percentage of hydrochlaric acid afixed point for the system may be obtained, since this percentage may be regarded as a function of the other two. A pair of samples mas therefore pipetted off from the solution,
and the percentage in question determined by titration with half normal sodium hydroxide. T h e system is now divided as nearly as possible into two equal parts, each of which contained about the same quantity of solution and crystals. T o each of these portions, contained as before in a stoppered Erlenmeyer flask provided with a thermometer, a weighed amount of powdered, anhydrous barium chloride was slowly and carefully added. T h e anhydrous salt had been prepared by heating the hydrate in a large evaporating dish for a number of hours over a sand-bath. T h e salt was then powdered and heated again, until, at a temperature somewhat above 100' there was not the slightest visible trace of moisture deposited upon a cold watch crystal repeatedly held close over the salt. Into one of the flasks was now poured a weighed amount of water, slightly in excess of the amount required for the complete hydration of the anhydrous salt added; into the other was poured an amount slightly less than the corresponding theoretical amount for that flask. After a period of time sufficient for the temperature -which had risen about ten degrees during the hydration of the salt - to return to the starting point, 21.3', two samples from each flask were analyzed for hydrochloric acid. I n the first flask, to which the larger quantity had been added, a smaller percentage of acid was found than in the second. And now assuming - as is perfectly legitimate in this case - that the amounts of solution originally present in the two flasks were equal, or so nearly so that the error resulting from their difference is negligible, we may obtain by interpolation the percentage of hydrochloric acid when exactly the amount of water equivalent to two molecules is added. This was effected in practice by plotting excess (or shortage) of water in grams against the change produced in the concentration of the hydrochloric acid. T h e necessity for the division of the original solution into two parts, and for this subsequent procedure in the determination of the hydrochloric acid after the addition of the new material arises from the practical difficulty of adding the exact equivalent of water.
Sy7zthetic Aizalysis iiz Ternary Systems
297
Results were as follows :
-
Before adding BaC1,2H,O No.
1
1
/I
Pct. HC1 11
Amounts added ( i n grams) BaC1,
After adding BaC1,2H,O No.
____
I,
Pct. HC1
1
Average
7-
10.794 2
I
lI
3.432 9.858
I
1
3.387 b 3.401 I 3.394 2a 1 3.444 1 b 3,439 3.442 By interpolation 3.433 Ia
'
1
A comparison of the final percentag; of acid obtained by interpolation with the percentage found at the same temperature before the addition of the new material, shows that the composition of the solution phase has not been altered. Therefore the solid phase originally present in the system must be identical in composition with the new material added, or must be a compound of barium chloride and water in the ratio BaClp:2HZ0.' (3) T h e system studied was ferric chloride, hydrochloric acid and water. T h e direct method was applied. About 250 grams of ferric chloride with twelve molecules of water were placed in an Erlenmeyer flask. A current of dry hydrochloric acid gas -obtained by adding concentrated sulphuric drop by drop to concentrated hydrochloric acid, and passing the gas through concentrated sulphuric acid contained in a Muencke wash-bottle - was passed into the flask until about half the salt had been liquefied. T h e generator was now removed, the solution diluted with about 2 5 cc of water, and the flask heated until the remainder of the solid had been melted. After the flask had been thoroughly shaken, a sample was pipetted into a small stoppered flask, quickly cooled to ordinary temperatures and weighed. It was then diluted to exIf the composition of the solid be assumed, to start with, then it would be possible to use the method in B case like this to ascertain the degree of completeness to which an anhydrous salt could be hydrated in a given time by bringing it into contact with water under such conditions that solution could not take place.
