Melting-point purity determinations: Limitations as evidenced by calorimetric studies in the melting region

80

ANALYTIGA CHIMICA ACTA

VOL.

MELTING-POINT PURITY DETERMINATIONS LIMITATIONS AS EVIDENCED BY CALORIMETRIC STUDIES MELTING REGION* JOMN 1’ McCULLOUGl-I

I.

AND

INTl~ODUCTf

17 (1957)

IN THE

GUY WADDINCTON

ON

Of present-day methods for determmmg the purity of organic substances, those that depend upon the effect of impurity on melting point are most rehable and best developccl. There arc three principal reasons for the wide-spread use of melting-point dcpressron as a mcasurc of purity. First, the meltmg-pomt clepresslon IS a colhgative property, and chemical ldentlflcatlon of the impurity 1sunnecessary Second, analyses of experimental results can usually be made reliably by appllcatlon of well-known theories of &lute solutions. Thlrcl, the rcqulrcd physical measurements - of temperature and of tlmc or energy - can be made with high precision and reprocluclblllty For these reasons mcltmg-point methods can be used to detect small concentrations of unknown nnpunty as small as 0.001 mole o/ounder favorable conchtions and arc most useful in stuclrcs of very pure samples for which other methods often fall. Comprchenslve articles on modern tcchmques for deternunatlon of purity by melting-point studlcs have been publishecl by ROSSINI and coworkersl, CINES~ and MATIIIEU~ In ~947, the late HUGH M. HUPFMAN discussed the problem of purity determination, with particular emphasis on the calorimetnc method used in this Laboratory4. HUFFMAN stressed the unccrtamtles mhcrent m any of the experimental methods then In use. He cxprcssed doubt that the condltlons realized in practice were always conslstcnt with the basic assumptions made m analysing experimental results. Smcc the time of HUFFMAN’S dlscusslon, the accumulation of data In this Laboratory has confIrmed many of 111sdoubts and has led to a clearer understanding of the hmltatlons of m&hods for melting-point purity detcrmmations The two most important expcrlmental methods are the dynamic (tlme-tempcrature) mcthocF and the static (calornnetrlc) method2~~. Although each of these methods has unique advantages and disadvantages, both should give equivalent results under ideal condrtlons, the fact that they often do not IS one of the reasons for reexaming the mhcrent hmitatlons of melting-point purity techniques. The limitations of the calorimctrlc method, m particular, and their sigmflcance are the primary concern of this paper. Because hmltatrons will be stressed, it should be ---_-_. * This work was supported In part by the Amcrlcan Petroleum Institute through Research ProJccts 48 and 52 and by the Umtcd States Au Force through the Au- Force Offrcc of Sclcntlflc Research Contribution No 65 from the Thermodynamrcs Laboratory, Petroleum Experiment Statlon Rejerertces

+, 96

VOL.

17 (1957)

MELTING-POINT

PURITY

DETERMINATIONS

81

emphasized at the outset that calorimetric studies usually are the most accurate means for detectmg small amounts of tmpurlty. The concern of this paper wzll be with the fact that, in some cases, impurity values may be m error by as much as a factor of 5. Such a large uncertainty m zm#~rri~~ generally corresponds to less than 0.1 o/0uncertainty In purity. To provlcle a basis for dlscusslon, the experimental method used IS in this Laboratory and some typical results wrll be grven first. II.

EXPERIMENTAL

All measurements were made m preclslon aclxabatxc calonmetric systems described by WUFFMAN and co-workers 6. In an cxperlmental study about 55 ml of material is sealed under Its own vapor pressure m either a copper or platmum calorimeter that contam horizontal, perforated metal drsks spaced z mm apart to promote thermal cqulhbratlon and prevent settlmg of the solid phase during fusion experrments. The calorimeters are provided with a re-entrant well into which is soldered a platmum capsule contaming a 55 Q (at OX) platmum-resistance thermometer The resistance thermometers element and a zoo !2 constantan heater elementbc. were cahbratcd on the Internatioll~ Temperature Scale of IC+$@ by comparison with standard thermometers cahbrated at the Nattonal Bureau of Standards bleasurements of resistance and potcntxal were made m terms of devices cahbrated at the National Bureau of Standards.

The low-temperature calorlmetrlc equipment In this Laboratory 1s used primarily m the determination of entropy and other thermodynamic properties of pure substances. Measurements are made of heat capacity m the sohd and liquid states between rr and 380°K and of the latent heats and temperatures of the sohd-sohd and solid-liquid phase changes that occur In this temperature range. Also, the purity of each sample studied 1s determtned from an mvcstlgatson of the melting point. Only the procedure used for the melting-point studies will be described here. s. C~ys~aZ~~za~~o~,- For studies of tltermodynamxc properties m the solrd state it 1s necessary to ensure that samples are completely crystallized In past work m this Laboratory, the same crystalhzatlon technique has been used before melttngpomt studies as before any other calonmetrlc measurements on the sohd phase Uecause experience has shown that it 1s difficult to crystalhze many substances completely, a somewhat involved routine procedure has been adopted that 1s successful m most instances. The sample 1s cooled rapidly (I to z deg. min-1) until crystalhzation begins. After crystallization 1s essentially complete, the sample IS allowed to cool to about 90°K m a 112 hour period. Next, It 1s heated to the melting point, and 5 to 10% IS melted. The sample is held at the melting point for about 8 hours and then allowed to recrystallrze and cool to about 30~ below the melting point m a 12 hour period. In all, this routine procedure requires about 48 hours, durmg which time the sample 1s at or very near the melting point for about 12 hours. 2. ObservahonaC ~rocedwe. - After crystallization, a measured amount of energy, sufficient to melt ro% of the sample, is supphed to the calonmeter. The temperature Refcvences

p. 96

VOL. 17 (1957)

