in such
a
study
as
desirable checks
on
the method, and as
pinpoint sources of systematic error (76). The basis for such an objective method exists and has been extensively used. This is the method of corresponding solutions developed by Bjerrum (7) to treat extinctiometric data, but which can be used generally to treat all systems involving intensive factors. In this method a set of [ , (L)] formation function data points are obtained finally from which the stability constants may be calculated. The method thus yields the type of input data required of the present computer program. Since there are several steps in the procedure, ample opportunity is available for the experimenter to obtain some objective feel for the accuracy and precision of the data set, and even to attempt a quantitative estimate of precision by error propagation calculations. The calculation of stability constants from formation function data obtained by the application of the method of corresponding solutions to enthalpy titration data will be illustrated. Aquo Complexes of Co(II) and Ni(II) Perchlorates in 1-Butanol. The enthalpy titration data of Harris and Moore (77) in their studies on the aquo complexes of cobalt(II) and nickel(II) perchlorates in 1-butanol illustrate nicely the advantages of the present computational system. The [ , (Z)] data set for each system (18) was input to the computer program with the results given in Table IV. Comparisons of the experimental and calculated formation curves are shown in
Anal. Chem. 1969.41:330-336. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 10/30/18. For personal use only.
means to
Figures 4 and 5. For both systems all 26-l
or 63
(omitting zero coordination) suggested by the application of combination theory, for a maximum water coordination number of six for Co(II) and Ni(II), were tested by the usual criteria (4, 5) that each stability constant and the stability constant minus one standard deviation be positive, and that the weighted root mean square deviation or goodness-of-fit parameter be 1.5 or less. The best fit for the Co(II) , system suggested the existence of the inner-sphere aquo complexes containing 1, 2, 4, and 6 water molecules, while for the Ni(II) H20 system the data were best interpreted in terms of the complex species containing 1, 2, 3, and 6 waters of hydration. The original computational method (19) did not exclude the presence of the hexaquo and even higher species, and it is significant that the completely objective treatment illustrated here required the existence of species of high coordination number even though ligand number data did not extend very far past ñ 4. These results are taken as strong evidence not only for the existence of a species of high coordination number, but also for its strong influence on the shape of the 4. For systems of overlapping formation curve near ñ complexes such as the systems considered here, the theory requires the presence of complex species of both lower and higher coordination number at any given average ligand number. The known coordination number of six for Co(II) ·
=
=
and Ni(II) in various solids and solutions made the existence of the hexaaquo complexes in 1-butanol appear reasonable.
possible functional models
(16) J. S. Coleman, L. P. Varga, and S. H. Mastín, “Graphical Methods for Determining the Number of Species in Solution from Spectrophotometric Data,” Los Alamos Sci. Lab. Rept. (1967). To be published. (17) P. C. Harris and T. E. Moore, Inorg. Chem., 7, 656 (1968). (18) P. C. Harris, private contribution.
Received for review July 8, 1968. Accepted November 4, 1968. This work was supported, in part, by the Research Foundation and Computer Center at Oklahoma State University. (19) A. J. Poe, J. Phys. Chem., 67, 1070 (1963).
Differential Scanning Calorimetry as a General Method for Determining the Purity and Heat of Fusion of High-Purity Organic Chemicals. Application to 95 Compounds Candace Plato and Augustus R. Glasgow, Jr. Division of Food and Chemistry and Technology, Food and Drug Administration, Washington, D. C. 20204 A method for determining the purity of organic compounds by differential scanning calorimetry is presented. The heat of fusion ( /) and temperature during melting are measured and a curve is plotted, the slope of which is the melting point depression (AT) due to impurities in the sample, and whose zero
intercept represents the melting point of a theoretical sample with zero impurity (T0). The total purity is computed by inserting these values into the equation: mol % impurity = 100 (AHf/RT01 2) X AT. Organophosphates, amides, ureas, carbamates, heterocyclics, chlorophenoxy acids, esters, and halogenated compounds were analyzed. Because the concentration of the contaminants, rather than the pure substance, is determined, the effect of experimental error on the resultant purity value is minimized. The method is accurate only for samples over 98% pure, and does not measure impurities which are soluble in the solid phase or insoluble in the melt. It is also inapplicable to chemicals which decompose at their melting points or have inordinately high vapor pressures. 330
·
ANALYTICAL CHEMISTRY
to analytical chemists is the deterproblem common mination of the purity of standards by definitive methods. Cryoscopy, where applicable, has long been acknowledged as the best method of analyzing pure substances because total impurity is measured directly. This method depends only on the physical-chemical behavior of the compound, and no
One
reference standard is necessary. We have developed a routine laboratory procedure for the cryoscopic determination of purity, using the differential scanning calorimeter (DSC). The need for the complex equipment, large samples, and long analysis time associated with traditional procedures (7) has been eliminated.
