BY DOXALD H. ASDREWS.
G I R A R D T. KOHMAS, ASD JOHS JOHSSTOS*
In the course of the investigation of the solubility equilihriuin in hinary mixtures of the three isomeric s;ubstances,-oltho, metn and p(1m XY-benzene, respectively-it as found that, the inethod antl apparatus conmionly U S P ~for this type of work yield imults of insufficient accuracy for our purposes. It was therefore necessary to go into thc tlcsign of the whole apparatus, in order t o ascertain wherc refincnicnts could lie introrlucec!, and t o consider the theorj- underlj-ing thci moclc of experiment as a means of evaluating the results correctly. To a discussion of these points3 which have not always received due consideration, the pri.sent paper is clevotecl. The general type of method n.hich may i w i i m l is largely tleteriiiinecl 1.1:; the fact that it is not practicahlc- a t least. licforc thr tquililjriruii diagram is known-accurately t o analyze niixtures of ortho. wctrr or pnrn isomers. (’onsequently we cannot use a method in which tlw solution is analyzed after thc temperature of equilibriuni has heen ~ b s c n - c t lhut . ~ ii:ust have recourse t o a determination of the temperature at JT-hich the stable solid phase just appears (or disappears) in a niisture niatle up to a given composition. JIorcover. the former method ~voultlrequire relatively large aiiiounts of tlie p u r e >ubstaIices, amounts which, as we have founcl. can not in niany cases IF rcatlily obtained by reason of thc shrinkage of illaterial attending repeated rccr;\-stallisation. It is necessary therefore to use the familiar inethotl of taking timr-teniperature curves, and t o refine thc inode of esperinicntation so that the desired accuracy may he attained. In the first place. by reason of the sniall heat concluctivitj- of the substances under investigation. the temperatiire-niea~iiriiig device Inlist have a small heat capacity. a sinal1 lag, antl must itself conduct away from the solution as little heat as is possible. These conditions arc h t fiilfillecl hy t h e thermoelement ,? especially if it is macle of v ~ r >finc - wires, which is iiioreovei’ an altogether convenient and satisfactory iiistruinent t o usc. antl incoinparably better adapted to this purpose than is the iiiercury thernioineter which has been used by sonie authors:. I n t h r secontl place, and for the saiiie reason again, inuch clearer indications can IF olitainctl with a small quantity of
S O L C B I L I T I E b O F ISOMERIC O R G h X I C C O M P O U S D S
915
material-namely. of the order of I cc.-than with large quantities;l for, in the latter case, there will be appreciable difference; of temperature throughout the mass, and the heat set free hy the transition of the outer layers (which cool most quickly) i; transferred only slowly to the thermometer. Moreover, one must see t o it that the degree of undercooling. when crystallization is induced, iq not escessive ; otherwiv the heat set free does not suffice to bring the mass up to the equilibrium temperature and a t the qaiiie time to compensate for the losses 1.i~ conduction and radiation. The forin of the timetemperature curve is, of course, itself the best criterion of the usefulness of any refinement : though it ib possible t o deduce. from Sewton‘s Law of cooling. the main conditions nhich a satisfactory set-up must fulfil. In brief, it is necesqary to have ai1 apparatus such that the rate a t which --a the material lose9 igains) heat can tie closely controlled-e. g., such that this rate i; very nearly constant while the -s material changes IO’ ( o r niore) in temperature; and this iiiiplie. that the eft’ective temperature heat1 n.hich -m --B controls the rate in question can lie nieasured and controlled. T l w e conditions are fulfilled t)y the form of apparatus illustrated in Fig. I , M hich --b will now be described in detail. I
The Form of d p p a ’ a t i i o ii\ed. The external vessel is a Dewar tube (one quart size) silvered except for a longitudinal slit, for viqual ohervation of the melt: it is cloqed hy a cork stopper CI into which wa1 fitted: ( I ) n siiialler stopper C ? ; ( 2 ) a I--shaped tuhc carrying a nichrome resistance element which serves to heat the bath fluid (usually paraffin or, a t temperature> above IOOO, air): (3) a thermo-
FIG.I Sketch sliowine the form of apparatus used. The glass tulic €3 mntaining the sample 11 is attached IIY a ruhher band t o the central tube A, through which t h e thermoelement TI passes. The thermoelement 1’1 gives thc effrcatire temperature head ljetn-een surroundings 8 and tube B. H is an air heater to rrhest 11; and D a nichrome coil to heat the fluid in the outer Dewnr vewel.