J. P. MCCULLOUGH, G WADDINGTON

82

of the sample is then observed periodically until It becomes constant. In the same way, the temperatures corresponding to 25, so, 70 and 90% of the sample m the liqurd state are dctermincd. ‘I’he sample 1s then completely melted and heated 5 to xo” above the meltmg point. The results provide a melting curve. All observations are made under adlabatlc conchtlons so that a value of the heat of fusion may be calculated from the results. (Generally, separate heat of fusion experiments are made before a melting-point study ) It ha5 been found necessary to observe the temperature for al leasl one hour after each fraction of the sample is melted. Usually, the temperature is considered to be “constant” If the rate of change 1s o.oooo3 deg. mm-1 or 1~55for 20 to 30 mm In 5ome ca$ccj, the temperature decreases for the entire perlod of observation, while in others the temperature fluctuates rn a o.0002~ range over a 20 to 30 mm period A different techmque has been employed occaslonally to determine melting curves, with interesting results to be discussed later. The sample IS @n&y crystalhzed (25 to 500/Om the hquld state), and allowed to come to equllibrmm. After the equllibrlum temperature has been determined, successive fractions of the sample are melted and additional temperature observations are made as described previously. Determmatlons by this technique ~111 be arbitrarily termed /veezzng-@o&t studies to dlstmgulsh them from the customary melling-$oi?zl studies that arc preceded by careful and conr~letc crystallization. From the obscrvatlons descrlbcd rn the prccceding 3. Calculalaon of reszrlls. paragraphs, values of the cqulhbrium melting temperature, Tob,d, arc obtained as a function of the fraction of total sample melted, I;. A plot IS made of robqd us. r/l;, and the triple point temperature, cl‘*r IJ, is detcrmmcd by linear extrapolation to zero value of x/F ‘. The mole fraction of total impurity, NZ. IS calculated from the relationship N’,-

~~'(~Ti'--~dml)

.

.

.

(1)

where A IS the cryoscopic con5tant, ~N~u,l,,,l/fZT-~ p 2, and ANfuvlo,, 1s the latent heat of fusion. This procedure 1s based on the four assumptions (I) that the values of ‘f’ot,st~ arc thermodynamic equilibrium tcmperaturcs, (2) that an ideal solution IS formed m the liquid phase, (3) that the impurity IS insoluble m the solid phase and (4) that N:c cr. Departure from hncarlty in a plot of Tobscl vs. r/F may be taken as an mdlcatlon that one or more of these basic condltlons IS not met fully.

c.

Typical

resulls

Smce the establlshmcnt of this Laboratory in x944, the calorimetric method has the melting point and purity of over 125 samples of organic compounds ranging m purity from 99.6 to 99.999 molt o/0. l’hc materials studied include hydrocarbons of various types and hydrocarbon derlvatlves containing nitrogen, oxygen, fluorine, sulfur and lead. From the results of these investigations, examples have been chosen to illustrate both the reliability of the calorimetric method and, in particular, its inherent hmitatlons. I. Bemolviftrcoride and I-/reg5ttwtethaol - Very few of the melting curves obtained are linear over the entlre range of I/F values as would be expecter if equation (I) been used to determine

Refererrcec

p g6

iOL.

17 (157)

MELTING-POINT

PURITY

DETERMINATION5

83

were applicable. However, about r/3 of the curves show only slight departure from linearity chiefly at hrgh values of r/F. The melting curve of benzotnfluoridee (Table I and Fig. I) is linear within o.ooo2°, which is not surprising since the sample 244 145 Y 0

IO 0 0005. l

k!

244 140 CI -

-2

9 2

Np*-

0 001

molr

Y.

5 E

244 l35O

2

4

6

l/(FRACTION PIN

I

The melting curve (TObl TAULE DENZOTRlPLUORIDE TT

-.. ._--_--

._-_---.-

II

26 so 70 90

I’

=

.__ . __ -_---

b Calculated

r/F) I

hlELTlNC-POINT

SUMMARY

14 f o 05Ol<, A = o 02781 deg.-1, Iv; - 0 001 molc Ok,”

-----.----___-_

8921 3 826 I 962 1411 I 102

21

14 98 8G 75

IO

bcnzotrlfluorlde

of

--__-l_

100 00 Pure _-a A straight

z.(.+

us

a

MELTED)

244 13980 1423 1429 ‘432 ’

-

24.1 1398 1421 1430 1433

434”

1 000 0

_-__ _----.-_ thcsr: points was cxtrapolatcd to z/F = o to obtam ‘fT I’. from the slope of the straight hnc of footnote a by use of cquatlon (I).

1434 1434 1439

---

hnc through

contained only 0.001 mole O/Oimpurrty. A more typical example of melting curves that are nearly, but not quite, linear IS given by the results of four separate meltingpoint studies on a sample of r-heptanethiole (Table 11 and Fig. 2).

Y .

i z

s x I v

22990

N,*

-

a 0 04

mole

%

dlo -0 003’

l%g 2 The melting curve of x-heptancthlol , the different symbols Indicate results of four separate determtnations. References p 96

j.

I’.

MCCULLOUGH,

G.

TABLE

___-_---

-.

-

.^- _

M died, %a __ _

-_--_-

p

=

229

_.

’ 4 l l 3 4 ’ 4

70 85 84.36

= ’

9092 95 58 100 00 Pure

3 4

f

=

0

. -

05%;

SUMMARY

POINT

A

=

0

o 04 mole T&c

..- _

- --.--

IIF

-_- - -.. ..- - ____ ---

229

_

r; OK-

_____

229

9203 9209 9213 9217 9290

.9196 .92X1

.

8578 8857 8907 8955 9020 9044 9103 9152 Qr80 gr88

9138 9174 gr88 .9206

___- -.

b

7G26

s9049 a9013 .9082

_

--. ---- _ _____._.- _ Graph

~-_-----

8559 8868 ,888 I 898x

5 568 4 359 3 893 2 847 ‘I 969 1 530 14x1 I 185 I 100 I 04G I 000 0

__ _ .. ._ _ _ -

clcg -1,

Obrd -_____

7 698 6 502

.-.

05775

_.. . _... .-

-.-. -

4;sz

2 648’ 6 544’ 1299 1538 1796 2294 2569 3513 so,78 65.36

N;

. -

_ _ _ __ --

-

93

17 (1957)

VOL.

