STUDY OF
THREE-COlIPOSEST S\17STElI
;Iltliou~ghit is ..;e\-ern1!-ears since the t r i a i i p l a r diagram in iiiipro\.ed foriii was proposed b\- lioozebooiii,’ and althou:,.li its acl\mitages lia\-e beeii 11101-ereceiitl J- illiistratetl l ~ ? . 13:incroft,2 there 113s been publisliecl, so far as the n-riter is avare, only oiie stiiclj- o f a tliree-coiiiponent system n-itli coiiiplete esperiiiieiital details iii respect to teiiiperature-coiiceiitratioii changes.; The object of the present paper is to present the esaiiiiiiatioii of such a s\-steiii. Iii order to deal with the simplest case possible, the coiiiponents ha\-e been so chosen that ( I they c1issolT-e n-itliont decoiiiposition to a lioiiiogeneous solution ; ( 2 tliej- foriii neither solid solutions, iiiised crJ-stals, nor double salts : ( 3 i their respectj\-e iiielting-points do not lie too far apart. I t was moreover tlioiiglit desirable to work if possible v-it11 inorganic substances since these do iiot appear to liave beeii studied to an!. extent in respect to their possiliilities as solvents. If one \vi11 deal with a true three-conipoiient sJ-steiii of inorciiiic salts, it \vi11 be found necessary that the substances sliall all 1iax.e the saiiie acid or basic radical. Other coiiclitioiis n-liicli the ideal inaterials for such an esaniinatioii iiiust fulfil are those of piiritJof iiiaterial and ease of haiidling. T h e choice of tlie nitrates of
iithiiuii, sodium, and potassium has beeii found to suit the iiiimeroils requireiiieiitsl enumerated above. It had heeii hoped that in place of ljthiuni nitrate, silver iiitrate might lie used, but it was found to decoiiipose too readil!. a t temperatures at which it vas necessary to work. Theoreticallj- this ~ v o u l dhave presented an important type since, accordiiig to Retgers,' the nitrates of silver arid potassiuin foriii a double salt, while neither the nitrates of sodiiuii and silver,3 nor sodium aiicl potassium form a double salt. T h e interest attached to this type theoreticall!- wonld have beeii increased by tlie fact that the melting-point of silver nitrate lies below the eutectic temperatiire of the sodium potassixiii nitrate inistiire. ,Is i t appeared adviFahle to ohtaiii a great iiuiiiber of iiieasuremeiits rather tliaii esceptioiial accuracy i n determining the freezing-points of the series of mixtures of the three coiiipoiieiits chosen, the following method was adopted. *Iii iron cj-liiider 3 cni in diameter and 2 0 ciii in leiigtli was closed at oiie end. It was then filled with a mixture of potassium aiicl sociiniii nitrates that melted at 2 2 j", or, in case the temperatiire of the bath needed to be lower than this, a TYoocl's fiisible iiietal was used as the bath. Into this fiisioii bath n.as plunged a test-tube which held the mixture whose freezing-point was to be cletermined. T h e mixture was thus fused, and b!- iise of a tlieriiioiiieter as stirring rod! solution was effected at as ion- a temperatiire as possible. The test-tulx was then taken out iiito the air a i d stirred constantly until the first crystals appeared. I t was then replaced i n the fusion bath for a nioiiieiit, taken out again, and the temperature at which the crJ-stals first appeared was noted. T h e observation was repeated several times for each mixture, the mean beiiig taken as the correct reading. F o r iiieasiireiiieiits above zlsoc, a nitrogen mercury theriiiometer svliich had been carefully coiiipared with tlie ReichThe work of Krickmeycr (Zeit. phys. Clietn. 2 1 . S9 ( 1S97): shows that lithium. sodium and potassium salts form neither isomorphous mixtures nor double salts. Zeit. phys. Chem. 5 , I j I i 1S90). Kricknieyer (loc. cit. regards silrer and sodium salts as capable of forniiiig isomorphous rnistures. This accords with the work of Retgers.
