A Simple Melting-Curve Method for Quantitative Purity Determ i nation STUART R. GUNN Lawrence Radiation Laboratory, University of California, Livermore, Calif.
b An apparatus for determining the melting curves of ca. 0.3-ml. samples, and its use for calculating purity, heat of fusion, and heat capacity are described. Results of measurements on samples of ammonia, water, and benzene with known amounts of contaminants are given. Sensitivity is of the order of 1 O P mole fraction impurity, and accuracy is 10 to 20%.
T
HE measurement of solid-liquid equilibrium temperatures as a function of the ratio of solid and liquid present is a simple and sensitive method of ascertaining the degree of purity of moderately to highly pure organic and inorganic substances which melt without decomposition a t experimentally accessible temperatures. The method has the advantage that the property being measured is a characteristic of the major constituent; the mole fraction of impurity is obtained without need for knowledge of its nature, the only limitation being that in the simplest treatment of the data, the impurity is assumed to be insoluble in the solid phase. Sturtevant ( 9 ) and Skau, Arthur, and Wakeham (8) have reviewed determination of heats of fusion and melting points, and purity cal-
Figure
1292
l.
The apparatus
ANALYTICAL CHEMISTRY
culations therefrom. -1symposiwm on the subject has been published ( 1 ) . Skau (’7) described a siml)le apparatus for determination of freezing and melting curves and their use for qualitative estimation of purity. hlathieu (3) described a similar apparatus and quantitatir e calculation of purity from the melting rur\.es. The present paper describes another similar apparatus, a more straightforward method of quantitative purity calculation, and also use of the system for approximate determination of heat capacities and heats of fusion. APPARATUS
The apparatus, shonn in Figure 1, consists essentially of a sample bulb mounted on a thermocouple nithin a metal block which is heated electrically and also has a thermocouple; heat is transferred from the block to the sample bulb largely by air conduction. The block is anodized aluminum, O.T5 inch in i d . , 2.00 inches in o.d., 7 inches long. A KO. 35 Manganin heater is wound bifilarly in a square helical groove on the outer surface. The block is suspended by wires from a Transite lid and is held in alignment by a glass tube of the same inside diameter. The whole assembly is suspended by the lid in a I-quart wide-mouthed Denar flask. The thermocouples consist of KO.24 constantan and S o . 3 i copper, both enameled, twisted together throughout their length; the junction is soft-soldered. The block thermocouple is wrapped once loosely around the block and the junction is inserted in a hole a t the bottom with grease. The upper part of the sample thermocouple is taped to a n inner glass tube which fits loosely in the well; beloiv this it is wound in a spiral of several turns fitting fairly closely into the well above the sample bulb to minimize heat leakage, and has one turn below the sample bulb to help center the junction, which is the sole support of the sample bulb. The two constantan leads are soldered together with a copper lead and the junction is placed in an ice bath. The three copper leads are then brought to a selector switch which permits measurement of either the block or sample bulb temperature (or the difference directly; however, this function is not normally used). Voltage is read with a Rubicon B potentiometer and an enclosed lamp-and-scale galvanometer ;
sensitivity is ca. 0.2 pv., but nccurncy, because of varying thermoelectric potentials in the ciwuits! probably is around 1 p v . The sample bulbs are shown in Figure 2. ‘ h e y arc about 2 cm. long and 6 mm. in o.d., with nnll thickness \-ari:ihle hut averaging ca. 0.2 mm. They :ir(’ strong, usually holding the 10-atm. vapor pressure of ammonia a t room tcmperature. The re-entrant thermocouple well is about 1 cm. deep and 1 mm. in i d . I t flares considerably a t the hottom; better thermal contact with the thermocouple would be achieved if the well were narrower and more uniform. The tube a t the top of the bulb is about 2 mm. in diameter, and connects to a ball joint. Xormdly the bulb is mounted on the vacuum line and the sample, if low-boiling, is distilled in; if high-boiling, as benzoic acid, the solid is loaded into the tube above the bulb and, after evacuation, melted into the bulb, usually under a low pressure of helium; the bulb is then sealed off. In the present lvork, however, the same bulb was used for all water and benzene runs; the tube was cut off just above the bulb, loading was accomplished with a hypodermic syringe, and the bulb was closed with a cap consisting of a 3-mm. length of 2.5-mm. diameter plastic tube and a small glass plug. To improve thermal contact between the bulb and thermocouple, the well is filled with some material, preferably a solid, to prevent tilting of the bulb on the thermocouple. For water, benzene,
Figure 2.