'
actly zoo cc and set aside for subsequent analysis. Immediately after the sample had been reiiioved, the large flask was quickly stoppered and placed in a cold water-bath to prevent loss of water by evaporation. A minute crystal of the dodecahydrate of ferric chloride was added. A solid phase slowly separated out at about 15'. When this had appeared in considerable quantity, the Bask was thoroughly shaken and a second sample obtained, which as before was dilrited to 2 0 0 cc. I n two ten cc portions of each of these samples the percentage of iron was determined gravimetrically by precipitating with aiiimonium hydroxide and weighing. as ferric oxide. T h e precipitate had been thoroughly washed with hot water until no reaction could be obtained for chlorine in the filtrate. T h e filtrate, including wash-water, was then analyzed for chlorine. T o calculate the percentages of the three components, the difference between the total percentage of clilorine found and tlie chlorine equivalent of the iron found was reduced to terms of hydrochloric acid. T h e percentages of ferric chloride and hydrochloric acid being then known, that of water was found by difference. Results were as follows :
Component
I 1
Percentage composition of
~
~
i
Illother-liquor
Solution (by analysis)
( b y analysis)
I
47.25 44.63 4.46 4 z 48.29 Water of crystallization for E'eZCl,= 12.14 t 0.2 molecule. I n the first attempt made to apply the method to the analysis of the solid phase appearing in this system, care was not taken to dilute the solution with a little water after leading in the hydrochloric acid gas. As a result some of the acid was lost by evaporation during tlie gradual separation of the solid phase (and the consequent increase in percentage of the acid in the solution) and the final result for the molecules of water of crystallization was rather high. Fe,Cl, HCl H,O
Component
H,O K,SO, (",),SO,
Solution (by analysis)
Mother-liquor (by analysis)
52.38
58.88
41-71
37.48
Since no water separates out in this case, these percentages
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300
are reduced to terms of water equals one, and the other components compared as usual. T h e final result was as follows : for each one of Number of molecules of ("$SO, K2S04= 4.13 5 0.05. So the two salts form a solid solution, though in this particular case the mixture chanced to be very nearly a molecular one. Discussion of results T h e graphical method of calculating the composition of the solid phase from the data obtained by analysis involves the use of the triangular diagram. For a complete general discussion of this form of diagram and the manner of its use, see an earlier paper by Professor Bancroft.' There is obviously nothing to be gained by plotting the results obtained in the application of the zero method, for the final composition of the system is the same as the initial composition, and the Composition of the solid phase is obtained by simply keeping a record of the new material added. When the direct method is applied, however, the triangular diagram affords a quick and easy method ( I ) of obtaining the composition of the solid phase from the results of analysis, and (2) of assigning the limits of error. I
Either percentages or molecular weights of the three components may be used as the coordinates of the diagram. In each case it is of course required that the sum of the coordinates of any point on the diagram shall be equal to one hundred. Two points are located on the diagram by plotting the data obtained respectively for the original solution and for the mother-liquor, T h e straight line drawn through these two points also passes through a point, the coordinates of which show the composition of the solid phase. Obviously this point may not be definitely located by a single line of this sort. Starting from the point 1
Jour. Phys. Chem.
I,
403 (1897).
Syizthetz’c Aizalysis i i z Ternary Systems ‘ representing
301
the composition of the mother-liquor after the separation of the solid phase, we may expect to find the desired point on any part of the line beyond the point representing the composition of the original solution. Rut if a second series of data be obtained, the line drawn through the two new points will intersect the first line at the point representing the coniposition of the solid phase. If molecular weights have been taken as the coordinates, the relative molecular proportions of the components present in the solid phase may be read directly from the diagram, where they appear as the coordinates of the point of intersection of the two lines. If percentages have been taken, the readings must be divided by the molecular weight of the respective components in order to obtain the molecular coniposition. T h e solid phase is shown to contain one, two or all of the three components according as the intersection of the two lines is ( a ) at one of the vertices of the triangle, (b) at a point on one of the sides of the triangle, or (6) at a point within the triangle. In either of the first two cases one line would have been sufficient to locate the desired point could the assumption have been made at the outset that only one or two respectively of the three components would be present in the solid phase. In some cases this assuniption is possible. Suppose for instance that a given salt is known to crystallize with X molecules of water. To evaluate X, a new i‘indifferent’’ component- that is, one known to form no compound with the two components already present - is added to the system. T h e line drawn through a single pair of points determined by analysis will now intersect one of the sides of the triangle at the point representing the composition of the solid phase. Figures I and 2 illustrate the application of this graphical method to two of the experimental cases described above. It will be observed that in neither case the complete diagram is shown, but only that portion which is of particular interest in the case under consideration. T h e data were first roughly plotted on the full-sized diagram, in which of course each com-
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A. W. Browne
ponent is represented over a range from zero to one hundred molecular weights. Then, as the points located were found to have grouped themselves within the limits of a comparatively small portion of the entire diagram, that particular portion was enlarged, and the rest left out of account. Since in both cases only two of the components are present in the solid phase, the final result will be represented in each case by a point on the side of the triangle opposite the vertex, which in the complete diagram represents IOO molecules of the absent component. Care was taken, therefore, in selecting the limits of the smaller
Fig.