II

MELTING

I-IIIH’TANETHIOL TT

WADDINGTON

_

_ _ .__ _

-

- - -. -_. __ _

mcllcatc pomts from four separate dctcrmlnatxons b Tcmpcratures rcatl from a smooth curve through a plot of Tobd us r/r;’ c Calculated by USC of cquatton (I) from the slope of the cllrvc of footnote 6 bctwcen and r/F = 0

--

0 Supcrscrlpts

I/F=

I ooo

2. Cycldtcptatriem. The results for at least half the samples studied show moderate to pronounced dew&on from hncarlty m plots of Tobsd vs. r/F-a possible indicatron of the formation of a sohd-solution of the impurity m the major component. In some cases, the sohd-solution treatment developed by FINKI@ and by MASTRANGELO AND DORNT@ adequately accounts for observed non-hnear melting curves. The results given for cycloheptatriene” in Table III and Fig. 3 illustrate the application of the solid-solution treatment.

LYCLOEIISI’TATRIBNE TT

-.---_-

A____._ -

-----

- _- - -.

p

=

197

92

f

MRLTING 0

0501cb,

~4 =

POINT

SUMMARY

Chg.-‘,

0 003564

I< = o 128x1, N; = o 0 I 43 molt Ojob _ ___ __.-_ ____ - ._ -.--.----------

---- -_--.-_------

----

T, Oh’ IIF ---

---I--

-_

-_

-..---

11 49

25 36 49.55

_-

_-

_

_-.--__-.__

Obsd, ______

8 703 3 943 2 OOG

---__

-.-_-

-

197 7655 8rG7 8543

----I----.-

C&d

-- --

b

197 764 817 855

,870 878 882 0 9x7 .I- _ ____~.__ - -e---m---_-_- ---_- __- _ _...- -- - --- --- -. .- -- - -- - -- ---..---n I( 1s the Hanry’s Law constant for dlstrlbutlon of lmpurlty bctwcen the sohd and llquxl phases. b Calcukkcd from the rclatronshlplo Tr: - TT.~. -(Ng/A)/[F + K/(1 K)] z”, :: 100 00 Pure

References

p

96

I 4x9 I22 I .ooo

.8Gg2 8789

-.A

VOL.

17 (1957)

MELTING-POINT

PURITY

85

DETERMINATIONS

Y

N2*=

mole %

0 0143

w I19780E I 0

2 Iilg

3

rhc

6 MELTED)

4 l/(FRACTION melting

curve

8

3

of cycloheptatrlcne

Py77oLe The melting curves of some of the samples studied m this Labora3. tory have been dctermmed both by the normal meltmg-point technque and by the modified “freczmg-point” procedure (section II.B.2). In every case mvestigated curve is sigmflcantly lower than the melting curve, as shown to date, the “freezmg” by the results for pyrrolee given in Table 1V and Fig. 4. The results of the melting-point study on pyrrole (curve B m Fig. 4) also illustrate an anomaly that has been observed m several other instances. The value of Tobsd at I/F = 1.104 is esscntlally the same as that at r/F = 1.431, and is significantly lower than an extrapolation of the meltmg curve based on results at the htghcr values of r/F.

_-._.-. _ _

3fM, -% _ A

“Z;rcczrng”

_

. _

PYRROLC . .

Point

iLicltlng

r

SUMMARY _ -. _

-

T,

.- .

249 7+, f 0 05OiI;. A = 0 01525 N’ _, = 0 015 mole o/oh

tT

-

___.

OK -_-

_--__._

_____._

______

c&d --.__ __ -

b

dcg -‘;

249 724Sa 7365=

0

249 7245 -7365 -7388 7485

Point TT P = 10

84

a, b See footnotes

p g6

249 740 f 9 3 2 1 1 I

25 59 4921 69 89 90 57 100 00 Pure

References

POIN ^

Obsd

2 478 1 244 I 000

40 36 80 39 10000

I3

_._

z/i;‘

-fT 1J 5

I’ll

MELTING __-_-__

225 908 032 43’ 104 000 0

Table

I

o 05OK,

IV: = o 006 mole %b 249 7075 7301’ 5;:: P 7397

249 7092 -7301 7374 7398 7411 74x5 7454

__-

_

-__--

86

J. I’. MCCULLOUGH,

249

G. WADDINGTON

TOT-2

0

FIIJ r( The meltmg curves of pyrrolc

wFA&ION

6

MELTED)

A, results of a “frcczmg-pomt” melttng-pomt study

VOL.

6 study;

17 (IQ57)

1

B, results of a normal

- Results of two melting-point studres on a sample 4. Cyclopentyl-x-llriaelttane. of cyclopentyl-x-thiaethanes (methyl cylopentyl sulfide) are given in Table V and Fig. 5. -AAt hrgh values of r/T; the values of Tobsd determined in the two studies doffer by about 0.0~’ although the precision of the results from either determination is about & o.ooo2°. Also, the values for the amount of impurity m the sample calculated from the results of the two studies differ by a factor of three. 16987-

8(N,*=OOl

A(N2*‘.003

mole %I

mole%I i

3 Fig. 5 The meltmg curves of cyclopentyl-I-thlaothane crystalllzatlon; B, results obtamcd

Refevences

p g6

A, results obtamed after relatively after slow crystalhzatlon

“fast’ ’

VOL.

17 (1957)

MELTING-POINT

PURITY TABLE

CYCLOPENTYL-I-THIAETHANE.

DETERMINATIONS V MELTING

POINT

I4f&?d. 9.