Melting-point bulb
The block heater is operated from a variable voltage transformer, which is left at constant setting throughout a run. The heating rate is a function of the heater resistance and heat capacity of the block, which change with temperature, and of the line voltage, 1% hich may also vary, but in practice the heating rate proves to be very constant over extended intervals. PURITY DETERMINATION
'
-
-800
'
I'
2:
'lo
60
80
100
120
140
Figure 3 shows melting curves for water and sucrose solutions, indicating qualitatively the behavior to be expected. Quantitative calculations from the curves will be explained by reference to Figure 4. Assuming Xewton's law, the heat transfer to the sample is
t m in.)
Figure 3.
Melting curves
and benzoic acid, Apiezon Q, a puttylike vacuuni sealing compound, was used. For ammonia, the bulbs were warmed to about 0" C., filled with mineral oil, mounted on the thermocouple, and inserted in the already cooled block. At around -30°, the oil was solidified, and the thermocouple was raised briefly and bent to position the bulb axially. The assembly is cooled when necessary by pouring liquid nitrogen in the Dewar and then dumping it out when the desired starting temperature is reached. Unless the vapor pressure of the substance is too great, the sample bulb is mounted on the thermocouple at room temperature and inserted in the already cooled block. If the curve to be recorded passes through 0' C., it is important to avoid condensation of moisture on the bulb which would introduce a perturbation at its melting point. With water and its solutions, to avoid breakage from the expansion upon freezing, freezing is started by touching the bottom of the bulb, mounted on the thermocouple, to the surface of a flask of liquid nitrogen and the bulb is then quickly inserted in the already cooled block; the ice thus grows upward, and in this case frost on the surface is of little consequence. The sample is normally frozen with the block held 10" to 30" belox the freezing point; supercooling of several degrees may occur, but crystallization then starts, possibly with the help of shaking the whole apparatus, and is completed in 5 to 15 minutes.
Table 1.
t
w
12 16 20 21 28 32 36
16.0 23.1 33.2 47.3 65.6 88.4 115.6
dH/dt = k(Tb - T , )
where Tb is the temperature of the block, T, is the temperature of the sample, and k is the heat transfer coefficient. The rate of temperature change of the sample is dT,/dt
=
k(Tb - T.)/(nCa 4- c,) (2)
where n is the number of moles of sample, C, is its molar heat capacity, and C, is the heat capacity of the glass bulb, well packing, and part of the thermocouple. If Tbis increased a t a constant rate, r , T, will approach asymptotically and follow a parallel time-os.-temperature line such that dTa/dt = dTb/d.t
=
r
(3)
displaced in temperature at a given time by a thermal head, h, h
=
Tb
-
T , = r(nC8
+ C,)/k
(4)
and displaced in time at a given temperature by a lag, I: 1 = (Tb - !I'*)/r= ( n C ,
+ Cg)/k
(5)
Thus I is a function only of the heat capacity and k, but h is also a function of the heating rate, r: h
=
rl
(6)
The present treatment of purity calculations assumes that k is a constant, but its value need not be known; likewise the values of n, C, and C, need not be known. Curve A B of Figure 4 represents the block temperature, increasing a t an
Purity Determination of NH3 Containing CHINHz
Z = 212 sq. cm.; h = 48 ~ v . 1' X Y F-1 10.9 13.1 2.9 73 32 6.6 12.9 15.5 16.6 12.8 16.6 13.8 7.0 16.9 30.4 14.1 4.39 17.3 48.3 14.4 2.99 17.4 71.0 14.5 98.1 2.16 17.5 14.6
', Figure 4. curve
(1)
E.M.F.
