NOTES
Dec. 5, 1955 the instantaneous moles of minor component in the solid and liquid phases and the total moles of sample, respectively. I n the region of partial melting, the identity shown by equation 3 is applicable. Since the total moles of minor component, nl, is constant and n{ = n2 n4, equation 4 follows from equation 3.
+
(4)
Solving for n2 equation 5 is obtained
The instantaneous concentration of minor component in the liquid phase is given by equation 6.
where nl/no = X:, and y is the fraction melted a t the corresponding equilibrium temperature T,. This form is then substituted in equation 2 with a rearrangement of terms to yield equation 7, the form of the melting point equation suitable for plotting calorimetric data when solid solutions occur.
Equation 7 may be compared with equation 8, the ordinary equation used for plotting calorimetric data in the absence of solid solutions.
The K / ( 1 - K ) term in equation 7 corrects the upward curvature of the ordinary plot of T, vs. l / y and yields a straight line for the case, 0 < K < 1. For the determination of K , values of Tl.0o, T0.50, and To.25 are read off the ordinary curve a t reciprocal fractions melted of 1.00, 2.00 and 4.00, respectively. These values are then substituted in equation 9 (derived from equation 7 by solving for K a t the indicated values of T,).
after determining K , equation 7 is used to replot the data for better extrapolation and interpolation of values of T1.00, T0.50, and T0.26, and €or recalculation of K by equation 9. Equations 10 and 11 are then used for calculating To and Xz. To = Ti.no
+ (TLOO- TO.^) r + KE
(10)
This treatment was applied to data taken from a curve of equilibrium temperature vs. reciprocal fraction melted given by Aston and Fink5for a mixture of 95.47, 2,2-dimethylbutane and 4.67, 2,3dimethylbutane, known definitely to form solid solution^.^^^ The purity, estimated from the T, vs. (7) H . L. Fink, M. R. Cines, F. E. Frey and J. G. Aston, THISJOUR69, 1501 (1947). (8) J . W. Tooke and J. G. Aston, ibrd., 67, 2275 (1945).
NAL,
6201
l/y plot, calculated by Aston and Fink, was 99.78 mole yo,and To, estimated from this plot in the usual way, was about -104.85' instead of -98.86°.7 By applying the treatment outlined above, K was found to be 0.675, TOwas calculated as -98.86' and XB as 4.6 mole %, in excellent agreement with the theoretical values. As an independent check on this treatment, equation 7 was used to calculate the solidus temperature of this mixture by setting y = 0 and allowing K = 0.675, TO= -98.86' and X Z = 0.046 as calculated from our treatment of the melting data. The calculated solidus temperature was - 109.2' ; the observed value6 for this mixture was -109.4". Agreement to a few tenths of a degree for this calculation is good. NOTE ADDED I N PRooF.-The treatment outlined above is for one minor component. A general treatment for two or more minor components does not exist because of the uncertainty in the number of unknown parameters (distribution coefficients and concentrations), and the variability of their relative magnitudes. However, the probability of having more than one minor component in a calorimetric sample which has undergone extensive fractional distillations or crystallizations is relatively rare. Also, replotting the data as suggested above assures the absence of more than one minor component (with different distribution coefficients), when a straight line is obtained for T y versus 1/[K/(l K ) ] y over the entire range of the experiment. More than one minor component whose distribution coefficients are the same is, of course, allowable.
-
+
BARRETT DIVISION ALLIED CHEMICAL & DYE CORPORATION & DEVELOPMENT DEPARTMENT RESEARCH PENNSYLVANIA GLENOLDEN,
Deuterium Exchange between Trichloroethylene and Water. Infrared Spectral Data for Trichloroethylene-d BYTHOMAS J. HOUSER, RICHARD B. BERNSTEIN, RICHARD G. MIEKKAAND JOHN C. ANGUS RECEIVED AUGUST 30, 1955
Base-catalyzed deuterium exchange reactions between water and CC13H,1-3 C C I Z B ~ HCCIBr2H,4 ,~ CC1BrHZSand C2C13H6have been noted. The study3 of the CC13H-water exchange offers support for the halocarbanion mechanism; the base-catalyzed exchange of CC&D with CBr3H7 is a related example. The only datum reported6 in the trichloroethylene exchange is that some deuteration resulted when CZClaH was heated with Ca(OD)2in DzO. Measurements on the exchange rate of C2C13H with NaOD in D20 and on the reverse exchange of C&D with NaOH are reported here. Purified CzClaH (nz5D 1.4741) was refluxed with sodium deuteroxide (cu. 6 N NaOD) a t 81-84'. The phases were separated and the trichloroethylene weighed, washed, distilled and analyzed for deuY.Sakamoto, Bull. Chem. SOC.J a p a n , 11, 627 (1936). (2) T. 1%'. Newton and G. K. Rollefson, J . Chcm. Phys., 17, 718 (1949). (3) J. Hine, R. Peek and B. Oakes, THISJOURNAL, 76, 827 (1954). (4) R. H. Sherman and R. B. Bernstein, i b i d , , 73, 1376 (1951). (6) R. B. Bernstein, unpublished data. (6) L. C. Leitch and H. J. Bernstein, Can. J. Research, 28B, 35 (1)
(1950). ( 7 ) G. P. Semeluk and R. B. Bernstein, THISJOURNAL, 71, 4830 (1960).