A

l4Fast”

SUMMARY

calcd b

Obsd

crystalhzatlon

TTP

=

1Gc)8G,&-oo5~K, W

1702 44 38 66 76 8913 100 00 Pure B

87

*‘Slow”

crystnlll7.1

5 2 I I I

-003846deg-‘,

o 03 mole o/“b

875 253 498 122 000

~ti 841 I 8498 853x= 8557”

169 8229 8479 8531 8557 ,8566 8635

0 tlon TI-P

=

13 bz 26 93 5: 65 70 65 89 61 IO0 00 Pure a, b See footnotes,

=

A

86, f

1%

o 0501<, N:

7 342 3 7’3 1 936 * 415 I 1x6

= o 01 molt O/O’) 169 8495 8550 8576 8593” 8604”

169 8775 8508 8574 8593 8Go4 8Go8 8645

I .ooo 0

-

Table I

Curve A 111Frg. 5 was determmcd after the sample had been crystallitcd by the routme procedure described in paragraph II .B.r . A modlfred cry\talhzatlon technique was used before determining curve B. In this experiment the sample was maintained at the melting point with 10% in the liquid phase for z days and was then recrystallized slowly over another z-day period. In all, the sample was m the melting_ region about four times as long in the second study as m the first. _ z- Decene. - A more striking example of the effects of prolonged “annealing”

200

I

202 204 TEMPERATURE, -I(

206

20.66

0

2

4 1IWAACTION

6 HELIE

0

I

8

Fig 6. lhc haat capacity of r-deccne between the transltlon-pomt and triple-pomt temperatures (6a) and the correspondmg meltmg curves (6b), A, results obtamcd after relatively “fast” crystalhzatlon, B, results obtained after prolonged “annczllng” In the prcmcltmg region; C, heatcapacity results corrected for premcltmg Rcfertnces

p

g6

88

J

I’. MCCULLOUGH, TABLE I-DIXRNE

------

17

(1957)

VI POINT

SUMMARY

“Fast”

I’, “K r/F

Obsd

Co&d tJ

cryst.tlll/ation TT I’ I

892 -& o 05’1C,

206

N; 9 72 ZI 42 59 75 100

A = o 03880 dcg -I,

=I 0 11 molt (%,I)

IO 29 4 575 2 352

86 .5x 10 7’ 00

206

1 692 I 32x I 000

Ih rc

B

VOL.

-

hf rllcd, %

A

MZLTING

G. WADDINGTON

6281 7662 R=59’l 8440 8.547.’

206

6Q45 7640 8259 8444 8.547 8637 8916

0

~~Slow” crystdlw~tlon ‘1 I r’ =

88,

206

& o og”I<.

N:

=

o.og

nmlc

%,b

II 04

9 057

206 7373

206 66gg

26 47 51 52

3 78’

8004

2 090

8397

7974 8383

45 8~ 68 31’

68 7lC 71 13 go 56 100

00

1’11re

1 935 912

8461 84GG

1 455 I 4oG I 104

8497 8548n 8621a

I

footnotes, Table I C Smgle pornts obta~ncd In the course of scparatc hat

8536 8548 862

1

8646 8888

I 000 0

a, b See

8420

8420

of fusion dctcrmlnntions

of crystals m the meltmg or “pre-meltmg” region 1s shown by the results for r-decene12 m Table VI and Fig. 6 This compound undergoes an lsothcrmal transition about 8” below the melting point, but the transition 1s easily supcrcoolcd. When the sample was crystallized m the routme manner - but not allowed to transpose to the polymorph stable below the transrtion temperature - the values for the heat capacity of the crystals stable at the melting point fell on curve IA of Fig. Ga, and the results of a melting-point study on the samc__crystals fell on curve A of Fig. 6b. In order to transpose r-decene to the polymorph stable below the transltron temperature, it was necessary to hold the sample at temperatures just below the transition point for about 3 weeks. During this time, approximately 0.5% of the sample was m the liquid state as a result of pre-melting After the low-temperature polymorph had been formed and then heated above the transltlon temperature to reverse the transformation, the heat capacity of the high-temperature polymorph fell on curve IB of Fig. 6a and the results of a melting-point study on the same crystals fell on curve B of Fig. 6b. Both heat capacity and both melting curves were obtained reproducibly under the conditions described.. Refererrces

p

g6

VOL. 17 (1957)

MELTING-POlNT

PURITY III.

A.

Ex#lanatzon

DETERMINATIONS

89

DISCUSSION

of cwatwktlous melting_ ctcrves -- . -_ The results given m the precedmg section for benzotnfluoride, x-heptanethiol and cycloheptatriene (Figs. 1-3) show that the melting curve of an orgamc substance can be detcrmmed by the calorimetnc method with high precision (& o.oo~)z’) and good reproducibility ( f. 0.003’). In most cases, the results obtamed are m accord with the theory of dilute solutions, either when the impurity is essentially sohdtnsoluble (Figs. I and z) or 1s sokd-soluble (Fig. 3). Nevertheless, the melting curves obtained for many samples studled in this Laboratory are rn some way anomalous. and I1. Soairces of error. - The curves for pyrrole, cyclopentyl-r-thiaethane decene (Figs. 4-6) are clearly anomalous Neither the shape of the meltmg curve m Fig. 4 (curve B) nor the depcndencc on crystalhzatlon procedure shown by the curves m Figs. 4-6 could be predicted by theory These anomahcs may be due to observational errors or to failure to realize the assumed conditions of equihbrrum states and ideal solutions Both observatronal errors and non-ideal behavior can be eliminated as primary causes of the anomalous meltmg-point results. The prccrsron of the thermometry is within & o oooz’ in a single determination and 1s at least j= o.oooS” in repeated determinations; and departure from ideal behavior should not be a function of the crystallization technique employed. Consequently, it has been concluded that failure to obtam true thermodynamic equlhbnum is the cause of anomalies typified by the results m Figs. 4-G. I~seztdo-eqtrilsbritnr~ meltang cwves. 2. Nearly all of the samples investigated approached thermal equihbrium by coolmg Although the coohng rate usually becomes o.oooo3 deg. mm-l or less wrthm an hour after the addition of energy, longer equihbratron penods are often cncountcred It 1s possible that equrlibratlon 1s actually a very slow process requirmg many hours or days A @c&o-equlhbrium state - not easily recognized as such m the course of esperimcntal observations mrght be obtamed by two different mechamsms. First, a $sezldo-equrhbrmm state may result from factors inherent m the desrgn of the calorimeter vessel and in the properttes of the substances studied. The closelv spaced heat-distnbutmg d&s and the solid phase of the sample undoubtedly mterfere with the diffusion of ltquid throughout the vessel. Particularly at low fractions melted, blocked diffusion paths may lead to an mhomogeneous distribution of impurity in the liquid and solid phases. Because the thermal conductivity of organic substances is poor and the process of diffusion IS slow, an mhomogeneous distribution of impurity may cause the final approach to thermodynamic equllibrmm to occur at an almost undetectable rate For example, isolated cells contammg relatively large amounts of impunty may remain superheated long enough after a fraction IS melted that the “final” temperature observed is significantly higher than the equlhbrium value. As the fraction of sample m the liquid state increases, isolated cells wrth high concentration of impunty may be destroyed, and a more homogeneous distribution of impunty may occur. As a result, the values of Tobsd at lower fractions melted would be high relative to the more nearly correct values at higher fractions melted. The anomalous melting curve of pyrrole (curve B, Fig. 4) may be explained by this hypothesis. It is believed that mhomogeneous distribution of impurrty m the liquid phase References

p. g6

J. P. MCCULLOUGH,

90

G

WADDINGTON

VOL.