(1) A. R. Glasgow, Jr. and G. S. Ross in “Treatise on Analytical Chemistry,” Part I, Vol. 8,1. M. Kolthoff and P. J. Elving, Eds., Interscience, New York, N. Y., 1968, Chapter 88.
EXPERIMENTAL Instrument. The Perkin-Elmer DSC-1B with the Leeds and Northrup Speedomax W recorder was used for all measurements. The heart of the DSC consists of a sample cell and a reference cell. The base of each cell contains platinum resistance thermometers and tiny heaters to provide constant thermal control. During one half of the 60 cps operation, the circuit into which the heating rate is programmed controls the instrument. This circuit reads the two thermometers, averages their readings, compares this average with the programmed temperature, and applies enough power to the cells to enable them to follow the program. This circuit also activates an event marker for each degree Kelvin.
During the other half of the cycle, another circuit is in control. It reads the two thermometers and applies enough differential power to the cell with the lower temperature to make the two isothermal again. (This is the critical difference between DSC and differential thermal analysis, which records the temperature differential without compensating for it.) The differential power required is recorded as millicalories per second. The direction of pen excursion indicates whether the transition is endothermic or exothermic. Because the pen deflection records millicalories per second and chart travel is in seconds, the area under a peak becomes a quantitative measure of the heat evolved or absorbed during transition. Earlier articles in this journal describe the capabilities of the instrument in detail (2, 2). Standard. Indium, 99.9999%, is used for both temperature and heat calibration [m.p. 429.7 °K (4); heat of fusion 780 cal/mole (5)]. Area calibration is accomplished by measuring the area corresponding to the melting of a weighed sample of indium and calibrating the planimeter units from indium’s heat of fusion. The precision is good. In the past year, daily calibration gave a range of 0.0196 to 0.0204 meal/ planimeter unit. Differential temperature calibration ensures that the sample and reference cells are at the same temperature. The absolute temperature is calibrated by adjusting the controls so that the melting peak of indium lies between 429 and 430 °K. The observed transition temperature for a sample can vary more than a degree between determinations. This lack of reproducibility, coupled with the variation in the indium setting, means that the absolute value of the recorded temThis perature may be in error by two degrees or more. error does not affect the accuracy of AT values, as the temperature difference between two points on the same curve can be measured both precisely and accurately. Procedure. For purity determinations, the instrument is operated at its maximum sensitivity, hence the cell assembly must be kept immaculately clean to eliminate noise. For best results the temperature should be raised to 700 °K for a few minutes after each day’s use, and the instrument should be left at 400 °K with N2 purge when not in use. If the cell is known to be contaminated or if the base line becomes noisy, the cell should first be removed and boiled in methanol for 15 minutes, then baked clean in the instrument at 700 °K, and the base line checked for noise. Repeating the procedure seems to be more effective than prolonging either step, and the methanol wash should precede the baking-clean operation. The curve shown in Figure 1 is a trace of an actual determination; note the lack of noise.
Figure 1. Calculation from DSC curve; 99.55 mol % Methyl 4-(2,4-dichlorophenoxy)butyrate DSC Curve: The parallel dotted lines represent the superimposition of the low temperature slope of the indium peak to correct for thermal lag inherent in the system (see text) Temp
Area
=K
sum
308.119 308.256 308.422 308.590
52 146 371 781
=
Area
1 IF
sum
1 IF
15 % corr.