The same ronclusion !vas reached by IV. P. K h i t e , with rrspect t o silicates (Am. J. S(ii.,2 8 , 453, 47; f I y : $ who i n d e d . in the pap-rs cited. give; :I di.qcuvion in many respects
similar t o that whic,h f o l l o a ~ .
916
D O S A L D H. ASDREJV'S. GIRARD T. K O H U A S , J O H K J O H S S T O X
element TS. The stopper C'? rupport3 centrally a gla.> tube -4,on which has been fitted a third stopper C 3 which in turn fit. into the shield S1; this was in some experiments a .mall empty iinsilvcrccl Ilewar tube (as illustrated in Fig. I), in others merely a thin-walled glass tube which proved to be practically just as effective. The -uhstance under invc.tigation 11 i- contained in a thinn-allecl glass tube R 16 111111. diameter. 3 0 mni. long) attached to A by means of a rubber band: its teinperaturc i h i i i c a ~ i ~ r cby d the thermoelement T I , made of copper i 46 R antl S gauge. 0.04 n n i i . ~and constantan ( = l o , 0.08 mm.). the copper wire being wound helically ahout h i t not in contact with) the other for a distance of about 5 ems.. so a- to ininimize the heat f l o along ~ this mire. The junction of TI n as. nhererer practicable, immersed directly in the melt to a depth of 2 - 3 cni.: ot1ierni.c it mi-protected by a verj- thinwalled capillary tube filled with paraffin oil. This .afeguard however may cause differences of as much as 2' between the temperature as recorded antl the real temperature of the melt when the latter iq no more than 2.;' above room temperature. The melt is stirred -iifficiently 11y means of a small electric vibrator (not shown in Fig. I ) attached t o the shield tube of TI: but stirring is unnecessary vhen crystallization i q oncc itarted throughout the melt, and indeed becomes iinpovible when about a foul th of it has crystallized. One junction of a second thcrnioelement T? is arranged t o touch tube B external t o the melt, the other junction to tonch the outside of the shield S; this enables one to read directly the effective temperature head. The temperature of the material is raiqed. nhen clcsiretl. by a stream of heated air directed down through the tube H. This tube is ~enletlt o a wider glass tube closed by a cork through n-hich passes an inlct tube and a porcelain tube carrying a resistance coil in the axis of the gla+ tube; the air pressure and the voltage can both be rcgulated. This arrangenicnt was found t o be very convenient, as it proved very desirable to be able to re-heat the v m p l e without otherwise disturbing it. Indeed we replaced the paraffin and its heater in the large Dewar vessel, by air and a second hot air blast when a temperature higher than 100' was required there. and found it very satisfactory. Xn experiment is carried out in the following manner. From 0.5 - 0.8 gram of the material (11)t o be investigated i. placed in tube B, which is then, with the thermoelement T1 antl T?.set in position within the shield S. Paraffin in amount appropriate to establish of itqelf a cooling rate of about 0.5' a minute within the temperature ranpe investigated, is put in the external vessel; its temperature iq raised I O or 2' abo3-e the melting temperature of M, and ?tl is melted directly by a stream of heated air. The melt is then agitated by means of the electric vibrator. the system is allowed to cool, and the electromotive force of T1 is observed on the even minute, that of T? (or of T? connected in opposition to T1) on the half-minute. M-hen the temperature of 31 has fallen about half a degree belovi it< melting temperature (as obSome form of shirld a t a cwntrollahk ti,mpcratiire is essential; othernisc the rate cf cooling, over any reasonable range of temperaturr, would he too rapid. Quite recently, we have been trying another form of shield, consisting essf,ntially of n brass tube about which a heating coil is ~ o i i n d ;and the results are vcry promising.