Stiidjc of' n T~i2,re-Coiiipoizeiid Sji.Ytcm
211
saiistalts of the chemical and phj-sical departments was used. T h e iiieasiireiiieiits below 2So@ were made by means of an ordinary mercury thermometer which also had been compared with tlie Keichsanstalts. n'heii lithium nitrate is fused in ordinary glass tubes, the sodium of the glass is replaced., the glass becomes opaque as if etched bj. hydrofluoric acid, and is then reaclil!- broken. Tlie thermometers had therefore to be protected by a casing of \-er!. thin glass. It is apparent that with the use of such small amounts of material m d this inetlioti of measurement, there is possibly an error of :Z 2' as the maximum. Ak 110 conclusions will be drawn v h i c h such ail error would invalidate, it has not seemed advisable to spend inore time in avoiding this soiirce of inaccurac j-. T h e sodium and potassium nitrates were found quite pure after being crystallized se\-era1 times. T h e lithiom nitrate was prepared from well waslied lithium carbonate. It slion-ed spectroscopic traces of other elements (sodiiun and calcium) but 110 impurity was detected 1))- ordinary analytical tests. The sodium and potassium nitrates fused n-itliout noticeable decomposition : xvith the lithium salt ho\ve\-er, there is a very slight decoiiipositioii,I which however is iiot very apparent until the temperatiire reaches 290'. Since only 'one measurement was macle abo\.e this temperature when it \vas present in the mixture, it will be seen that no error is introduced i n regarding it :is stable. In order to coI-er all combinations which inaj- be represented i n tlie triangle and to do so in such a \va\. as to economize time and material the writer has chosen the amounts of each substance in tlie mixtures and examined tlie freezing-points after the following scheme : First of all the freezing-point of pure sodiiuii nitrate was taken. T h e n sufficient potassium nitrate was taken to make its weight I O percent of the total weight of the mixture. T h e freezing-point was then taken, and then more potassium nitrate was added, sufficient to make its weight 2 0 percent of the total weight. Tlie freezing-point of this mixture was then taken, etc. I
Detected hy el-olution of gas, iiot by weighi~ig.
TTIeii this plan is follon-ed, first for the mixture of the potassiuin arid sodium nitrates, tlieii for the potassiiuii aiicl litliiiuii, lithium and sodium salts? oiie 11ia~readily see that when the results are plotted on coordinate paper, the freezing-point of an?. combination of these t h e e coiiipoiieiits taken two at a tiiiie is re acli 1y det e riii i ii ed . Fi-om the properties of the triaiigle it is apparent that n-hen one selects any point 011 a side, as for example that representing 90 percent sodiuin nitrate 11-it11 I O perceiit litliiiuii nitrate. (al\va~.sl)!. weight) and ,joiiis that poiiit to the corner representiiig p i r e potassium iiitrate, ei.er!- poiiit I!.ing 011 this connecting line will represent a iiiisture in lvliicli tlie proportion of sodium nitrate is to the litlliiiiii salt as c ) : I . T h e var!%ig- factor i u passing aloiig this line is the aiiioiuit of potassinin nitrate iii the solntioii. Siiiiilarl!-otlier lilies dran-iifroni an!- poiiit represeiitiiig .I- perceiit of sodium nitrate and i 100 - ,I-) perceiit of the potassiiiin salt to the poiiit representing piire lithiuin nitrate \\.ill indicate mixtiires in which the ratio of sodium to potassium iiitratesjs as I- to I O O .I-, nliile tlie ainoiiiit of litliinin nitrate maj- \-ai-!. aloiig this line froin o percent to I O O perceiit. LAccordiiig-l!. lines 1iai.e lieen c1ran.n from points 011 the sodium lithiuni nitrate line repremitirig I O O percent of either coiiipoiient, 90 percent of one and IO percent of the other, So percent of first and 2 0 perceiit of secoiid, etc., to tlie corner represeiitiiig p i r e potassiuiii nitrate, aiid other- lilies iiiter,sectiiig these ha!-e been dran-ii in a siiiiilar fa,diioil froni the side 1-cpi-eseiitiiig sodiuiii potassiuiii nitrates to the coriier for 1x11-elitliiuiii nitrate. IIistiires have then lieen iiiacle u p coi-respoiidiiig to the points of intersections of these t\vo series o f lilies. T h e ad\-aiitag-esof this nietliotl of procetliire are that oiie actual deteriiiiiiatioii is used for tv-o ciii-yes, :is is later sliuu-ii~aiid that tlic iiiiinl~ei-of iiieasiireiiit-]its is diiiiiiiislied. T h e disad\-aiitage is tlint the corners of the cliagi-am are not tliuroii,ylil?. esniiiiiied \vliicli hon-ex.er, iti cases like tile preseut, is not a \.er!- sei-ioiis uiatter. I11 tlie tahles ivliicli folloiv, there is gii.eii iiiider the foriiinla of each o f tile coiiipoiieiits tile j c r ( ~ ~ ~ / h/ t~ w ~, ~~ s~ ~i ~rof~~ that ~r h f coiiiponent in the mixture. Til the coluinii headed F. P.are giimi tlie freezing-points as ol)sei-\-ed. ~~
Table’ I (a) so
KSO, I
2
3
*
...