55.2 19.7 7.74 3.68
6.84 5.72 4.12 2.72
483 577 802 1212
3302
2871
=
(2) E. S. Watson, M. J. O’Neill, J. Justin, and N. Brenner, Anal. Chem., 36, 1233 (1964). (3) M. J. O’Neill, ibid., p 1238. (4) E. H. McClaren and E. G. Murdock, Can. J. Phys., 41, 95 (1964). (5) R. R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelly, “Selected Values of Thermodynamic Properties of Metals and Alloys,” John Wiley and Sons, New York, N. Y., 1963, p 135.
Lower
curve:
uncorrected; · corrected.
Mole % impurity
100
=
=
100 X
X 0.11
=
0.45 mol % impurity
For all purity determinations, the instrument is operated 1 mcal/sec full scale sensitivity to minimize sample size, at the slowest heating rate for optimal equilibration, and at the fastest chart speed to obtain large areas for planimeter at
accuracy. All samples are hermetically sealed in an aluminum pan to prevent loss of solvent or other volatile impurities, using the sealer provided by Perkin-Elmer Corp. The pan and cover, which may be used only once, are dried initially in the DSC at the temperature to be used. Samples must be finely powdered; a larger-than-average crystal will give a lump on the melting curve because thermal equilibrium cannot be maintained with the main body of the sample. A small agate mortar is suitable for grinding. A 1-3 mg sample is weighed into the pan before sealing, as metal is occasionally lost by stripping during sealing. The DSC is then set to a temperature 3 to 5 degrees below the melting point and the pen is set at zero on the margin adjacent to the event marker to ensure accuracy in temperature measurements. When the base line has stabilized, the DSC is programmed up at 0.625 °/min until several inches of base line have been run past the melting peak. The module containing the cells must not be touched while in operation, because it is extremely sensitive to mechanical shock and extraneous peaks will result. The chart paper must feed at an absolutely even rate, as the distance corresponding to one degree rise in temperature will be used to calculate the melting point depression and variations will introduce a significant error. If the paper tends to ride off the drive teeth, it must be held down manually. The actual temperature increment recorded by the event marker varies slightly with temperature, but this correction was not applied to the data presented. Planimeter work should be done with the chart taped to a large, smooth surface, preferably the same day as the deVOL. 41, NO. 2, FEBRUARY 1969
·
331
ascertained by a simple mathematical treatment of the data from a DSC scan. The computation is based on an equation whose derivation is presented in physical chemistry texts— i.e., (7). Although a more familiar form is used in determination of molecular weights, the form most convenient for use in DSC work is:
Mol % impurity
/ Fraction melted
I
Figure 2.
Mol % impurity gas constant, To
Liquid-soluble, solid-insoluble impurities =
=
100
T where AH/
RTo2 mp zero impurity, and
heat of fusion, R
=
T
=
=
mp depression
termination, for aged charts may not lie flat. An adjustable planimeter with a weighted end is recommended. A base line is drawn, the indium standard trace slipped under the sample trace, and the low temperature slope of the indium peak transferred to the sample chart (see Figure 1). Lines parallel to this slope are drawn at arbitrary intervals up to the point where the sample is half melted. Beyond this point, about 2/3 up the peak, melting is too rapid for equilibrium conditions to prevail and the equation does not hold. The indium slope is used to delineate portions of the melting curve because it corrects for thermal lag inherent in the system (6). Temperatures corresponding to the base line intercepts are noted. Precision of area measurements is ensured by the fact that only the purest compounds require the use of partial areas smaller than 100 planimeter units when the planimeter is adjusted so that one unit equals 0.02 meal.