S O L U B I L I T I E S O F IbOBIERIC O R G A S I C COJIPOUSDS
917
served, if necessary, in a preliminary approximate experiment), the melt is inoculated by introducing through tube A a minute crystal of the solid phase and touching it to the surface of the melt. I n this process. it is very important that no appreciable amount of heat should thereby he conducted away, as otherwise the equations of heat loss will not be valid. A good procedure is to use tn-o glass threads, a short one n-hich remains in the melt but extends above its surface: on the tip of the other iq placed the seed-crystal, and it is then touched to the surface near the other thread, which aids in the growth and spread of the nuclei through the liquid. This form Gf apparatus, in which the rate of temperature change can readily be regulated at willqcan be used in place of the method, now used in metallurgical work where accuracy is desired, of lowering the specimen through a furnace in which a uniform temperature gradient has been established. For instance it proved easily possible, with an alloy of 69c"c tin 3 1 7 bismuth, t o maintain the rate of cooling practically constant over a iange of more than IOO', and t o determine from a single time-temperature curve both the primary and the secondary freezing temperature. For work a t high temperature the paraffin or air of the external bath would be replaced by a lolv-melting alloy or salt-mixture. Heating curves too may be readily made by slowly raising the bath temperature. In the case of these organic suhtances, however, heating curves are less satisfactory than cooling curves, which may be due in part t o the fact that in the solid the temperature distribution, as indicated by a number of thermoelements frozen into it, is uneven. I t WVRSfound that a spiral of aluminum foil imbedded in the solid and attached to the thermoelement improves the results of heating curves.
The Interpretation of Time-Temperature
Curves
I . For a Single Substance. The form of the time-temperature curve for the peiiod of freezing of a single pure substance is given in Fig. 2 , the dotted portion at B representing the limiting case of 110 undercooling before freezing sets in. The temperature of a mass of a pure liquid, surrounded by a shield cooling at a uniform rate (along RS), falls alcng the line XB t o C, a t which crystallization is initiated. The heat supplied by crystallization raises the temperature t o that of the true equilibrium between solid and liquid; and the curve is horizontal, along DE. When crystallization is substantially complete, a t E, the effective temperature head is relatively large, and so the solid mass at first cools rapidly; but finally the curve, at F, again becomes parallel to RS'. The shape of the time-temperature curve during freezing is one of the best criteria of purity. With a perfectly pure sample, the temperature remains quite constant during freezing (DE, Fig. 2 ) ; and in fact readings differing The curve for the solid would however he slightly nearer RS t h a n t h a t of the liquid, sinre the specific heat of the sTlid is somewhat the smaller.
D O S A L D H. .%NDHETVS. GIRARD T. K O H J I A S . J O H S J O H S S T O S
918
by no more than I microrolt ( 0 . 0 ~ ' )oyer an interral of five minutes or inore can readily be obtained. if the substance i q ieally pure. If the substance contains admixed impurity. the initial temperature of freezing will likely be depressed, the temperatui e falls off as freezing progresses and the concentration of the impurity in the solution increases. 11hitel has given a thorough discussion of this matter. and cf its usefulness as a means of estimating the amount of impurity. For the mea\urenients cf solubility. specific heat. etc., which ]!-e wished t o undertake, really Fure inaterial was iwquisite and one of the requirementq set for the apparatus was that it should yield cooling ciirws which could be trusted as a criterion c>f purity. I t was rather ciistur\iiiip t o find t h a t , without exception, the substances hciight as pure organic chemicals contained impurity ranging from zcC up to 105.In the case of the disubstituted benzenes, the prcsence of I niol per cent impurity cause< about 0.5 - 0.8' lonering of freezing temperature; so that in thif case v-hen the material is three-fourth. frozen. the freezing temperature would ha\-e fallen off by a t least 2'. By E fiactional crystallization we succeeded Y b in purifying sxmples of our materials $0 that when 7 5 7 frozen the temperature cliffeied froin the initial freezing teinperature by less than o.I', indicaTINE ting therefoie lefs than 0 . 2 (~ impurity. I.l(, 2 During the last quarter of thP 1 \pi(sal tiine-tciiil)c~,i'ul(~ ciii\ c' f o r 'i freezing j,telval the temperature mny piiw wl>*T.inw fall off inore rapidly, but this is to he attributed in part to non-ideal conditions. For inctance it is likely that the last fraction crptallizing cannot supply heat t o the thermoeleiiient and it. surroundings fast enough t o enable the true equilihrium temperature t o 1 r 7