10.00 20.00
SA-0, 100.00
90.00 s0.00
4
30.00 70.00
%j
40.00
60.00
b
j0 00
jO.00
jj 00
4j.00
7
so,
. ... .... .... .... .... .... ....
S
60.00 40.00
(>
;0 00
30.00
I0
So00
11
c,o.00
* . 20.00 10.00
100.00
KSO,
....
I 2
7.21
3 4
14.90 23.0s
j
31.S2
6 41.17
a . . .
* . . e
.. .... . ... *...
L
46.11
9
62.02
jI.23 1
IO
67.74 73.63
(b)
..
*
...
~~
;os’
10.00
283
9.09
271
8.16 2 6 0 7 . 2 2 243 6.25 2 2 s
j.26 215 j.C0
3.s0
209 217
2,;9> 18.3: 2 j I 66.67 16.66 244 14.S9 233
80.00 73.47
20.00
....
~~
I
13.04
221
2
j.26
12.09
21-is that along this ciirve it is possilile to have eac'h of tlie three components separating as solid phase. There should therefore lie three distinct branches to the ciiri-e, and while it is possible to observe this from tlie data for series i f ) . the change of direction is T-er!. slight at the first break, where the percentage of potassiiini nitrate in tlie mixture is about tliirteen. T h e occiirreiice of the breaks in the ciirl-e is shon-ii better in Fig. 3,where the line drawn from the point representing equal amoiiits of lithium and Fodiuni nitrates to that deiiotii:g piire potassium nitrate will pass first through the field where the lithiuni jalt occiirs as solid, then through the sodium and into the potassiiiin nitrate field. As ma!. be seen from the direction of the boundary ciirl-es in Fig. 3 this class of cur\-es ia bj. no means of infrequent occurrence. Had one no other guide, tlie difference between the ciir\-ef;F;fi and the other curves iii Fig. 2 n-onld 1iai.e led one to suspect a change in the nature of the solid separating. I t is not uninteresting to note the iiieasnrements which have lieen made 1 1 ~ 7 other obser\.ers on the freezing-points of tlie three salts in question. These are sumniarized in Landolt and Bornstein's Tohclletz. For the melting-point of potassium nitrate, Person ( I 849) observed 339", Schaff,qotsch (IXj7) 338.3",Braiin (187jj 332', Cariielley (1876)353 I= I C by the calorimetric method, (1876) 332 z j"and (1S;S) 339 3: 2 ' , Guthrie 32o0,while lIaiimeri6 ( 1S83)foiiiid327". Tlie value obtaiiiedhy the writer was 327"1111corrected, and 337" corrected. For sodium nitrate the followiiig 1-alues had heen obtained : Person 310.5'. Brauti 314'. Cariiellej- 319",316"and 330k 2', Gntlirie 3" j", hla1i111erli. 29s". T h e writer foiiiid 3~8". T h e onl!. previous measiireiiieiits on litliiam nitrate appear _
I
_
' Jour. I'liys. ''
Ibitl.
I,
~
~
Cliern. I, 1 6 j (rS96). 71s (1S97).
