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DISCUSSION As indicated by the d a t a in Table I, there is good agreement between t h e two log K values and also between the adsorption capacities calculated for aniline by the two different methods. It is therefore concluded t h a t titration calorimetry can provide reliable thermodynamic values for reactions involving adsorption on solids. The speed and wide applicability of titration calorimetry makes it preferable to other methods for the study of solid adsorption reactions especially when decomposition of products or reactants can occur with time. T h e calorimetric titration curves given in Figure 1 clearly show the adsorption capacity regions for aniline and nitrobenzene but not for toluene. T h e gradual change in slope of Q us moles of added toluene (Figure 1) results in highly correlated adsorption capacity and K values. Thus the two parameters could not be independently measured as previously mentioned. T h e calculated adsorption capacities for aniline and nitrobenzene are similar as would be expected for these similar size molecules. Whereas log K values for nitrobenzene and aniline are significantly larger than t h e corresponding value for toluene, this is not observed in the case of the AH" values. Rather,
the AW value for adsorption of aniline is significantly more negative than t h a t for either nitrobenzene or toluene. T h e change in AH" values does not parallel the change in dipole moments in going from toluene with the smallest dipole moment to nitrobenzene with the largest. T h e larger negative A H " value for aniline may be attributed to the presence of a free electron pair on the nitrogen in aniline which allows Lewis acid-base interactions with the zeolite. This argument is strengthened by the results of Abramov et. al. (11) who observed an unusually large change in the infrared spectrum associated wiLh the adsorption of aniline by the zeolite, which they attributed to the effect of t h e free electron pairs in aniline. However, in the case of nitrobenzene, the change in the spectrum was less pronounced and was attributed to the presence of the benzene ring.
ACKNOWLEDGMENT Appreciation is expressed to Linde Inc. for donation of the zeolite used in the study and to E. A. Butler and John L a m b for helpful discussions. Received for review May 3, 1973. Accepted ,July 5 , 1973. Contribution No. 40 from t h e Center for Thermochemical Studies, Brigham Young University. (11) V. N. Abramov, A. V. Kiselev, and V. I . Lygin, Zh. Fiz. Khim., 38, 1044 (1964); Chem. Abstr., 61,38209 (1964).
New Method of Purity Determination by Means of Calorimetric Differential Thermal Analysis Heiner Staub and Werner Perron Mettler lnstrurnente A G , CH-8606 Greifensee, Switzerland
Purity determinations with adiabatic calorimetric measurements based on Van't Hoff's law have been successfully performed for quite some time [see, for example, the work by Glasgow et al. ( I ) ] . Gunn (2) has described a method which allows measurements also with dynamic melting tests. Various authors ( 3 , 4 ) have modified this method for use with DSC or calorimetric DTA. Both the DSC and DTA methods require a correction factor for the calculation of the molar impurity which has no physical basis. Its magnitude is determined by trial and error or according to a formula by Sondack ( 5 ) .Relative errors of u p t o more than 1070of the determined impurity concentration do occur. T h e present article proposes the use of a new "step heating programming technique" which does not require the above mentioned correction factor and which yields results t h a t are more accurate than those obtained by the dynamic method. (1) A. R . Glasgowetal.. A n a / . Chim. Acta. 17, 54 (1957). (2) S.R. Gunn. Ana/. Chem.. 34, 1262 (1962). (3) G. L. Driscoll. I . N. Duling, and F. Magnotta, "Analytical Calorimetry," Plenum Press, New York, N.Y., 1968, p 271 (4) "Mettler TA2000 Information," No. 1 , 1972, Mettler Instrument Corp.. Princeton, N.J. (5) D.L. Sondack, Ana/. Chem.. 44, 888 (1972).
128
THEORETICAL T h e method is based on the following equation which is derived from Van't Hoff's law:
T.
=
RT,?x,* 1 T,, - A H , F ~
whereby x-* = x2F = mole fraction of the impurity in the liquid phase = mole fraction of the impurity in the original substance F = fraction melted T , = equilibrium melting temperatuie [K] T o = equilibrium melting point of the pure substance [K] R = gal constant = 1.987 cal/mol K AHi = melting enthalpy of the pure substance {cal/moll x2
x2*
The validity of Equation 1 depends on the applicability of Van't Hoff's law and, for this reason, is subject to the following limitations. Only eutectic systems can be investigated. The impurity may, therefore, not form a solid solution and must, in it5 liquid phase. be ideally soluble in the main component. Moreover, the impurity concentration must be small, and the solid and the liquid phase must be in thermodynamic equilibrium.