(1
Time AI inut es 0
I 2
3 4
5 6
5 8 9
bOLTBILITIES O F ISOMERIC O R G A S I C C O V P O T S D S
919
maintained. I t has therefore seenied best not t o make use of this last portion of the curve in judging purity. -4s an illustration. the original data on two cooling curves on a purified sample of iii-dinitrobenzene are appended; in the more rapid the surroundings were at 2340 microvolts, in the second a t 2980 microvolts ( 5 microvolts = 0.1’) I n order t o he sure that the time rate of heat loss by the material 11 in our apparatus is proportional t o the effective temperature head, in accordance with Sewton’s law, we made m i l e observations of the rate of cooling cf liquid naphthalene under various heads. The results show that Sewton‘s law is very closely followed. as is evident froin the last column cf Table I. even for a head much larger than any used in our n-ork. \ITe are therefore justified in using this lsuwin the interpretation of time-temperature curves observed with this forin of apparatus. TsBLF
I
The rate of cooling of naphthalene, for various temperature heads. (I’ = about j o microvolts) Timr 1i:ilf-mimitrs
Ttxrnp. of mntcrinl inicro\-olt s
% 6178
I 2
1627
3
4
0.351
j608 1192
5188 6
883
8
338 4890
I
662
352
49 i
,358
9 IO I1 12
4479
13
I4
350
3 i 2
4349
280
15
16 17
210
4175
Mean 0 . 3 5 2 Sewton’s law may be written
where 8, and e,,,are the temperature of shield and melt respectively, t is time, and K’ a constant for the particular set-up and material. X c w if H is
920
D O S A L D H. ASDREIT'S, G I R A R D T. K O H J I A S . J O H S J O H S S T O S
the heat content of the melt, and C' its heat capacity, dH = C d 0 hy definid H de tion, and __ = C - = CK' (8, - On,). I n the case of the oiganic subdt dt stances under discussion we are justified in considering C t o be effectively constant over the temperature interval in question1, and also in taking the heat capacity of the solid t o be sensibly equal t o that of the liquid, which implies in turn t h a t the heat of melting is. for this purpoqe. independent of the temperature. On this basis n e may write I< instead of C'K', and the heat lost from d t o B (Fig. I ) is -
AH
=
HB - H,
=
s
I
- constant throughout) and BCDEF to its latent heat of freezing. This was confirmed by a series of curves taken on ~iaphthalene.which shqwed that this area (as measured by counting squares on the plot of the several curve>) is very closely proportional t o the weight of naphthalene taken. Thus from time-temperature observations it ii. possible t o dctluce both the heat capacity arid heat of fusion of a substance 11y measuring the appropriate areas and multiplying by a factor evaluated from a similar curve, made under identical cmditions with the same set-up. for ionic reference suhtance. This method of "radiation" calorimetry has been propow1?, though little has been done with it; it appears however that resdts of satisfactory accuracy could be secured, especially at temperatures up t o zoo3 or 250'. by proper design of apparatus, arid that such a method might prove t o he very convenient. I n this connection it niay be remarked that temperature may not be uniform throughout the cooling body, especially if it is not a good conductor of heat. On this point White3 has published solile interesting observations. He found in a cylinder of naphthalene, about ;mm.diameter, cooling about i o a minute, no difference of r,s much a$ 0.1Oso long as the naphthalene was liquid, but immediately after freezing the difference from outside t o center exceeded I ', Burger? also has made similar ohservations. This has been shown 11:- actiinl meaeurrments o f h w t cnpacit>- of a series of these organic substances. both as liquid and :is solid; thcsr mensiirements nil1 1)e described in a lat,er paper. ?Ruff and Plnto: Ber. 36, 2377 (19' 3 ) ; Hiitrner a n d Tnmmann: Z. anorg. Chpm. 43. 2 1 5 , (19og);W.Plato: Z.physik.Chrm.,55,721, (19'>61;58,3j0,(190S): 6 3 , 4 j 3 , (19oS):\Y.P. White: Akm.J. Sei. 2 8 , 485, 1 9 ~ 9 R : . Schn-arz and H. Sturm: Rer. 47. I 733, (1914). G . D. Roos: (Z.anorg. Chem., 94, 329 (1916)) has used it t o olitain values of hrat of melting of some metals. IV. P. K h i t e : J. Phys. Chem.. 24, 392, ( I ~ z o ! . H. C. Burger: Proc. Acnd. Amstcrdam, 23, 13 11920). "Otisc~rvrttionsof the temperature during solidifirntion"; Ihid. p. 616. "The proccss of solidification as a problem of ronduction of heat."