to have been macle by Carnelley who obtaitied 267 So by his calorimetric nietliod, while direct observation gave 264". In the present instance, the melting-point was found to be 2 j33. T h e only systematic measnrements which have been made on mixtures of two of these substances appears to have been taken by Schaffgotscli.' A coinparison betxveeii his results and those of the writer are given in the following table. T h e n11111hers refer to the mixtures given in series ( ( r ) ; in tlie series S are gi\-eii the melting-points observed b y Scliaffgotscli, i n C those of the n-riter. 3 4 j 313 298 287 2 6 2 2 4 4 308 293 276 2 j 9 240 I
s
C
2
6 229
224
7 22j 221
8
9 1 0 1 1 1 2 2 230 5 0 280 3 7 1 33s 22s 248 277 308 337
;Is d l be obserr-ecl Scliaffgotscli's values al\va>-slie higher than those obserx-ed by tlie present writer, T o tliose interested in the melting-points of inorganic materials, the great discrepancies wliicli occtir in tlie measurements made by different obserl-ers iiiaj. occasion some surprise. It is not to be forgotten that accurate iiieastireiiients at high temperatures are difficult to make by means of a mercury tlierinometer. while tlie tlieriiioelectric method in its present form may iiot he suited ta eyer!. laboratory. tliorongli revision of tlie melting-points of inaiij- of tlie important inorganic coinpounds n-ould be of coiisiderable service for work at high ternperatures in nianj- of tlie fields of clieiiiistr\-. Had the nietliod of thermometry been dficientlj. accurate it nould ha\-e pro~ecl extremely interesting to have noted whether these salts depress tlie freezing-points of each other according to the general laws. is knowii these laws do not hold in concentrated solutions and since one lias here to do Jvitli solutions of great coiicciitratioii there is not to he espected a rigid agreement in this case. Making iise of the data given b>Person' for tlie heats of fusion and the melting-points of sodiniii and potassium nitrates, one finds it possihle to calculate the
,StuT(JI qf n ~ ~ ~ J I ’ ~ c - C OSjlsfi’ii2 J ~ ~ P O J ~ C2J2 ~3 ~ nioleciilar lowering for each solvent by making use of tlie formala 1: 4
-
0.02TP
11-
\\-liere E represents the molecular lowering of the freezing-point, ’I’ is the freezing temperature expressed in absolute degrees, a i d TY is the latent heat of fusion. Person gi\.es for K S O ; T :::- 333.5 - 273, for TT 48.9. Hence ERSo5 --=:I 50.4. For S a S Q he gil-es T =:= 305.8 - : ~ 273, TI- = 64.87>hence ESas,,,.-l 103.2. Despite the fact that the soliitions are all very coiiceiitr-ated, \ r e shall applj. to series ( 0 ) the forinnla &I
v
E af
where :
AI is the molecular \\-eight of the solute, E is tlie molecnlar 1oTveriiig of tlie freezing-point, g-is tlie relation (percent) of tlie solute to solvent, f is tlie lowering of tlie freezing-point obser\.eel.
C:ilcnlation slion s that for a ten percent solntioii of K S O ; in SaSC)->the molecular \\-eight of tlie former is founcl to be
76.7
instead of 101. I\Ieasureiiieiits (31,(4)> (5)aiicl ( 6 ) of series ( n ) x-ive 80.6, 90.3. 101.1 aiid 1 2 2 . 8 respecti\-ely. TVlieii the K S O acts as sol\-eiit for the XaSC),, a siinilar 1-ise in the inolecular \vei:,rht is ohser:d on passing to the i i i o r ~ concentrated solution;. JIeasiireiiieiits ( I I 1% (IO), (0)aiid i S ) of series ( 0 ) giye as the niolecular weight of SnS07,~7~ 62.6. 72.4niitl 91.9instead of tllt: actual T-alne 85. These iiieasiirriiieiits \roulcl iiitlicate that the salts iisecl abol-e \vi11 pi-o11al)l!~a t iiifiiiite dilution ..;lion it-lieii clissol\-ed iii each otliei-, ;I iiiolrcular \wiglit coiisideralil!. Ion-er tliaii the actual value. T h e iiieasiii-eiii~iitsgiyen aboye may be used to ascertain if it is possible to einplo!- tlie freezing-point Iiietliod in aiial!...;is of salts. If oiie a s s ~ i i i i ~ that ~ i wlien S a S O , is acided to K S O , i t cii-es at ordinary diliitioiis a depression correspoiitling to lialf its inolec\ilar \ieiglit, it ;xppears tliat for this method t o b e (if ser\-ice iii anal!.sis. the fi-eeziii,y-point iiiiist he deteriniiietl to the ~
tenth part of a degree if one would determine 0.028 percent of S a S 0 3 . JTitli ordinar)- methods, such accuracy of nicasureinent is at present impossible ; but it appears not unreasonable to suppose that such a method could be made to apply as a verj great help to the anal) st when dealing with compounds such a3 the alkalies. T h e two requirements ~vould be a considerable amount of material for the test, and a delicate method of therniometry. *At a time when great interest is taken as to whether the presence of two solutes gives a clepression of the freezing-point equal to greater or less than their siiiii nlien taken separately, it would have been interesting to have subjected this case nit11 i t i inorganic qolvents to tlie test. a general statement it may he remarked that here the depression is as a rille greater than the siiiii of the depressions when the substances are added siiiglj . T h i s would seem to coliform to the rnle gix-en by -\begg‘ ant1 supported by his iiieasurements. Later work by McIntosh’ showed that the Xbegg rule is by no iiieatis general-that iii fact ((when the three components are iiiiscible tlie siiiii of the single depressions is usually greater than the clepression for the mixture ; hut this is iiot always triie owing to disturbing condition5 which are iiot yet definecl.” I h r i n g these experiments no evidence has been found which points to the existence of tlvo liquid la\-ers or n-ould indicate that the three coiiiponents are not infinitely miscible one nitli the other. This case therefore is one where disturbing influences come into plaj-. I t had been hoped that sufficient nieasiireiiients might he found in tlie literature to illustrate the use of the triangular iiietliocl of representation in a three-component iystem of metals. Despite the great number of measurements which have been made with various mixtures of three metals, the data are insufficient for the construction of a complete diagram. T h e very niiineroiis atid accurate experimental results of Heycock anti Keville were the subject of considerable manipulation, but when they were represented in the diagram it was invariably found I
Zeit. phys. Cheni. 11, 2 j 9 (1S93). Jour. P h p Cherri. I, 171 I rS9;).