A N A L Y T I C A L CHEMISTRY, VOL. 46, NO. 1, J A N U A R Y 1974
2300
4000
600C
ROO0
Figure 1. Purity determination by step heating programming technique. Sample: 10.7 mg phenacetin contaminated with 1.06 mol
YO
benzamide The temperature steps are 10' from 80' to 130" and 0.5"from 130" to 134.5'
Equation 1 shows that the graphic representation of T , us. 1/F is a straight line which has an ordinate intersec-
tion point T , and a slope x2* R T o 2 / A H ~ . From this, it is simple to calculate impurity concentration x p * . Thus, all that is to be done in a test is to measure S H f and value pairs of Ts and 1 / F to determine the impurity concentration by means of a graphic representation of these value pairs.
EXPERIMENTAL New Step Heating Programming Technique (6). During a melting test, the temperature is raised in steps to measure the molten fraction, F, under actual equilibrium conditions. After each temperature increase, one waits until equilibrium has occurred, t h a t is to say until the signal on t h e recorder has returned t o the base line. Figure 1 shows a typical test. With uniform temperature steps, increasingly larger peak areas can be seen to occur between the eutectic melt a n d the clear melting point. For this reason, the test was run in such a way t h a t the step width was decreased as t h e temperature was increased. Under certain circumstances, the last peak may even be smaller than the preceding one. This would occur if the clear melting point is only slightly higher t h a n t h e initial temperature of the last temperature step. T h e last peak also shows a more or less abrupt end (see Figure 1). T h e peak areas of the temperature steps before the eutectic and after the clear melting point are caused by the differing heat capacities of the sample a n d the reference. These peaks provide the "background area" which is proportional to the respective step width and must be deducted from each of t h e peaks to obtain the actual heat of fusion. The sum of t h e heat of fusion of all the peaks between the eutectic temperature and t h e clear melting point is equal to the total heat of fusion. A H , can be calculated from this sum. By adding the partial heats of fusion u p to the corresponding temperature, it is possible to determine T , a n d 1 / F pairs. To and t h e slope are determined from t h e graphic representation of these value pairs and molar imourity concentration x p * is calculated from these results. Figure 2 shows t h e diagram which corresponds to t h e test shown in Figure 1. Since the graphic determination of this straight line requires, in principle, only 2 points, it is possible to reduce the number of peaks in the case of routine measurements. Test Conditions. All these tests were carried out with a M e t t ler TA2000 System which has already been described in a previous paper (71. The test substance was phenacetine with benzamide impurities. (6) H . Staub and W. Perron. presented in part at the 23rd Pittsburgh
Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 1972. ( 7 ) W. Perron. "Thermal Analysis. ICTA 1971, ' Vol. 1 , Birkhauser Verlag. Basel. Switzerland, 1972. p 35.
Figure 2. Curve of equilibrium temperature T vs. reciprocal fraction melted 1 / F ; experiment of Figure 1 Contrary to expectations, it was difficult to produce specifically defined impure substances. Using such various methods as mixing, melting, or crystallizing from solutions, it was virtually impossible to distribute the very small quantities of impurities uniformly in the main component. For this reason, we used a Mettler ME22 microbalance to weigh the two components directly into the crucibles which were then closed airtight. Peak area integration was done with a computer in the following manner. T h e DTA signal was digitized with a Mettler CT d a t a transfer system and stored on a punched tape. The d a t a were then processed by a Honeywell H-316. P a r t of the test was evaluated on-line with a Hewlett-Packard 9810 desk-top calculator.
RESULTS AND DISCUSSION T h e results of typical tests are compiled in Table I and show t h a t impurities of u p to 10% can be determined with approximately 5% relative accuracy. In all cases, the graphic representation of T , L ' S . 1/F resulted in straight lines. This fact is important because it allows us to decide whether Van't Hoff's law is at all valid in a test with a given mixture of substances. In their work on calorimetric measurements, McCullough and Waddington (8) have pointed out that if one of the conditions for the validity of Van't Hoff's law is not satisfied, the graphic representation of T , cs. 1/F is not a straight line. To confirm this finding, we have used the new step heating programming technique to determine the purity of a substance which forms solid solutions. For this purpose. we have chosen hexacosane with octacosane, respectively, pentacosane impurities. Figure 3 shows the curvature which occurs when T , is plotted us. lib'. (8) J. P. Mc Cuilough and G . Waddington, Anal. Chim A c t a . 17, 80 (1 957).