bOLUBILITIES O F ISOMERIC O R G A S I C C O l I P O U S D S
921
I I . For a Bzrzaiy Mixture. h binary mixture cools similarly along -AP (Fig. 3 ) until the component X begins (in absence of undercooling) t o separate at P, when there is a change in direction (along the curve P D ) but no horizontal portion of the curve. The heat set free now causes the rate of cooling of the melt t o change in a perfectly definite \yay, because t o any temperature below P there corresponds a definite composition of the residual liquid, hence a definite amount of the component has crystallized and a definite total amount of heat has been disengaged. The composition of the residual liquid approaches that of the eutectic as the eutectic temperature is approached; at that temperature the liquid still remaining- behaves as a pule substance. I n this case therefore the momentar\composition of the solution is a factor in the cooling curve and in its interpretation. The typical experimental curve for a binary mixture differs only in that some undercooling is unavoidable and, indeed, not undesirable provided that the curve he interpreted properly. K h e n crystallization is induced, a t C, equilibrium between S and solution is soon attained and maintained thereafter, and the heat set free raises the temperature rapidly t o a maximum D, beyond which it then falls off as before, a state of equilibrium being maintained. It is clear that the compoTIME sition of the liquid phase at D differs from FIG.3 that of the original solution by the pro- Typical time-tcmpernture curve for a binary mixture. portion of S which has then crystallized; and in careful work this fact must be properly taken into account. The usual methods of making this correction are not based upon sound principles and are unsatisfactory, as will be shown on a later page. I n order properly to learn how t o interpret this form of curve, it was necessary t o consider the theory of the process, as based upon Xewton’s law cf cooling which is-as we have seen-valid under our conditions of experiment. I n proceeding along the curve from B t o D the system passes from solution at el t o a mixture of solution with n mols solid X, again at el; and the heat lost by the cooling mixture is nL, where L is the molal heat of fusion of X. But the heat lost is also, as we have seen, proportional t o the area B C D J L . Now if, for the given mixture of X and T,8 0 be the real equilibrium temperature-i. e. the temperature at which the first trace of X would tend t o crystallize-the system passes from a state of equilibrium at P (0,) through an unstable region t o substantial equilibrium again at D (el). For this small range of composition the equilibrium concentration (solubility) of X is practically a linear function of the temperature; that is, the lowering cf equilibrium temperature is proportional t o n, the (small) number of mols of X which
922
DONALD H. ASDRETVS. G I R h R D T. KOHLIAX, J O H X J O H S S O S
then have separated. Hence this lowering, namely (0, - O1). is proportional to nL and therefore t o the area BCDJL (estimated for instance. by counting squares). From this it is clear. in the first place. that by varying slightly the point C a t which the mixture is inoculated, h t h this area and the maximum D (e,)will change correspondingly: and, in the pecontl place. that the several values of 01 plotted against those of the area will lie on a straight line; and. in the third place, that this line extrapolated t o zero area corresponds t o n = o-that is, the particular point so obtained is the equilibrium temperature 0 0 corresponding t o the knon-11 initial composition of the solution. This method has been used in the determination of the solubility diagram of a number of systems composed cf 0 , m , p isomers-namely.. e. g. the chloronitrobenzenes. nitroaniline~.dinitro1)enzeiiw xiid nitrohenzoic acid.. Indeed
124.0
0
I
I
10
20
TIME
Frc;. -1 Shows three a o t u d CUI'VCS foi, thc siiiir s a n i ~ ~ lwith r . diffcrcnt degrees of undcrc>ooling. superposed; showing that t h c maximum chs.ngrs. :ind that hack extrapolation is iincrrtain. It also shows t h r graph of nrrn against mnximum. lcnding t o a ?ormat extrapolation.