The procedure for liquids is basically the same as for solids, except that the sample must be induced to crystallize in the DSC and the low-temperature cover must be used. The sampling tool preferred is a microliter syringe with its point filed off so the opening is at the end of the needle. While volatile liquids must be sealed before weighing, the possibility of losing metal in sealing makes weighing before sealing preferable when feasible. The instrument should be programmed down from room temperature with the chart running to permit observation of the crystallization exotherm. The sample is maintained below the crystallization temperature for several minutes to ensure complete solidification. The type of temperature manipulation necessary to induce crystallization varies with the sample, although slow cooling may prevent the formation of a glass. Once the compound has solidified, the determination is made just as for a solid. A large correction factor for premelting indicates incomplete crystallization, and a longer time at low temperature may give better results. Calculation. The purity of a sample for which only the molecular weight and sample weight are known can be (6) A. P. Gray, Instrument News, 16 (3),
332
·
ANALYTICAL CHEMISTRY
9
(1966).
=
100 X
^ RTo2
X AT
(1)
where AH¡ is the heat of fusion per mole; R is the gas constant, 1.9872 cal mole-1 deg-1; T0 is the melting point of a sample with zero impurity; and AT is the melting point depression. With this equation, the amount of solute (or impurity) in solution can be determined by multiplying AT by the constant, AH¡¡RTq2. In molecular weight determinations, the constant, Kf, which is used, must be computed for the solvent. In purity measurements, the pure compound is the solvent, and the constant, which is different for each chemical, must be computed. The area under the DSC melting curve gives the heat of fusion for the sample in millicalories, and the heat of fusion per mole is readily computed. T0 and AT are obtained from the DSC data. Analysis of a melting curve is best understood by looking at the reverse process, freezing. In Figure 2, the right-hand box represents a sample with zero impurity with the melting point of Ta. The next box shows a real sample with X concentration of impurity, and its melting point, T¡. The difference between T0 and T is the melting point depression, AT, for the sample. Two assumptions are now made which will be discussed in detail later: the impurity is insoluble in the solid phase and soluble in the melt. Under these conditions, it is evident that when the sample is half melted, all the impurity is in the liquid phase, now reduced to half its former volume, and the impurity concentration is increased to 2X. Because concentration and melting point depression are linearly related, the depression at this point is twice that of the original sample T2 2AT). In the last box in Figure 2, one third of (T0 the sample is liquid, the concentration of impurity in the liquid phase is 3X, and the melting point depression is 3 . When the increase in impurity concentration (or reciprocal of the fraction melted) is plotted vs. the corresponding temperature, a straight line results whose slope is the melting point depression, AT, and whose zero intercept is the extrapolated melting point, To, of the theoretically pure but nonexistent chemical. As a solid melts, the impurities dissolve in the initial liquid phase and the same relationship between fraction melted and temperature depression is obtained. The melting curve is better suited for analysis than the freezing curve, as the former is easily done under equilibrium conditions, whereas freezing introduces the problem of supercooling, a nonequilibrium condition unsuitable for calculation. Reduction of data from a DSC curve is shown in Figure 1. Because the amount of heat absorbed is directly proportional to the amount of sample melted and to the amount of area presented on the chart, fractions of these values may be used interchangeably. The fraction melted at any temperature is equal to the fraction of the total area occurring below that temperature. The reciprocal can be obtained directly by dividing the total area by the partial area. These reciprocals are plotted against their corresponding temperatures. In the case of very pure samples (over 99.99 mol %), the plot is linear. Curvature is observed in the case of less pure compounds; as the sample becomes less pure, its melting range increases and the point where melting actually begins is difficult to observe. A correction must be made for this -
=
(7) S. Glasstone, “Textbook of Physical Chemistry,” 2nd ed., Van Nostrand Co., New York, N. Y., 1946, p 642ff.
Table I.