ANALYTICAL C H E M I S T R Y , VOL. 4 6 , NO. 1, J A N U A R Y 1974
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Table I. Purity Determinations of Phenacetin Contaminated with Benzamide with the Isothermal Step Method
-
Impurity weighed in [mol % ]
Impurity measured [mol %]
0.51 0.63 1.09 1.57 1.77 2.53 3.65 4.92 7.33 10.09 13.51 20.23
0.49 0.63 1.08 1.55 1.73 2.37 3.48 5.25 7.09 10.29 13.61 23.32
-
..
222
-~
.3
-
Relative error [%] -3.9
0.0
impurity weighed in [mol % ] Heating rate 0.5
0.15 0.55
-0.9 -1.3 -2.3 -6.3 -4.7 +6.7 -3.3 +2.0 +0.7 +15.3
1.03 1.50 1.99 2.62 3.09 4.02
5.00
0.14 0.59 0.94 1.32 1.79 2.16 2.56 3.25 3.87
Impurity measured [mol % ]
3
20
Comparison with the Dynamic Method. Using the same test substance, we have made a series of determinations with the dynamic method whose results are compiled in Table 11. These tests were always started below the eutectic temperature. Evaluation was again performed by computer with our standard computer program (9). T h e melting enthalpies thus determined agreed to better than 2% with the calculated values. This shows that the melting enthalpy in the premelting region was also recorded and that no correction for "lost" heat is required. (This is a frequent explanation for the correction t h a t is required in dynamic experiments.) Nevertheless, the plot of Ts us. 1 / F did not yield straight lines. Rather, the lines were curved and corrections of about 5% of the total heat quantity were necessary to linearize them (Figure 4 ) . Thus, it is apparent t h a t one of the conditions for the validity of Van't Hoff's law was not fulfilled. Since the substance system was t h e same as t h a t used in the step heating experiments, b u t since on the other hand a thermodynamic equilibrium can, by definition, never occur in a dynamic test, it must be assumed that the latter is the reason for the nonlinearity of the graphic representation of T5 us. 1/F. This fact is also illustrated by the results shown in Table 11. T h e faster the heating rate, the larger is the error of the determination. Further, with increasing impurity concentrations, it is also necessary to select increasingly smaller heating rates to still obtain acceptable results. If the purity of a substance with unknown impurities is determined, i t is not possible, with a dynamic test, to de(9) "Mettler TA2000 Information." No 2 , 1973, Mettler Instrument Gorp., Princeton, N J
0.1 '/min
0.2
(6.7) (7.3) (8.7) (12.0)
1.01 1.45 1.92 2.22 2.59 3.35 3.99
(10.1) (17.6) (17.1) (19.2) (22.6)
2
~~
Figure 3. Curve of equilibrium temperature T vs reciprocal fraction melted 1/ F of impure hexacosane
130
Table I I. Purity Determinations of Phenacetin Contamined with Benzamide with the Dynamic Method Using Different Heating Rates (Relative Errors in Per Cent Are in Parentheses)
3
4
5
o
(1.9) (3.3) (3.5) (15.3) (16.2) (16.7) (20.2)
7
1 .OO 1.47 1.88 2.74 3.18 3.52 4.29
(2.9) (2.0)
(5.5) (4.6) (2.9) (12.4) (14.2)
6
Figure 4. Curve of temperature J vs
melted rected
1 / F of
reciprocal fraction a dynamic melting test, uncorrected and cor-
Sample 5 371 mg phenacetin contaminated with 0 71 mol % benzamide
termine from the bending of the curve whether t h e lack of equilibrium alone is responsible for the nonlinearity or whether there exists a n additional factor, e.g., a solid solution. With the new step heating method, however, this can be done without any problem. Likewise, and contrary to the dynamic method, it is also possible to determine even relatively high impurity concentrations with sufficient accuracy, as can be seen from a comparison of Tables I and
11. CONCLUSIONS Purity determinations with dynamic melting curves can be used for routine analyses if it is known that the substance system has a fairly ideal behavior and if the heating rate is sufficiently low so as to keep the sample as close as possible to equilibrium conditions. The inaccuracy may be relatively large. Moreover, the method is limited to small impurity concentrations. With its step-by-step temperature increase, the new method yields more accurate results-for impurity concentrations of u p to 10%-without requiring arbitrary or empirical corrections. I n addition, the linearity or nonlinearity of the graphic representation of T , us. 1/F has a significance and makes it possible to decide whether a substance system has sufficiently ideal behavior to permit purity determinations which are based on Van't Hoff's law. Received for review March 8, 1973. Accepted August 9, 1973.
A N A L Y T I C A L CHEMISTRY, VOL. 46, NO. 1, J A N U A R Y 1974