17 (1957)

may well affect the results of any meltmg-pomt determination, although the effect may not be so pronounced as m the example given here A second type of ~setrdo-eclulllbr1um mcltmg curve may result as a consequence of non-cquihbrium drstribution of solid-soluble impurity between the solid and liquid phases. In a comparatively rapid crystalhzatron, differences in the relative rates of deposition of impurity and major component might result m crystals that contain non-equibbrium amounts of impurity m solid-solution. On the other hand, long “annealing” of the crystals near the melting point, with at least some hcluid present, provides the opportunity for the impunty to be distributed in cquihbrium between the solid and liquid phases. The dependence on crystalltzatlon technique illustrated by the results in Figs 5 and 6 is consistent with the assumption that non-equilibrium distribution of impurity between solid and liquid phases does occur. It IS believed that the melting curves obtained after relatively fast crystallization of cyclopcntyl-r-thiaethane and r-decene (curves A in Figs. 5 and Gb) arc lower than those obtained on “annealed” crystals behaved (curves B in Fogs. 5 and 6b) bccausc the impurity m the former Instances as if it were less solid-solzrbde than m the latter. Curve A rn Frg Gb IS as nearly linear as would be expected for a solid-ntsohble impurity It IS not possible to decide in every case which of the two proposed mechamsms may bc responsrble for a fisezcdo-equillbnum melting curve, and tn fact, both may operate in a particular dctcrmmatron. For example, it IS possihlc that mcltmg curve B of pyrrole may be higher than “frcezmg” curve A (Fig 4) either bccausc of mhomogeneous distribution of impurity or because of differences 111 the extent of sohdsolution formation. However, as will be discussed later (paragraph IlI.B.z), the anomalous curves for cyclopentyl-r-thiacthanc and r-deccnc are more hkely the result of solid-solution formation. 3. Evidence from fwemelting heat cafiac~ty data. - ‘The heat capacity data for r-dccene in the premeltmg region (I’ig. ha) lend support to the prccedmg analysis of the observed melting curves (Fig 6b). The heat capacity values for crystals obtamed by more rapid crystalhzation (curve IA, Fig Ga) arc higher than those for the “annealed” crystals (curve 113, Fig. 6a) because the effect of prcmelting was larger when the impurity behaved as if it were sohcl-insoluble. A quantitative test of the explanation offered is afforded by the apphcation of premeltmg corrections to the heat capacrty values. Upper Grtifs for the concentration of e//ectiveZy soladznsohble impurity calculated from the slopes of the melting curves at low fractions melted are 0.09 and 0.05 mole “/o for curves A and U m Fig. Gb. M’bcn heat capacity curves TA and IB arc corrected for premeltmg on the basis of 0.085 and 0.035 mole o/o solid-insoluble impurity, the results of both determinations fall on a single straight line, curve IC of Fig. 6a. Evidence obtamed m this Laboratory mdicatcs that failure to obtain an equihbnum distribution of impurity throughout the solid phase usually results m less than equilibrium concentration. Only one example has been found of the reverse situation - a greater than equllibrlum conccntratlon of impurity m the solid phase Like r-decene, czs-decahydronaphthalenes undergoes an isothermal transition lust below the melting point, and its heat capacity and mcltmg curves are similar in appearance to those given in Fig. 6. In contrast with r-decene, however, the higher melting curve and Zowev heat capacity curve of czs-dccahydronaphthalene were obReferetrces

fi 96

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PURITY

DETERMINATIONS

91

tamed by the more rapid crystallization procedure. It seems likely that m this case rapid crystallization caused absorption of impunty m solid-solution m greater than equrlibnum concentration and that long annealing m the premeltmg region permitted the rmpurity to diffuse out of solid-solutron. Although only one example of this behavior has been detected, rt is reasonable to expect that it may occur fairly often B. Lamatalions of the calortmelric method Analysis of the results of more than 125 meltmg-point studies, illustrated by examples m forcgomg sections of this paper, has led to a better understanding of the limrtatlons of the calorrmctric mcthotl. A pseztdo-cqurhbnum meltmg curve may be obtained as a result of mhomogcneous drstrrbutlon of impurity m the sample or non-eclulhbrrum drstnbutron of impurity between the solid and hqurd phases. Such psczrdo-cqurlrbrrum results cannot be recogmzed easily on the basis of single determinations or even rephcatc studies m&e Z?Zessenkially Iltc: same way For thus mason, the mterprctatron of melting curves 15 sublcct to greater uncertamty than was formerly realized. I. U*tcerlrcznly of a?rrpurzty valzces. Inhomogeneous distribution of impurity in the liquid phase may result in low values of Nf because the slope of the melting curve is usually decreased by thus effect (curve U, Fig 4). However, a more important cause of error 1s the fairly common formation of soled-solution. For reasons to bc discussed later, the methods for treating solid-solutron formatron are often unreliable in practice. Impurity values reported from this Laboratory have usually been calculatccl from the slope of the meltmg curve at high fractions melted by use of eq. (I). If solid-solutions actually arc formed, it IS evident that the impurity values so calculated will be too low by an unknown and variable factor. The formation of sohdsolutrons has long been recognlLed as a possible lrmltatron of all melting-point purity methods, but it has not been realized that the phenomenon is so common. Consequently, rt will be worthwhile to consider In more detail the evidence for the assumption that solid-solutrons are often encountered m practice. Evznence of solad-solzrtzo?t formaltotr. It IS not unreasonable to expect that 2. solid-solutrons may be formed in highly purified samples, for the rmpuritres may often be 1somerlc with the major component and may have nearly the same molecular shape. About half of the melting curves determmcd m this Laboratory show moderate to pronounced deviation from lmcarity in plots of Tobud vs. r/F, mdrcatrvc of soled-solution formatron. Melting curves linear over the entire range of fractions melted (Fig I) are rare. If the departure from lineanty is slight and prrmarrly at high values of r/F (Fig 2), it is possible that the obscrvcd curvature 1s due to non-ideal behavior of the more concentrated hqmd solutrons at low fractions melted or to mhomogencous drstrrbution of impurity, but it does not seem reasonable to attribute pronounced curvature (Figs. 3, 5 and Gb) to such effects. ‘Ihcre are two pnncrpal considerations that lead to the conclusion that sold-solutron formation often has an important effect on mcltmg-point studies. (I) The results in Figs. 5 and 6 show that melting curves obtained after slow crystallization procedures (the B curves) arc higher and depart from lmearity more than those obtained after relatively fast crystallization (the A curves). Because slow crystalhzation and proReferences