I
diagram, to retain in each case as one of the sides, a portion of the side of the larger diagram along which none of the component absent from the solid phase was present. In Fig. I are plotted the analytical data obtained for the system sodium sulphate, sodium chloride and water. T h e point
Syizthelic AnaL'ysis ivz Terizavy Systems
303
AI was located by synthesis, and BI by analysis after the solid phase to be studied had separated in sufficient quantity. T h e straight line drawn through these points intersect the right-hand side of the triangle at a point representing the system composed of 90.7 molecules of water for every 9.3 molecules of sodium sulphate. T h e quotient of the first of these values by the second gives 9.75, which is the number of molecules of water indicated by this experiment as present in the solid phase for every molecule of sodium sulphate. T h e points Az and B2were located respectively, by synthesis and analysis in the next ex-
Fig.
2
perinient made upon this system, as described above. T h e line drawn through them intersects the side of the triangle, as nearly as may be read from the diagram, at the same point as does the line obtained in the former experiment. T h e points A3 and B3 were in the next experiment located by analysis, and the line
304
A. E’. Byowne
drawn through them intersects the side of the point corresponding to 90.91 molecules of water and 9.09 nlolecules of sodium sulphate, or to 10.0molecules of water for one of the salt. I n Fig. z are plotted the analytical data obtained for the system ferric chloride, hydrochloric acid and water. T h e point A shows the composition of the solution before the separation of the crystals, and the point B shows the composition of the mother-liquor after the crystals have appeared. T h e line drawn through the two points intersects the base of the triangle, along which are represented systems containing no hydrochloric acid, at the point C, the coordinates of which are respectively 92.4 H 2 0 and 7.6 Fe2C1,. T h e quotient of the first of these values by the second is 12.16, which is the number of molecules of water indicated by the experiment as present in the solid phase for every molecule of ferric chloride. 2
By using the graphical method of expressing results it is possible with very little trouble to assign with considerable accuracy the limits of experimental error for any given case, All error to which the final result in any case is subject arises of course primarily from the errors inherent in the methods of chemical analysis applied in the course of the experiment. If the percentages of the different components in a system under given conditions could be determined in the first place with absolute accuracy, the final result would be likewise absolutely accurate. But this is unfortunately not possible. And moreover, a small initial error in the chemical analyses may during the subsequent course of calculation be greatly multiplied in many cases. If the probable errors involved in the determination of the composition of the system at each point considered be used as radii in describing circles respectively about the points, and if two tangents be drawn for each pair of circles, then the intercept between the intersections of these two lines with the side of the triangle represents the probable error of the final result. By inspection of the diagrams shown in Fig. 3 it will be
Synthetic Analysis in Ternary Systems
30.5
seen that the magnitude of this total error depends upon (I) the diameter of the circles, ( 2 ) the distance between the centers of the circles, ( 3 ) the distance of the circles from the side of the triangles toward which the tangents are drawn, and (4) the angle at which the straight line connecting the center intersects the side of the triangle. T h a t is to say, the final error becomes smaller ( I ) as the error of the original chemical analyses and the
Fig. 3
accompanying calculations is diminished, ( 2 ) as the amount of solid phase allowed to separate from the system between the two points is increased, ( 3 ) as the concentration of the component absent from the solid phase becomes less at the point nearer the side of the triangle, and (4) as the change in the concentration of the component absent from the solid phase becomes greater between the two points. These last two considerations in their present forin apply of course only to the cases in which but two
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A. W. Browne
components are present in the solid phase. When all three cornponents are present the error will be ininimized if, in addition to fulfilling the first two conditions mentioned above, the concentrations are so chosen that the two straight lines connecting respectively the pairs of points determined by analysis intersect each other a t right angles. This is illustrated in the last diagram shown in Fig. 3, where X is the point representing the desired composition of the solid phase, while the circle drawn abont this point as a center indicates the limits of experimental error. In all the diagrams i n Fig. 3 the size of the circles has been exaggerated for purpose of clearness. One of the experimental cases described in the preceding pages affords an excellent illustration of the influence of calculation in niultiplying the error, even when all other conditions were rather favorable. This is the case of the system ferric chloride, hydrochloric acid and water, especially selected, because of the great opportunity for error, as the crucial test of the applicability of the new method of analysis. In changing the iron, which had been weighed as ferric oxide, to terms of ferric chloride, the original error was multiplied by at least two. A comparatively large error was therefore introduced into the value for hydrocliloric acid, which was deteriiiined by difference, and also into the value for water, determined in this case by double difference. Obtaining the quotients of the values for the two other components, respectively, by that for the hydrochloric acid, caused still further tnultiplication of the error, a process which received its final impetus when one of these quotients was divided by the other to obtain the final result. T h i s error called for comparatively large circles about the points located by analysis ; so that although other conditions were not very unfavorable, as may be seen from Pig. 2 , the probable error of the final result was cornparatively large. It is of great importance, therefore, if any considerable accnracy is desired, that the percentages of at least two of the three components in each case be determined directly by analysis. Thus if the percentage of hydrochloric acid in the case just referred to could have been directly determined