225
that these scientists had worked o\.er a very small portion of the triangle [usuallj- one corner 1 aiid that the same iiieasiiretiient was soiiietiiiies repeated appareiitlj- n-itliout being iioticed. -1plotting of their results for gold, cadiiiiuiii aiicl lead' would show a tj-pica1 case of this. Of coiirse it is permissible and will often prove very useful to iise the triangular cliagraiii in such a fashion that an\- or all of its corners iiiaj- represent a inistiire of tlie three components taken two at a time pro\-icled aln-a>-sthat the ratio of the t\vo remains constant. Tlics i ~ studying ] the results of Heycock and Sel-ille on gold, cad~iiiuiii and lead. the \Triter found it convenient to use as corners, IOO percent lead, So percent lead and 20 percent cacliiiiuin, So percent lead aiid 20 percent gold. ;ln attempt was made to iise the data gi\-eii h>. Carnelley to construct a cliagraiii for tlie three metals, bismutli, tin aiid leacl. Here again the data are insufficient-a fact vhicli is not siirprising when it is considered that all the ineasurenieiits taken during tlie present Xvork are not siifficieiit to stamp the tlediictioiis as to changes of direction of the boiindarj- cur\-es as alisolutel\- acciirate. T h e stud?- of sticli a s>.steiii of ~iietals--n-liether of three or iiiore coniponeiits-ofTers a most interesting fielcl to the chemist or metallurgist ; tlie isotherms and the lioundaries of the fields caii gix-e iiiiicli useful iiifoi-iiiation in siich technical \\-ork as the desil\-eriiig of lead. etc. T h e stud>-of the crj,stalline structure of nllo!.s, lvliicli is at present attracting so niiich attention. caii uiitloul~tedl!- be g-ready facilitated b y tlie itse of ~ u c l ia cliagraiii. 117leii it is distiiictl>- understood that as a rule, oiilj. \Tithin a certaiii field, oiie metal can cr>-stallize out first, that iii other portioiis it is possible to 1iaT.e t\vo metals c r j ~ s t a l l i z i iont i ~ side li>. side, and at one point three metals, tlie iniportaiice c.)f 3 iiniforiii rate of cooliiig- liecomc~sapparent \vlien rigorous comparisons are to lie made. T h e iise of the diagi-niii is not hon-e\-er to he coiifined t I cases u-here tlie mixture is perfectly liotiio:,.eiieous : cases lvliere two liquid la>.er..; appear, it is at present tlie onl? iiietliod of graphic representation. ' ( 1
1
~~
I JOUT.
Clieiii, S O ~65, , 6s 11941 .