p 96

J.

92

P.

MCCULLOUGH,

G

WAT)DINGTON

VOL

0957)

17

longed annealing before a mcltmg-pomt study should lead to more nearly equlhbrlum results, it seems likely that the B curves arc “eqtnhbrium” meltmg curves and are non-lrncar as a result of solid-solution formation. (2) Comparison of impurity values calculated from heat capacity data m the premelting region with those calculated from meltmg curves affor& strong evidence of solid-solution formatton. The heat capacity m the promcltmg region 15 extremely sensltlve to the presence of lmpunty, bzcl only &I LJcrtlwhck zs nd an solad-~okhon. In this Laboratory, it IS the practxc to calculate Impurity valuc~ from premeltmg heat capacrty data as well as from meltmg curve5 *. Table VII lists typical results Values calculated by equation ~rmu.5 CO?4

PARISON AhD

Olr

Ihll’URi

ZY

VIL VALULS

--_~-----

-Iinpurlly,

0

(A) (13)

Pyrrolc Cyclopcntyl-I -tlllactilane Cyclopr2ntyl-r -tht.;rctllnnc r-Dcccnc (A Ji: IA) I-Dcccne (U c! 113) 4,5-l~ttin~or.t~kncn l~luorobcn~cnc*

___ ---a ‘1hc Icttcrq A, 13, IA

04 0’5

u/ 3d

0 025

0 03 006

OOG

(A) (13)

mole SF pp---

fb

-w__c_l_---

I-Hcptan&11101

---

INL-POINT

me-------

--

--

Pyrrofc

MEL? DAlA

Compou*t&~ -

lWOM

I’RLhfI:I,CINfi-ill:Ar-CAPACITY

01 OOG 09 05 011 05

03 01 .I1 09 035 05

_.I I3 refer to the mcltlng

_-

005 )

j

_ ^-_-____

00.5 085 035 0x0 05

---

and hcat capacity curvc4 In P tgs 4-6 b CalcuL~tctl from the slope of mclt~ng curve bctwccn J/P values 1 1 Cmd I 4 C CXculatcd from the slope of meltnlg curve bctwccn x/F vnlucs 4 ,~rltl so (1 C.rlculatcd from Premcltlng-llcat-capnclty ciatn .rnd

fr) from the slope of the mcltmg curve between r/F = x.4 and r/F = x.1 are glvcn in column I, values calculated from the slope of the melting curve between x/I; = ro and x/F = 4 are listed m column z; and values calculated from premeltmg heat capacity data are tabulated m column 3, (If the value calculated from melting-point data at IczgjLvalues of r/l; IS stgnifxantly lower than that calculated from data at ZOWvalues of r/F, the melting curve IS apprectably non-lmcnr.) In every Instance, the Impurity value calculated from prcmeltmg data IS less than or equal to the ZOWLY of the two values calculated from meltmg-point data. The heat capacity below the melting pomt IS so scnsltlve to solid-imolzcbh impurity that the use of the higher Impurity values determmed from meltmg curves in calculatmg prcmeltmg corrections would yield “corrected” heat capacity curves of absurd shape Thus, it 1s likely that some Impurity entered solid-solution m over half of the samples studled m this S Laboratory, I~)~~~r~~~~c~ of Ihe ~a~~~a~ci~ao~Ls of ~~~~~~~~L~-poa~t ~~~~~~io~s. Both the formatlon 3. of solid-solutions and inhomogeneous dtstrlbutlon of lmpurlty will usually cause rmpurity values calculated from melting-point studies to be too low. The procedure used m this Laboratory - calculation of impurity values from the slope of the melting curve at high fractions melted - will mmimlzc errors in most cases. The results _ _ --__-_ * Thcso impurity values arc dctcrmmed for the purpose of corrcctmg observed thcrmal properties

for prcmcltmg

References

p 96

and usually

have not becn pubhshed

as such

VOL.

17 (1957)

MELTING-POINT

PURITY

DETERBIINATIONS

93

for I-decene, (Fig. 6b) for example, show that the concentration of lmpunty calculated as described IS not affected slgrufrcantly by sohd-solution formation. On the other hand, it 1s clear from the results for cyclopentyl-r-thlaethane that solidsolution formation occaslonally will cause large percentage errors m calculated lmpunty values. Study of the results obtamed m tlus Laboratory indicates that as many as r/3 of the meltmg curves determined were affected by solrd-solution formatlon to the extent that calculated lmpunty values were probably x/z to I/IO of the actual value. theory. If a melting curve shows evidence 4. ‘1’Jzeupplzcatao9t of sokd-sol2ttson of appreciable solid-solution formation, appkcatlon of a sohd-solution treatmenW0 may glvc a more accurate lmpunty value Unfortunately, the method often has failed to give an adequate representation of observed melting curves -- perhaps because measurements were made on a system at @e&o-equlhbrlum or because several lmpurlties were present. In other instances the solid-solution treatment has given an excellent representation of experlmental data, but the high sensitivity of the method to small thermomctnc errors makes the calculated lmpunty values unrcliable. For example, the difference in temperatures observed with 70 and 90% of a sample melted may easily be m error by & o.c~oo~~. It can be shown that if the solid-solution treatment 1s used such an error may correspond to an uncertainty of 500’s m the impurity value for very pure compounds with normal cryoscopic constants, whereas the same 0.0005’ error corresponds “only” to 150% uncertamty if solid-msolubihty 1s assumed Thus, unavoidable observational errors may produce such large uncertainty m impunty values calculated by the sohd-solution method that values calculated with cq. (r), while obvrously low, may bc more nearly accurate. For this reason, it has been concluded that the solid-solution treatment 1s best applied to compounds with low cryoscopic constants (< o or deg.-l) or to relatively lmpurc samples (c gg o mole %). In such cases, observatlonal errors are likely to be small enough relative to the melting-point depression that they are not important. 5. Cotnparason of resdts by the sbaczc und dynamzc methods. - CINES~ AND MATHIEU~ have noted that impurity values dctermmed by the calorimetric method m this Laboratory are systematically lower than those determmed on the same sample by the dynamic method. Acldltlonal evidence based on twice as many compansonse as were available to either CINBS or MATEHEU conflrms their observation. In most instances, the discrepancy