Data for Purity Determination by Differential Scanning Calorimetry Purity,
#/,
,
To,
mol %
mole
°K
°K
0,0-Dimethyl ,S-(W-methylcarbamoyl)methyl phosphorodithioate,
99.41
5600
0.22
324.6
(a)
0,0-Dimethyl 0-(cis 2-methylcarbamoyl-1 -methylvinyl) phosphate,
99.78
5450
0.09
328.5
(b)
0,0-Dimethyl O-p-nitrophenyl phosphorothioate, methylparathion
99.83 99.01 99.64 99.56 99.11
5750 4750 6950 5700 9000
0.06 0.32
(b,y) (c) (a) (d)
0.27
308.9 279.4 323.9 315.9 368.4
99.14
7700
0.26
343.0
(e)
99.13
7800
0.23
321.9
(0
99.68
7400
0.10
344.5
(e)
99.72 99.94
7400 6200
0.09 0.02
345.2 316.4
(g)
Source1
Organophosphates 1.
dimethoate
2.
Azodrin
3. 4.
, -Diethyl
O-p-nitrophenyl phosphorothioate, parathion 5. 0-(2-Chloro-4-nitrophenyl) , -dimethyl phosphorothioate, dicapthon 6. 0,0-Dimethyl 0-(2,4,5-trichlorophenyl) phosphorothioate, ronnel 7. , -Diethyl 0-(3-chloro-4-methyl-2-oxo-2Ff-1 -benzopyran-7-yl) phosphorothioate, coumaphos 8. , -Diethyl 0-(3-chloro-4-methyl-2-oxo-2Ff-l-benzopyran-7-yl) phosphate, coumaphos oxygen analog 9. 0,0-Diethyl S-(6-chloro-2-oxobenzoxazolin-3-y 1-methyl) phosphorodithioate, phosalone 10. , -Dimethyl S-[4-oxo-l,2,3-benzotriazin-3(4/f)-yl-methyl] phosphorodithioate, azinphosmethyl 11. 0,0-Dimethyl S-phthalimidomethyl phosphorodithioate, Imidan 12. , -Diethyl 0-3,5,6-trichloro-2-pyridyl phosphorothioate, Dursban Halogenated Compounds 13. p-Dichlorobenzene 14. 1,3,5-Trichlorobenzene 15. 1,2,3-Trichlorobenzene 16. Hexachlorobenzene 17. 1,2,3,4,5,6-Hexachlorocyclohexane, alpha isomer 18. 1,2,3,4,5,6-Hexachlorocyclohexane, beta isomer 19. 1,2,3,4,5,6-Hexachlorocyclohexane, gamma isomer,6 lindane 20. Pentachlorophenol 21. 3,6-Dichloro-o-anisic acid, dicamba
0.11 0.15
(e, y)
(d)
39. 4,5,6,7,8,8-Hexachloro-3a,4,7,7a-tetrahydro-4,7-e/;do-methanoindene,
99.998 4100 0.001 325.9 (h) 99.98 4350 336.7 0.01 (i, y) 99.88 4900 0.05 326.9 (i. y) 99.99 5700 0.01 505.0 (h, y) 99.96 430.5 7400 0.02 (j) sublimes too rapidly to be run (j) 99.96 3800 0.03 388.9 (k) 99.75 4100 0.25 462.5 (0 99.15 5400 0.47 386.5 (1) two crystal forms; converted to higher melting before running 99.98 7300 0.01 404.4 (m) 99.26 6200 0.41 416.7 (n) 99.95 7800 0.03 466.8 (o) 99.92 9250 0.02 340.1 (P) 99.52 5700 0,17 322.9 (P) 99.73 6050 0.10 333.0 (q, y) 99.80 7400 0.08 382.3 (i, y) 99.58 6300 0.16 349.4 (i, y) 99.89 6100 0.04 337.9 (z) 99.72 6600 0.11 362.7 (m, y) 99.94 6300 0.02 383.0 (z) 99.59 6100 0.19 383.0 (z) 99.40 5900 0.30 383.0 (z) 99.41 6500 349.0 0.22 (z) 99.91 5800 0.04 363.0 (z) 99.25 7300 0.25 351.4 (z) 99.94 7150 0.03 420.1 (r) 99.76 6300 0.09 344.7 (q) 99.50 7700 0.15 343.8 (s) 99.25 7950 0,22 344.5 (s, y) decomposes (z)
40. l,4,5,6,7,8,8-Heptachloro-3a,4,7,7a-tetrahydro-4,7-e«cfc>-methanoindene,6
nonideal
1,4-Dichloro-2,5-dimethoxybenzene, chloroneb 2,6-Dichlorobenzonitrile, dichlobenil 2,6-Dichloro-4-nitroaniline, dichloran '-Butyl A'-ethyl-a,a,a-trifluoro-2,6-dinitro-/?-toluidine, benefin a,a,a-Trifluoro-2,6-dinitro-A,N-dipropyl-p-toluidine, trifluralin 1,1 -Dichloro-2,2-bis(p-ethylphenyl)ethane,6 p,p'-Perthane 1,1 -Dichloro-2,2-bis(p-chlorophenyl)ethane, p,p’-TDE 1, l-Dichloro-2-(o-chlorophenyl)-2-(p-chlorophenyl)ethane, , '-TDE 30. l-Chloro-2,2-bis(p-chlorophenyl)ethylene, p,p’-TDE olefin 31. 1,1,1 -Trichloro-2,2-bis(p-methoxyphenyl)ethane,6 methoxychlor 32. 1,1,1 -Trichloro-2,2-bis(p-chlorophenyl)ethane,6 p,p '-DDT 22. 23. 24. 25. 26. 27. 28. 29.