111the m e of tlie triangular diagram as represented in this paper, the axis perpendicular to the plaiie of the triangle has been chosen to represent tlie variable, temperature. I t ma!- lion-ever be chosen to represeiit other variables, c'. g. conductiI-it!,, time, pressiire, etc. Tlie first two will be gii-eii hut a brief coiisideratioii since experiiiiental data seem to be lacking. If coiiductivi tj- iiieasiireiiieiits of a three-coiiiponent sjsteni be plotted as shown in this paper? it will lie fouiid (the otlier 1-ariables such as temperature aiid pressnre being here constant ) that a surface or series of surfaces will resnlt. Tlie esaiiiiiiatioti of tlie discontinuities in such siirfaces iiiiglit afford iiiucli assistance in establishing tlie definitions of sol\-ent and solute, n-liile the grapliical iiietliod eniplo\-ed niixlit be of service i i i studies of the theories of dissociation or association. IYlien the perpendicular a is used to represent tlie 1-arialile time,' it is possible to represent in the triangular diagraiii cur\-es represeiitiiig speed of reaction. Takin:: for the moment :t concrete case of a hiiiiolecular reactioii-
dichloracetic acid
+
aiiiyleiie :::.;
ariiylene~ter
one nia! reac1ilJ- see that nitliiii the triangular diagram there will lie for each temperature a line passing tliroiigli the triangle from pure alii)-leiie to liiii-e acid, aloiig wliicli are represented tlir qiiaiitities of each substance present xt eciiiilibriuiii at this teniperature. If iiow the temperature be fised, and tiirie he represented oil tlie perpendicular asis, tlie ciir\.es rqt-eseiitiiig speed of reaction pass from tlie sides of tlie triangle to the coiiipositiontime line of equilibriniii. Of this line, little is kiio\\-ii. I t n-ill lie geiierall>- conca\-e to the plane of tlie triangle sirice it is el-ident that a piire component cannot of itself change into aiiother in ai1 infinit!. of time. T h e possibility is not precliided iion-e\-er, that this line may also have a \va1.>- appearance. For each temperatiire there \vi11 lie a different line ; the investigation of tlie relations between the series of lilies offers iiiaiij. iiiterestiiig features. 1
T I i L suggestion is (ILWto Professor I h i c r o f t
St2tdJ1Of
ff
T/1J*?P-
C0111$012t’12t
SJ’Sf(’111
227
T h e extension of the application of the triangular diagram to a four-component system offers another wa>-of presenting tlie La\\-of Mass -1ction graphically. Suppose \\-e choose as tlie four components the classical case-alcohol, acid, ester and \vater. This choice is so made because the final equilibrium is, within certain limits, independent of the temperature (\.an ‘t Hoff) aiid lieiice tlie representation of temperatiire is uiinecessar?-. T h e foiir-component s)-stein ma?- then lie represented by a tetrahedron as has been sho\\-ti previously by Roozehooin. Of this each point represents piire components, each edge tn-o-component, each face t~iree-coinpotlentand ever>- point within the tetrahedron a four-component system. &inexamination of all tlie four coinponent s>-steins a-hich can be in equilibriuni, shows that their compositions are represented by points lying on a certain surface witliin the tet-raliedron. It is owing to the niatheniatical properties of this snrface that tlie Nass Law may be applied rigorouslj. to the systcni chosen above. If in place of the sj-stem chosen above there liad been chosen one where tlie final eqiiilibriuin depends on the teinperatnre, a series of cliff erent surfaces of equilibriuni \\-onld have been obtained of such properties that they are connected by the \.an ’t Hoff equation
These surfaces IT-odd prove especiallj- interesting in the cases n-liere cloiihle decoiiiposition is possible. If in these cases there occiir an\- discontinuities in the surfaces of equilibrium finall?. obtained, it will he apparent that tlie Xass Law formula in its general forin is not applicable and that the eqiiation for each surface is deterininecl by the introduction into the forniula of constants-such as has been done recently in tlie work of Railcroft and his students on three-component systems. T h e data for the construction of such a diagram appear to be lacking. I n this paper has been given : ( 0 ) T h e experiiiieiital data as to the freezing-points of a considerable number of mixtiires of lithium, sodium and potassiiiiii nitrates.
228
SfZlKI' Of
c[
~ ~ l J ~ C ' C ' - ~ ~ ~ l l lS ~] 0J 1S2fr ~' ll 2? tl
(6) Tlie classification aiid iiiterpretatioii of these results according to tlie Phase Rule. ( 4 Tlie suggestion as to tlie possihilitj- of applying tlie freezing-point iiietliocl in tlie case of analysis of inorganic salts. id ) Reference to the probabilit!- that some iiiorgatiic salts when dissolved iii others show a molecular weight Ion-er thaii that obtaiiied bj. tlie iise of other solT-eiits. ( c ) A suggestion as to the iiiiportaiice of locating tlie fields of each component in an esainiiiatioii of the crystalline structure of alloys, aiid in technical iiietallurgical n-ork. Finally, attention has been especiall~-~dran-n to the relatiom subsisting between tlie Mass Lan- am1 the equations of surfaces of equilibriuiii. Camel/ c i i i;#crsifj,, yo ti iin / : I , , iS9S.