between

values

of iVf obtained

by the two methods

can

be

attributed

and sensitlvlty of the dynamic method, particularly if the value of 1\‘: is near or less than the normal hmlt of detection by the dynamic technique. Nevertheless, the calonmetrlc value of N: may be more m error in some cases as a result of solid-solution formation. The normal crystalllzatlon procedure used m this Laboratory often results m at least partial formatlon of solid-solutton. If solid-solution 1s formed to an appreciable extent, the calorimetric value of N: is likely to be slgmficantly low. The dynamic method, on the other hand, should be affected less by solid-solution formation because the period of observation mth this technique is so short that the impurity may not have time to enter sohd-solution m eqmhbrium amounts. to

C.

the

lower

preclslon

Modifwataon

of the calorimctras

The two principal References

9. 96

limltatlons

method

of the calonmetnc

method

brought out in the pre-

J. I’. MCCULLOUGH,

94

C.

WADDINGTON

VOL.

17

(1’957)

cedmg section - that due to inhomogeneous distribution of rmpurrty and that due to the common formation of solid-solutions - probably had a sigmficant effect on at least half the impurity values determined in this Laboratory. Perhaps 1/3 of the impurity values determined are in error by 2000/O or more. Such errors in impurity are rarely significant if expressed as uncertainty m sample fiuvzty, but it 1s worthwhile to consider means for reducing them. Whereas modification of the design of the calorimeter might reduce errors due to mhomogeneity, uncertainties due to soltd-solution formation are probably more important and cannot be affected by apparatus changes. As the results for r-decene show (Fig. Gb), a solid-soluble impurity can sometimes be made to behave as if it were solid-msoluble by crystalhzmg the sample rapidly. On the basis of this observation, a modified procedure for meltmg-point studies IS being tested. It is somewhat paradoxical that techniques should be chosen so as to produce aon-sqazlibrzum results m a classical thermodynamic study. Nevertheless, for purity dctermmations, more accurate mformation may often be obtainable from a non-equilibrium melting curve. In the revised procedure, a sample 1s crystallized as rapidly as possible and observations are begun as soon as essenltully complete crystallization is obtained. It is hoped that m this way the formation of solid-solutron, and resultmg errors in Nf, can be mmimized. Enough data have not been obtained to determine the utrhty of the modified procedure, but some advantages and disadvantages of the m&hod are obvious. It is much less time-consumrng than the procedure formerly used m this Laboratory - a fortunate circumstance if purrty determmation 1s the prrmary concern - but it is necessary to determme the heat of fusion in separate experiments rf an accurate value of this property is desired. If an rmpunty is forced mto sohd-solution as m the case of cis-decahydronaphthalcne, the rapid crystalhzation technique will give less accuracy than the slow crystallrzation method. Unfortunately, the modified procedure offers no advantages rn many studies because “fast” crystallization 1s often impossible. In studies that have been made by this method to date, there are mdications that mhomogenelty of the hquid phase may be increased and that equihbration times are longer. However, if the results at high fractions melted are used in calculatmg impurity values errors due to mhomogcneity should be mmimized.

D.

Conclusion

The limitations of the calorimetric method for purity determination undoubtedly apply to a greater or lesser extent to any meltmg-pomt method. Results such as those discussed in this paper show that uncertamtres assigned to impurrty values have sometimes been optimistrcally low. At present, it is not possible to assess the uncertainty that should be assrgned to impurity values unless extensrve studies are made in each instance of the effect of different operating techmques. In order to obtain quantitative information of general applicability about the effects of the hmitattons discussed on the results of melting-pomt studies, further systematic investigations of purity determmations should be made. The followmg are considered to be fruitful areas for study: (I) The effect of various types and amounts of rmpurity on the melting curves of samples of known high purity (about 99.999 mole o/oongmal purity); Referemes

p. g6

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PURITY

DETERMINATIONS

95

(2) the effect of crystalhzation and annealmg procedures on such known mixtures, and (3) the design of calorimeter vessels especially for use with two-phase systems. A concurrent study of identical samples by the time-temperature method would greatly increase the value of such mvestlgatlons.