Sample 2 Sample 3 33. 1,1,1 -Trichloro-2-(o-chlorophenyl)-2-0-chlorophenyl)ethane,6 o,p '-DDT 34. 1,1 -Dichloro-2,2-bis(p-chlorophenyl)ethylene,6 p,p '-DDE 35. 1,1 -Dichloro-2-(o-chlorophenyl)-2-(/>chlorophenyl)ethylene, 36. ¿>-Chlorophenyl-2,4,5-trichlorophenyl sulfone, tetradifon 37. 2,4-Dichlorophenyl p-nitrophenyl ether, TDK 38. /?-Chlorobenzyl p-chlorophenyl sulfide, chlorbenside
o,p'-DDE
Sample 2
chlordene
41. 42.
43. 44.
45. 46.
47. 48.
heptachlor 1,2,3,4,10,10-Hexachloro-l,4,4a,5,8,8a-hexahydro-l,4-ew/o,erafo-5,8dimethanonaphthalene, isodrin l,2,3,4,10,10-Hexachloro-l,4,4a,5,8,8a-hexahydro-l,4-eni/o,exo-5,8-dimethanonaphthalene,6 aldrin l,3,4,5,6,7,8,8-Octachloro-l,3,3a,4,7,7a-hexahydro-4,7-emfo-methanoisobenzofuran, isobenzan l,4,5,6,7,8,8-Heptachloro-2,3-epoxy-3a,4,7,7a-tetrahydro-4,7-e«rfomethanoindan, heptachlor epoxide l,2,3,4,10,10-Hexachloro-6,7-epoxy-l,4,4a,5,6,7,8,8a-octahydro-l,4e/ii7»,r?/iChlorophenyl(-1,1-dimethylurea trichloroacetate, monuron-TCA
99.86 99.88 99.95 99.66 nonideal 99.89 99.78 99.53 99.39
4800 6550 7600 5800 800 8100 7100 6850 8000
0.08 0.06 0.02 0.19 0.14 0.05 0.09 0.18 0.19
364.5 405.7 395.7 406.0 441.5 429.7 374.6 365.9 354.7
99.56 99.64 99.52 99.35 99.82
5800 5800 5500 4900 6200
0.26 0.21 0.21 0.26 0.08
415.5 415.9 357.7 315.7 374.2
99.57
6600
0.24
431.4
(v, y)
99.56
6150
0.26
430.6
(v) (m)
(q) (P)
(r) (m) (m) (m) (m) (m) (J)
Carbamates 69. 1-Naphthyl jV-methylcarbamate,
carbaryl Sample 2
Isopropyl carbanilate, IPC Isopropyl m-chlorocarbanilate, CIPC 2-Methyl-2-(methylthio)propionaldehyde O-(methylcarbamoyl) oxime, Temik 73. É.w>-5-Chloro-6-oxo-