VOl. 77
NOTES
6202
terium.8 The exchange was repeated with a new charge of NaOD using the same procedures; four exchanges resulted in the preparation of 91% C2C&D. The NaOD solutions were distilled to dryness; analysis of the recovered water for deuterium (by density) checked the values ( f1%) computed by material balance from the deuterium assay of the trichloroethylene samples. Assuming9 a classical equilibrium constant, the fraction exchanged could be calculated j
-
Pn
- Bn-1
an
Bn-1
-
where Pn = atom fraction D in the trichloroethylene after nth exchange; a, = atom fraction D in total reaction mixture (nth exchange). During refluxing, mild explosions occurred with increasing frequency; after several days, reflux was stopped and the trichloroethylene repurified (exchange equilibrium was never attained). The deOHcomposition reaction is probably: C2C1,H + C2C12 C1H2O. The rate of decomposition (based on weight loss of trichloroethylene and appearance of chloride ion in the aqueous phase), was 0.12%/hour. Table I summarizes the exchange data, which appear to be first order. The half-time for exchange was found to be 50 hr.; for the reverse exchange (C2C13D NaOH; smaller quantities were used under similar conditions) i t was 60 hr. During a typical run the alkali concentration (in the aqueous phase) diminished
+
+
+
+
TABLE I EXCHANGE OF TRICHLOROETHYLENE WITH NaOD Input Time trichloro- Input Ex- of ex- ethylD20 (g. atom change change m e no. (hr.) (moles) D)
1 2 3 4
96 48 72 96
1.12 0.91 .SO .71
1.36 2.27 2.27 2.27
(8) A Perkin-Elmer Model 21 Infrared Spectrophotometer (0.1 1 mm. cell) was used. A calibration curve for C K L H in CClr was prepared (3085 cm.-1 band). The absorbancy index was 0.021 per mole 70. The uncertainty in the analysis was *I% D. (9) Using frequencies for CtClaH and CzClaD as tabulated below, the equilibrium constant a t 350OK. was calculated; methods outlined by Urey, J. Chcm. SOC.,562 (1947); Bigeleisen a n d Mayer, J. Chcm. Phys., 15, 261 (1947). Results were sensitive t o the choice of frequencies for the isotopic water molecules. Using observed gaseous frequencies, K = 1.82; using liquid frequencies, K = 1.96. Since these calculations are considered unreliable in any case for liquid phase exchanges, the classical value ( K = 2) was assumed for the reaction CiCliH D10 F? CICI~D HOD.
+
+
a
TABLE I1 v (cm-:)
Assignment
v (cm.-1)
Assignment
C2CLH CzCLD 172" vg (a') 172" vg (a') 211" vl)(a") 213" v12 (a") 274" vg (a') 274" VB (a') 381" v7 (a') 381" v7 (a') 450" v11 (a") 427" V I I (a") 628" vg (a') 618" v6 (a') 780" v10 (a") 630" VIO (a") 802' ~3 - VI^ 840' v5 (a') ~ 9 7 vj~ (a') gosh 2L'll; v6 VB 856 2 ~ 1 1 930' VP (a') 8i3h v4 (a') 988 VIO f vi2 10136 v3 (a') 1015 v6 v: 1053* VIO f VII 1106 vj vg 1185 vs - ~7 1141 ~4 VIZ 1254* 2 ~ 1 0v;4 v7 122P VI0 VI1 1493 VP VI~I 1245~ v3 (a') 1563 vz (a') VP ~ 7 VY ; - ~8 1313 1586 2 ~ g (VKi f V I P )f V7 1366 1623 V3 f v6 v4 V I I ; V P - V ~ Z 1657 13i5 (v, f V I O ) v g 1565' 2~10 1666 ~4 VG 1748 2va 1587" v: (a') 1830 VZ v8 1676 2 ~ 6 2033 VI - VB ~4 vj 1758 1794 vz Jr V U 2177 v2 f v6 1857 2 V a ; V2 V3 2302d vi (a') (v4 v5) Vi2 1981 2387 (V? v6) Vi2 vz VI: 2040 2437 vz f V( 2091 vs f VG 2917 v1 f v6 2172 (vz ~ 1 2 ) ~7 2950 VI V I f va ( ? ) 2211 v2 f v6 3305 VI f ~3 2417 vz f VG 3821 VI VP 2469 2v3 3942 (VI Val 4- viii 2822 VP ~3 2950 (VZ f V I I ) vs 3085 VI (a') 3144 2 ~ 2 3718 v1 VS 3857 VI f V ~ O 3924 VI vs aRarn;rn data (ref. 12). bCS2 solution (1:20). CCClr Rechecked on Perkin-Elmer Model 12C solution ( 1 : 10). Spectrometer with LiF prism.