- 2738
2714 2704 2700 2697.5 2696 2695.5
'f
Idealized melting
approximately constant rate, r . Curve CGF represents the sample temperature, t, being selected before this temperature departs from a line parallel to .4B and t f after the temperature has returned to a line parallel to A B . From Equation 1, it follows that the heat transferred to the sample in warming it from T , to T I is HI
- H, = k l , ' { T b - T,)dt = k(AbpGC) (7)
If no latent heat were associated with the fusion, the sample would warm along path CDEF, where Tois the melting point and curves CD and EF are separated from AB by the differem lags, E, and 11, which reflect the different heat capacities of the solid and liquid, that of the solid generally being lower. The absorption of heat would be k ( A B F E D C ) . Hence, the molar heat of fusion, A H , of the sample is nAH = k(SBFGC) - k(ABFEDC) = k(CDEFG) ( 8 )
The area CDEFG will be called 2; it is eraluated by graphical integration-in practice by dividing the area into several easily measured triangles which cover an area judged visually to be equal. The heat transferred t o the sample to warm it from T , to T, is k ( A H 1 C ) ; we denote area A H I C as W . The heat required to warm the solid from T,to T,in the absence of melting would be k ( A J K C ) ; we denote area A J K C as X and instead of integrating it graphically note that X = rlc(tn' - t , ) = h,(t,' - t,) (9) The amount of heat which has been used to melt part of the sample at time t, is k ( W - X ) ; we use Y t o denote VOL 34, NO. 10, SEPTEMBER 1962
1293
Figure 5. Plot of T vs. slightly impure ammonia
F-'
for
IV-S. The reciprocal of the fraction of the sample melted, F-I, is F-I
=
z/y
(10)
F-1 may be calculated for as many points as desired on the melting curve. For ideal or sufficiently dilute solutions, the van't Hoff law of freezing point lowering has the form 1'0 - .\r,F-lRTo'/AH
7'
(11)
where TO is the melting point of the purr material and NI is the mole fraction of impurity. Hence, the values of T,, plotted against F --I should lie on a straight line whose slope multiplied by thr cryoscopic constant RToZ/AH is equal to AT2. Since the calculation of F-I involves only the ratio of areas, it is not necessary to convert the graphical area to degree-minutes. I n this work the data have been plotted a t a scale of 40 p ~ per . cm., 2 minutes per cm., and areas are expressed in square centimeters. The calculation procedure is simple; it is illustrated in Table I for a sample of ammonia slightly contaminated with methylamine. In Figure 5 , T is plotted us. F - I , and an cstimated "best" straight line is drawn, giving greatest weight to points in the middle region; points a t high values of F-I are sensitive t o the value of h used, and points a t low F-' will have small positive errors in the values of T (see below). For this plot, the slope is 0.60 pv., or, dividing by the thermocouple coefficient, dE/dT = 30.4 pv. per degree, the slope is 0.020 degree. The cryoscopic constant, RTo2/
Table 11.
AH, using (we 6) - ii.76" C. for To siid 1.351 kcnl. per mole for AH, is 56.1"; hence, the value of AT2 obtained is 3.6 X lo-'. In the case of less purr samples, a somewhat modified procedure may be used. Because melting extends over a long time, it is difficult to drtermine h near the melting point. -Accordingly, an estimated value of h is used. This may be obtained by comparison with h for purer samples of the same material; from an estimated heat capacity of the material; or from observation of the steady state, Zr, after melting is completed and correction to a lower value for 1, due to lower heat capacity of the solid. For the calrulation an arbitrary t, is selected; 2 is split into two parts, area 2%occurring after t , and an estimated Zl occurring before t , ; F-' is (Zl Z,)/(Y Zl). The calculation is repeated using trial values of 2,until a straight line is obtained for the F - l DS. T plot. r2n example is given in Table 11. Here the first set of F -l was calculated using 0 for Z1. The plot, shown in Figure 6, is highly curved. Since the value of Z1 affects F-* greatly a t high values, but very little a t low values, it is usually possible to select on the second approximation a value which gives a satisfactorily straight line. The second set of F-1 was calculated using 5.0 sq. cm. for 2, and is plotted in Figure 6. The line gives 0.0040 for ~ V Z .Subsequent examination of the heating curve for the same sample over a longer temperature range showed a bump a t -3640 pv. (-110" C.), the lag suddenly increasing from 3.9 to 4.3 minutes and then gradually decreasing slightly. This presumably is due to eutectic melting. It is difficult to estimate the excess area becsuse of melting all the way from this point to the melting point, but 5 sq. cm. is a reasonable value. A sample of ammonia containing 0.4oJ, water showed a similar, larger effect a t -3145 pv. (-92.8'); Timmermans (IO) indicates a eutectic a t -92.5". Integration of 2 from this point and use of the value of h occurring just before gave a straight-line plot of F-' us. T .