in these cases we have an independent proof of the accuracy of this method of interpretation : for these systems-as will he shown in a later paper-behave as ideal solutions and the solukility curve as calculated on this basis (from the melting temFerature, heat of melting and specific heat of the substance crystallizing) coincides with t h a t derived as above from cooling curves. For any given mixture, two or three time-temperature curveL: usually suffice; three such curves are given. w p e r p o d . in Fig. 3 , which also shows the corresponding plot of area against maxinium temperature. K i t h the apparatus described the error c,f dctciiiiinatioii is not more than 0.1' or 0 . 1 ~ ;in composition even near the eutectic point. For comparison the error introduced by assuming, as many author- have (lone, that the maxiinurn ternper-
SOLUBILITIES O F I S O N E R I C O R G A S I C C O M P O L X D S
923
ature 01 corresponds t o the initial composition may well be 3 O , equivalent to j - 8 mol per cent in cornposition.l Another method of interpretation has frequently been used, for instance. by Bell and Herty?, \Torking with systems similar t o ours. I t consists in considering the initial portion D E of the graph (Fig. 3) t o be linear. prodiacing it backwards t o meet A B . and assuming that this intersection represents the temperature ccrrespending t o the initial crystallization cf S from the given qolution. Xow with different degrees cf undercooling, of a single aolution, this procedure l e d s t o different values. as is evident from Fig. 4; and is therefore unsatisfactory wherr accurate results cn solubility are desired. AIoreover, with solutions initially near the eutectic p i n t , the curvature of the porticn D E is PO great as t o render back entrapolation very unceitain, if n d imposiible. The approximate character of thiq niethcd of extrapolation has also been remarked in two recent papers?.
Temperature-Heat Loss Curves I n time-temperature curves the scale of time if arbitrar\*. The fundamental factor is heat-low. X temperature - heat loss plot, which has some significant properties, may be constructed as follows. The temperature e,,’, taken at some arbitrary time as zero, is plotted on the zero axir of heat lo Fig. j. The temperaturr head (e,,,- e.) = hl is then measured one-half minute later: hl is assumed to be the average temperature head for that minute, and consequently the heat loss in that minute is proportional to hl. The temperature e’n, at I minute is therefore plotted hj units to the right of the zero axis: similarly h ? is measured in the middle of the second minute antl e”,, at the end. and e”,,is plotted at hl h?: and 90 on. S o w the heat lost by the system in passing from a stable .tale at one temperature to a stable state at anothcr is always the same: confequently if a second curve of this type. for the same solution, is plotted on the same diagram, with the same temperature as zero point, the two curves will coincide throughout the range of stable states. but not over the unstable range-that is. the central portion of the ciirve will be different with different degrees of undercooling. Thii is evident from the series of three such curves reproduced in Fig. 5 , which i i based upon the same experimental data as is Fig. 4. Kow the left hand branch of the curve,-that is, for the liquid-is linear if the specific heat ib constant, as over thi, range it is for practical purposes; and since, as we have seen, the initial lowering of equilibrium temperature is proportional to heat loss, the upper portion of the right hand branch is now also linrar. Thib straight line corresponds exactly to the straight line of the area-maximum temperature plot: and if extrapolated backwards it cuts the left hand branch
+
Severthclms tlik maximum temperntiire is, un:lrr constant experimental conditions. rluitr rrprodwi1)le. antl could be used as :I calibrated control method for the :indysis cf mixturcs. J. 11. Bell antl C. 13. Herty. J r . : J. Ind. Fng. C‘hcm. 11, 1124 (1919). 1.I,. l I n c L r o d , 11. (‘. Pfund a n d 11. L. 1iirkpatric.k. J. .Im. Chem. Soc. 44, 2 2 f o (19221: C. A . Taylor and 11.. H. Kinkcnharh: 45, 104 i 1 9 2 3 1 .