Syizfhefic Analysis in Ternary Systems
307
by titration, the final error would have been greatly diminished. This is impracticable, however, because of the tendency of the ferric chloride to hydrolyze under the conditions of the experiment. T h e results obtained in the first two experiments upon the system sodium sulphate, sodium chloride and water have been published without reserve becguse of their valtie as an illustration of the applicability of the method even under adverse conditions of another sort ; namely, when the initial composition of the system was determined by synthesis without the previous precaution of securing strictly pure components. T h e limits of error assigned in these two cases have reference only to the error which might have arisen in the course of the experiment as performed under normal conditions, and not to that introduced by the impurity of one of the components. These were the first experiments tried in applying the new method, and naturally the synthetic method was first resorted to, because of the smaller amount of time and labor involved. In all of the above experiments, the analyses were conducted with little or no more pains than must be taken in ordinary careful analytical work, and two analyses only were made for each determination, of whicli the average was used in calculating results. N o attempt whatever was made to introduce such refinements as are used for example in atotnic weight work, the object of the experiments being a thorough test of the efficiency of the new method under ordinary laboratory conditions, rather than an exhibition of the high degree of accuracy attainable by the exercise of tlie greatest possible care in manipulation. I n the ordinary cases to which this method tnay come to be applied there will often be but little call for a high degree of accuracy in the final result, so that unusual refinements will become superfluous. If for example the problem be the analysis of a solid phase known to be a definite compound of twoor more of the components, the final result need be accurate to such a degree only that there will be no doubt concerning the nzodecuhr composition of the solid phase. T h a t is to say, if the solid
308
A. PK Bvowne
phase is known to be, for instance, a hydrated salt containing x molecules of water, then would such a final result as 9.8 for x point unequivocally toward IO as the desired number, even though so large a probable error as +- 0.2 molecule were involved in the experiment. If however the solid phase is known or thought to be a solid solution of any sort, regional determinations will not lead to so satisfactq-y a result. If the different cqmponents or compounds of components which are present in the solid solution do not happen to be present in approximately molecular proportions, then the regional datum will point toward the fact that the phase is a solid solution, but will be of no further value. While this use of the method as a means of securing regional results for the composition of any solid phase in three-component systems would be no doubt of itself sufficient justification for this description of a few typical details of its application, it is by no means the only field of usefulness of the method. By the exercise of even ordinary care in conducting the analyses, results should be obtained in almost every case with a degree of accuracy equal to, and in the majority of cases, I think, much greater than that of, the results obtained by the method now in vogue of removing the solid phase from the system and analyzing i t directly. T o bear out this statement under conditions niost unfavorable to the new method, direct analyses were made of the solid phase separating from the system ferric chloride, hydrochloric acid and water, at ordinary temperatures. A large portion of the crystalline mass was removed from the system and carefully dried with filter-paper. Two pieces were now cut out from the heart of the mass, each of which was quickly weighed and dissolved in water. T h e iron was weighed as ferric oxide and calculated to ferric chloride. T h e difference between this value and the total weight gave the amount of water, from which the number of molecules of water was readily calculated. This was found to be 11.88, a result about as far from the truth as was that obtained by the new method, and with a probable error more or less indeterminate because of the impossibility of ascertaining (I) the amount of mother-liquor which may have
Syizthel'ic .47zn4ysis
i7z
Temary Systems
309