+
Purity Determination of NH3 Containing CH3NH2
t
W
t'
X
cm.; h Y
20 24 28 32 36 40 44 48 53 56
28.4 35.2 42.8 51.9 63.2 77.5 95.3 117.0 143.0 173.4
18.9 22.4 25.5 28.1 29.9 31.3 32.3 32.9 33.3 33.6
24.6 29.1 33.2 36.5 38.9 40.7 42.0 42.8 43.3 43.7
3.8 6.1 9.6, 15.4 24.3 36.8 53.3 74.2 99.7 139.7
Zz
1294
rn
+
= 239 sq.
ANALYTICAL CHEMISTRY
= 52 hv.
E.M.F.
F-1
F-1
2887 2845 2806 2776 2753 2736 2724 2716 2712 2708
63 39 24.9 15.5 9.8 6.5 4.48 3.22 2.40 1.71
27.2 21.5 16.4 11.7 8.2 5.72 4.10 3.02 2.28 1.65
.f@3,-
Figure 6. Plot of T vs. highly impure ammonia
F-'
for
The apparatus has been used occasionally in this laboratory for about two years for checking the purity of various materials, mostly covalent hydrides. The runs which have been done recently with samples of known contamination are listed in Table 111. The ammonia solutions were prepared by measurement of the components as gases in calibrated sections of the vacuum line; it is probable that the high results indicate that some material was adsorbed or absorbed in grease and subsequently condensed in the bulb. . h m o n i a and methylamine were distilled from sodium and lithium solutions, respectively; water was deaerated by repeated freezing and pumping. Reagent-grade benzene that had stood over sodium-lead alloy for two weeks was purified by four cycles of slow fractional freezing with stirring, about three fourths being frozen on each cycle and the liquid withdrawn. The nheptane was Phillips research grade, stated 99% pure. Solutions were made up by weight in serum-capped bottles, additions and removals being made with hypodermic syringes. The block heating rates used were about 0.35 degree per minute in all cases. The samples used were about 14 mmoles of ammonia, 18 mmoles of water, and 4 mmoles of benzene. With the pure samples of ammonia and water, T,shows no deviation from a straight line until TF, has passed through the melting point. It then curves- over rapidly into the plateau, which is a straight line with a total upward drift of about 2 pv. in its 30minute duration, a t the end of which the block is about 13' warmer than the sample. This slope indicates that the thermocouple "sees" the block temperature about 1/300 as well as the sample temperature-that is, thermal contact between the junction and the sample is not perfect, so the thermocouple responds partly to the block temperature. If thermal contact with the sample were perfect, the plateau for very pure samples would be perfectly flat. A truer measure of the
sample temperature would be T,0.003(Tb-T,). Use of this would improve the linearity of the T us. F-' plot and give a flat plateau for very pure samples. For very pure samples, the best value of the melting point is obtained by extrapolating the slightly sloping plateau back to the point where it intersects the block temperature, since a t this point there is no perturbation of the measured T. by Tb and when the sample is very pure the melting point is not significantly affected by the impurity content even a t very low fractions melted. By analysis of the curved portions of T, for water and ammonia, upper impurity limits of 10+ and mole fraction, respectively, can be set. This gives an indication of the sensitivity of the method; while it varies with cryoscopic constant, molar volume, and heating rate, it will in general approach mole fraction. The other melting points for contaminated samples given in Table 111 are by extrapolation of the T us. F-' plot to F-l = 0, which theoretically is the melting point of the pure solvent. Several runs with pure benzoic acid gave a melting point of f5426 fiv. Our observed melting points are compared with literature values in Table IV. The thermocouple tables of the National Bureau of Standards (6) were used. CALIBRATION AND HEATS OF FUSION