ACKNOWLEDGEMENTS

The work on which this paperISbased has been accomplished over the last twclvc years and mvolvcs the efforts of many of our associates The late Dr Hugh M Huffman, who began thcsc studlcs, rnflucnced the paper markedly, for his careful cxpcrtmcntation and perceptlvc analysis of results pointed the way to a better understanding of the calorimetric method WC arc lndebtcd also to the followmg past and present colleagues for thclr many contrlbutlons, both cvpcrlmental and lntcrprctlvc Dr H L FXNKLI, Dr D W SCOTT, Dr S S TODD, Dr G I3 GUTHRIE, Jr, - _ Mrs IM E GROSS, Mr J F. MIBSERLY and Mrs T C K~NCHELOI? We arc grateful to Dr F 1) ROSSINI, Director, AmcrlcanPctrolcum Institute Rcqcarch Prolcct 6, for tending us most of the samples of highly-purlfled hydrocarbons used in these mvestlgatlons. SUMMARY Typrcal melting curves, chosen from the results of more than rag melting-pomt studlcs, are presented to illustrate both the rehablllty and the mhcrent hmltatlons of the calorlmctrrc method of purity dctcrmmatlon It IS shown that this method usually IS one of the best mcdns of accurately analysis of anomalous niclting Curves determining small concentrations of impurity However. leads to the conclusion that pseudo-cqulllbrlum curves arc often obtained as a result of rnhomogcncous drstrlbutlon of impurity m the llquld phase or of non-cqulllbrlum dlstrlbutlon of impurity between the solid and llquld phases Evldcncc IS given to support the contcntton that sohdsolutions were formed in ‘m many .~s half of the samples studled and that for this reason, rmpurlty values calculated for perhaps x/3 of the samples are In error by zoooh, or more Although these large uncertainties in ltnfiur~fy values usually correspond to lcrs tti.m 0 xoh, unccrtnrnty in Plrrlfy values, modified procedures arc proposed to minimize sucli errors R@SUMl? Des courbcs de fusion typlques, cholslcs parml les rdsultats dc plus de 125 dtudcs tic points de fusion, sont pr4sentdes I)our lllustrcr aussi bicn la sfireM quc Its limitations mhbrentcs dc la m&hode calorlmdtrlquc de dhtcrmlnatlon dc purctb Lcs autcurs montrcnt quc Lctte mdthodc cst gdn&alemcnt l’un dcs mcillcurs moyens dc dbtcrminer exactcmcnt des petitcs concentrations d’lmpuretd Ccpcnclant, I’analysc dc courbes de fusion anormalcs ambnc a conclure qua l’on obtlent souvent dcs courbcs de pseudo-Lqulhbrc dues & unc dlstrlbutlon non-homoghne d’lmpurctb dans la phase hqulde ou d’une dlstrlbutlon d’lmpurcte non-dqulhbrde entrc lcs phases hquldc ct sohdc Des farta sont pr&cntcSs qui font qupposcr quc dnns la molt& dcs dchant~llons dtudlbs 11y auralt cu formation do solutions sohdcs ct pour ccttc ralqon lcs tcncurv d’unpurct6 calcutdcs pour peut-&trc un tiers dcs cSchantillons scralent fausscs dc zoooA, ou davantagc C)uolquc ccs grandcs mcertltudcs des tcncurs cn unpurctd correspondent gdneralcmcnt ?I moms dc o loA, dcs valcurs do puret6, dcs procBd6s sont propos6s pour rdduirc de tclles crrcurs ZUSAMMENFASSUNG Typrschc, aus den Ergcbmsscn von CIbcr 125 Schmclzpunkt-Studlcn fV$WZihltC Schmclzkurvcn werdon gezclgt urn sowol~l die Vcrl~sshchkclt ds dlc lnharcntcn Begrcn7ungcn dcr kalorlmctrlschen Mcthode zur Rcmhcltsbcstlmmung dcuthch zu machcn Es wlrd gczclgt, dass dacsc Mcthodo me&ens emes der bcstcn Mlttcl 1st urn niedrige Konzcntratlonen von Vcrunrcmlgungen gcnau zu bestlmmcn. Die Analyse abnormaler SchmclLkurvcn fuhrt abcr zu dem Schlusse, dass man oft Pseudo-Gloiclrgcwlchts-Kurvcn crhalt, doren Ursachc cntwedcr cme nicht homogcnc Vcrtcilung dcr Verunrcmlgung m dcr flttsslgen Phase odcr emc mcht dem Glclchgcwlcht cntsprcchendc Vcrterlung der Verunremlgung zwlschon dcr fcsten und flusslgcn Phase 1st Es wcrdcn Tatsachen angefdhrt dre darauf hmwclsen dass vlcllelcht sogar m dcr HYlftc dcr untersuchtcn Proben fcsto LBsungcn gcblldct wurdon und dass deshalb die fLlr die Verunrcmlgung bcrechncten Wcrto, in vlellelcht 1/3 der F&110,Fchler von zoo% odor mchr aufwelson Obwohl dlcso grosscn Ungcnaulgkclten ftir dlc Verunremigungsworte im altgemeinen einer UIIgcIIaulgkClt von wcnigcr ats 0 1% fur den Remhcitsgrad entsprechen, werden doch abgcanderte Verfahrcn vorgeschlagen urn dcrartige Fehler zu vcrxundern References

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17 (1957)

REFERENCES A R. GLASGOW, JR, A J STREXPF AND F D ROSSINI, J. Research Null BUY Standards, 35 (1945) 355, and rcfcrcnces cited thcrc M. R CINES, Plryszcal CJremzslry o/ fire Hydrocarbons (edtted by A. FARKAS), Chapter 8, Acadcmlc Press Inc , New York, xg50 M P. MATHIEU, Acud voy. Uelg., Classe set , Mkm , No 1639 (1953) 28 I-1 M. HUPFMAN, prosentcd at American Chcmlcal boclcty mectmg, New York, September, 1947. (a) R. A RUEHRWEIN AND H. M HUFPMAN, J Am CJrem SOL, 65 (x943) 1620, (b) G D OLIVER, M EATON AND H M HUFFWAN, zbzd, 70 (x948) 1502; (c) H M HIJFFMAN, CJrem Revs., 40 (x947) I H I; STIMSON, J Researclr N&l BUY SLundards, 42 (1949) zag S S. TODD, G D OLIVER AND 1-I M I-IUPFNAN, J. Am CJrem Sot, 6g (1947) 15x9 Unpubhshcd rerults, this Laboratory 1-I L PXNKE, presented at the Seventh Annual Calorlmctry Conference, Washmgton, D C , September, 1952 S V R MASTRANGIZLO AND R W DORNTC, J Am CJlettr Sot, 77 (1955) 6200 H L FINKE, D W SCOTT, M E GROSS, J 17 ME~SERLY AND GWY WADDINGTON, J Am.

CJretn Sot , 78 (rggG) 5469 J

I? MCCULLOUGI~,

H

L

FINKS,

M

E

GROSS,

J

I? MHSSLRLY

AND

GUY

WADDINGTOF.,

J. PJrys. Chetn , 61 (1957) Roce~vccl December

x7th,

1956