been occluded in the crystals, and ( 2 ) the degree of incompleteness (or overcompleteness) of the drying process, but probably of a magnitude just as great, if not greater, than that of the error to which the newer method was subject. This was undoubtedly an unfavorable case for both methods, since the error mas in each case greatly enhanced by calculation, an effect much inore pronounced in the case of the new method, however, than in the other. T h e amount of care exercised in conducting the analyses was as nearly as possible the same in both cases. While I do not care to make any further claim for tlie accuracy of the method, because none of the experimental work yet performed has been carried out under conditions guaranteeing minimum error, I am not prepared on the other hand to decry the possibility of applying the method, under extremely favorable conditions, to work of greater dignity than that suggested in the preceding pages. If certain conditions were carefully fulfilled it might be practicable, for example, to nse the method - either as a direct or as a zero method -in the determination of the atomic weight of an element, such as sulphur in the compound sodium sulphate, or phosphorus in the compound hydrogen disodium phosphate. I n either case the ratio of the anhydrous salt to the water of crystallization, or that of the ailhydrous to the hydrated salt could be used to obtain the desired result, assuming the atomic weights of the other elements involved. If the direct method were used, care would have to be taken to exclude analytical processes involving the atomic weight of tlie element under consideration. If for example the atomic weight were to be determined by analyzing the decahydrate of sodium sulphate in the system sodium sulphate, sodium chloride and water, the percentage of sodium sulphate in the original solution and in the mother-liquor could not be determined by precipitating with barium chloride. T h e procedure followed i n the last of the three experiments upon the system as described above could however be adopted. T h e method of calculation for this particular case is shown in the following equation :
A .W. ~ Browize -I:
+
$- m1
HZ,
ab‘ - a’b cb’ - c’b
’ 5 in which ml,wz2 and m3 denote respectively the atomic weight of sodium taken twice, the atomic weight of oxygen taken four times, and the molecular weight of water taken ten times, while a, b, c, a’, b’, c’ denote the percentages of the three components sodium sulphate, sodium chloride and water in the original solution and in the mother-liquor respectively, x represents the atomic weight of sulphur, and may be evaluated by solving the equation. T h e zero method could probably be most advantageously applied to a case like the above by carefully measuring the electrical conductivity of an aqueous solution of sodium sulphate and sodium chloride at a certain temperature, adding a known weight of pure anhydrous sodium sulphate, and then diluting with known amounts of water until the conductivity at the same temperature became exactly the same as before. T h e final result would then he obtained by solving the equation :
+ + nz, ’=I
m3
-3 w2
’
(2)
i n which x , nz,, mn2and m3 have the same significance as in ( I ) ; while w Iand w 2denote respectively the weights of anhydrous sodium sulphate and water added. When either of these methods is used, the difficulties resulting (I) from occlusion of the mother-liquor by the solid phase. and ( 2 ) from the possibility of incomplete or overcomplete drying of the phase, difficulties which hitherto have constituted a stock objection to the use of hydrates in atomic weight work, would of course be entirely avoided. T h e conditions to be fulfilled in securing maximum accuracy in the application of the direct method (most of which have been already alluded to above) are briefly as follows : ( I ) care in the selection of analytical methods which give as directly as possible the percentages of the different components, thus avoid. ing error-multiplying calculation ; (2) extreme carefulness in conducting the analyses, including the introduction of all useful
Sydzetz'c Aizalysis in T e m a v y Systems
311
refinements, and the carrying out of a large number of analyses for each determination, so as to secure the most reliable average ; (3) selection of temperature and concentration conditions so that ( a ) the largest possible amount of solid phase shall be allowed to separate out between the initial and final points determined by analysis, (6) the concentration of the component absent from the solid phase becomes as small as possible at the initial point, and (c) the change in concentration of the component absent from the solid phase becomes as great as possible between the two points. T h e conditions to be fulfilled in order to secure maximum accuracy when the zero method is applied are too obvious to merit especial consideration. T h e graphical method can only be applied satisfactorily to systems containing three or, at most, four components. An analytical treatment becomes necessary for the general case of ?z components, all of which may be present in the solid phase. Let A, 13, C, D, etc., be the percentage concentrations in one initial solution, and let d A , dB,dC,dD, etc., be the changes in the percentage concentrations, as shown by analysis of the final solution. Let AI, BI, Cr, DI, etc., and dAI, dBI, dCI, d D I , etc., bethe corresponding values obtained from another initial and final solu*tion. Let Ao, Bo,Co,Do be the percentage concentrations of the unknown solid phase. If the percentage concentration of any component be higher in the initial solution than in the solid phase its percentage concentration will increase as crystallization proceeds, while it will decrease if the reverse be the case. Froin the two sets of analyses we get the relations : -A A, -~ d B -- B -- Bo
dA ~
A - A, ___
dil dC
-
dA
_ _ A-A, __
--
c - c,
~
dD
- Do
d-4 dB,
A,- A,
i - ~-
'
B, - Bo
dL41 A,-A, -dC, C, - C,
__
dA
A, - A, D, -Do
~1 --
dD,
etc. etc. In these equations Ao, Bo,Co, Do. etc., are the only unknown
312
Synthefic Analysis in Ternary Systems
quantities and can be determined by solving the equations. When a solution contains a large number of components, it seems probable that the zero method will give more satisfactory results than the direct method. In concluding, I wish to express my sincerest thanks to Professor Bancroft for suggesting the line of work, and to acknowledge my grateful appreciation of the numerous invaluable suggestions he has kindly offered during its prosecution. Cornell Universily