If the cryoscopic constant is not known, the heat of fusion must be estimated or measured to permit its calculation. This can be done with the apparatus described, if it has previously been calibrated to determine the value of k as a function of temperature. From Equation 5 it is seen that the lag, I , is a function of only n,C,, C,, and k. The calibration procedure consists of measuring 1 with a known amount of a substance of known heat capacity, and correcting for C, to determine k. A bulb weighing 340 mg. was loaded with 3.55 mmoles of benzoic acid and 30 mg. of Apiezon Q and heated from -180" to +140" a t rates of 1 to 2 degrees per minute, corresponding to thermal heads of 3 to 5 degrees; the lag, which was measured a t frequent intervals, ranged from 1.8to 2.8 minutes. A solid glass dummy of similar geometry, weighing 1.584 grams, was made up and loaded with 140 mg. of Apiezon Q and extra wire in the same proportion to the length of the thermocouple in the well, and the lag was measured similarly. Denoting the two series by subscripts 1 and 2,
ZI
=
12
=
k =
+
(nC* Cg)/k 4.66 Cg/k nC,/(Il - 0.215 1 2 )
Table 111.
Tests of Melting-Curve Purity Determination
Extrapolated Melting Point,
iV2
Solvent "8 "2
3" 3"
NHa Hz0 HzO HzO Hz0 C& c6Ho c6H6
Solute
Taken 0
CH,NHz
CH&H 'z Hz0 HzO ... Sucrose Sucrose Sucrose n-C& n-Cdb6
0.00029 0.0040 0.00032 0.0035 0
0.00049 0.00347 0.0296 0
0.00180 0.0101
and a table of k as a function of temperature can be prepared using tabulated values of the heat capacity of benzoic acid (2). The values obtained vary rather smoothly: about 0.042 cal. deg.-' min.-' from -170" to -120°, 0.050 a t -60°, 0.067 a t 0", 0.080 a t 40°, 0.100 at 80°, 0.106 at 100°, and 0.110 a t 125". Determination of either a heat capacity or heat of fusion requires knowledge of the amount of samyl-, n. A heat capacity determinatioi consist, simply of observation of 1 and calculation from Equation 5, with experimental or estimated correction for C,. For heat of fusion determinations, C, need not be known; area Z is measured and Equation 8 is applied. The melting areas, 2, of the various samples of ammonia, water, benzene, and benzoic acid were in constant ratio to their masses within a few per cent. However, the heats of fusion obtained were respectively 25, 8, 11, and 3y0 below literature values. While such accuracy would often be adequate in the determination of an unknown cryoscopic constant, it is probable that better values of k could be obtained for this purpose by measuring fusion areas of known substances melting a t various temperatures in the range of interest instead of using k obtained from heat capacity measurements on benzoic acid or other substances. I n this manner the method would become more strictly a comparative one for interpolating unknown heats of fusion between nearby known ones. The present treatment for determination of both purity and heat of fusion assumes that k is independent of the temperature gradient between the block and the sample bulb. This may be reasonably true for radiative and conductive heat transfer, but not necessarily for convective transfer, if this becomes important. A second series of lag measurements was made with the solid glass assembly, with heating rates twice as great as in the first series, the faster heating giving gradients of
Found
fiv.
c 10-5
- 2695 - 2695 - 2695 - 2694 -2698 - 1/;
0.00036 0.0040 0.00049 0.0039