924
DOXALD H. A S D R E W S , G I R h R D T. KOHRIAS, J O H N JOHKSTOK
at the true equilibrium temperature 0 0 corresponding to the initial composition of the solution. It was in fact found that both methods of extrapolation yield identical results. If a time-temperature curve is taken under conditions such that 0, - 0, is very large, and hence liable t o change by only a few per cent in the course of the curve, then the heat loss will, if Sewton's law holds, he nearly proportional to the elapsed time; under these conditions the time-temperature curve is effectively a temperature-heat loss curve, and the method of hack extrapolation (as commonly used heretofore) would lead t o accurate results. On the other hand, a temperature head large enough t o be taken as constant, would in most cases cauSe the rate of cooling to be too rapid for accurate
I
5L
130.0
,
I
4
2 WEAT
6
LOSS
FIG.j Shows the same three mrves as in fig. 4 plotted in tr>rmsof heat loss agalnst temperature; the right hand branch is now a singlc curve which when produced liackwards, lwds again t o the same extrapolated va!ue.
observation of the actual temperature. Consequently the temperature head is usually in practice small, and hence liable t o considerable relative change unless special precautions are taken to maintain it constant. hIoreover if the temperature head is small, the portion DE of the 0, curve-corresponding t o the gradual crystallization-must be more or less parallel t o the 0, curve', hence also to the 0, curve before freezing set in; consequently this point of view leads again to the conclusion t h a t back extrapolation can yield only approximate results. T h a t the 8, and 0, lines must be parallel, if the former is straight, may be proved as follows: The differential equation for heat loss in a cooling binary (or ternary) system from which X is crystallizing, may be written: - K dH= c - + de,L dn dt xdt where C is t h e heat capacity (assumed constant) of the system, n the number of mols X separated as crystals, a n d Lx the molal heat of fusion of X. If the 0, line is st,raight, d%/dt is constant: for the short range considered, d n / d t is also constant. Consequently d H / d t is constant and hence, from Newton's law, (e,- Om) is constant, i. e. the two lines are parallel.
SOLUBILITIES O F ISOMERIC O R G . I S I C COJIPOUSDS
92.5
In order therefore t o secure an accurate value of 0 0 , the temperature at which X tends first t o crystallize, for any given solution, it suffices t o take two or three cooling curves on that solution, inoculating it at slightly different temperatures (point C, Fig. 3) : t o note in each case the maximum temperature 01; t o measure (e. g. by counting squares) in each case the area BCII J L ; to plot this area against 01and extrapolate to zero area which corresponds to the true value €30. This method of interpretation is simple, satisfactory and free from the uncertainties which attach to the other methods which h a r e been used for this purpose. Detailed results, obtained in this way. for a series of systems of the orfiio,m e f a and para isomers of disubstituted benzenes will be presented in other papers; and it will be shown that these solubility curves are in very close accord with those predicted, by means of the law of the ideal solution, from thermal data.
Summary I . A form of apparatus is described which enables one to make accurate time- temperature curves for systems such aq the disubstituted benzenes. singly or in binary or ternary mixture. I n this qet-up. the effective temperature head is controlled and measured; a wiall quantity only (about I cc.) of the material is needed: and its temperature is read by means of a thermoelement of very fine wire, hence of small heat-capacity and small lag. 2. On the basis of KeTTton’s law, which was found t o be valid for the apparatus as used, the theory of cooling curves under a controlled temperature head is discussed. This leads t o a mode of interpreting the cooling curve of a binary mixture which yields correct results; whereas the methods hitherto generally used for this purpose are inexact and unsatisfactory.