+ + + + + +
+
Fig. 1.
p
0.378 0.548 0.690 ,597 ,822 .493 ,792 .897 ,650 ,906 ,950 .722
SUMMARY OF IXFRARED SPECTRAL DATAA N D ASSIGNMENTS
+
+
+
+
+
+ + + + + +
~-
0.14 .13 .13 .13
DzO
from 6 to 3 N, so kinetic treatment was not warranted. Figure 1 shows the infrared spectrumlo of liquid Cd213D (91% D). The previous infrared" and RamanI2 studies did not report overtones or com-
+
-
Input Na (g. atom)
AND
+ +
+
+ +
+
+ +
(IO) Perkin-Elmer Model 21 Spectrophotometer (NaC1 optics, 0.05 mm. cell). (11) H. J. Bernstein, Can. J . Research, 28B, 132 (1950). (12) G . Allen and H. J. Bernstein, C o n J . C h i n . , 32, 1044 (1954).
NOTES
Dec. 5 , 1955 binations above 1250 ern.-'. The present data (summarized in Table 11) are in good agreement with ref. 11, except for the VI(&') fundamental for C2C13D. The present value is considered reliable to A 2 cm.-l and is identical with the Raman value.12 Acknowledgment.-The authors appreciate the financial support of the Atomic Energy Commission and the Michigan Memorial-Phoenix Project. DEPARTMENT OF CHEMISTRY UNIVERSITY OF MICHIGAN ANNARBOR,MICHIGAN
The Behavior of Uranyl and Neptunyl Ions with Dowex-50 Cation-exchange Resin'
6203
Then any of the standard techniques for the calculation of association constants can be e m p l ~ y e d . ~ This approach ignores the change in composition of the solution and the resin caused by the exchange reaction as well as assuming constancy of metal ion activities. At the metal ion concentrations used the loading of the resin is negligible. Thus the equilibrium constants are concentration ratios for solutions of the given composition. Included in Table I are the results of the distribution of uranyl ion between 0.955 M He104 and the resin as a function of time. Figure 1 graphically
TABLE I DISTRIBUTION COEFFICIENTS OF UOZ+2, NpOs+* BY J. C. SULLIVAN, DONALDCOHENAND J. C. HINDMAN NpOz+ BETWEEN D o w ~ x - 5 0A N D 1 M HCIOl AT 25O, JULY 5, 1955 RECEIVED
During the course of an investigation of the kinetics of an oxidation-reduction reaction in a mixed sulfuric acid-perchloric acid media i t became desirable to attempt to ascertain the degree of association between Np(V1) and bisulfate ion. The distribution of a metal ion between an aqueous phase and a solid phase composed of a synthetic cation exchanger has been demonstrated to yield quan titative data on the composition of complex ion systerns2 I n order to demonstrate that the method was indeed applicable under the conditions of this investigation it was deemed advisable to first determine the association constant for some system that had been previously studied by other means. Accordingly we have determined the complexity constants for uranyl sulfate, Experimental The ion exchanger used in this study was Analytical Grade AG 50-X12 processed from Dowex-50 by Bio Rad Laboratories. The hydrogen form of the resin was 200-400 mesh. In addition t o the intensive puriiication by the processor the resin was treated with molar perchloric acid followed by exhaustive water washes. The resin was then oven dried a t 80" for three hours. The U233 was purified by an ether extraction just prior to use. The NpZ3'was from a pure stock and the oxidation states prepared as previously d e ~ c r i b e d . ~ Known masses of the resin (usually about 0.2 8.) were introduced into 10-ml. erlenmeyer flasks. Measured volumes of solution containing the metal ions in concentrations of the order of magnitude 10-e10-6 molar were then introduced into the flasks which were then agitated in a constant temperature water-bath for timed intervals. After equilibration the phases were separated. Aliquots of the aqueous phase mounted on tantalum plates were assayed using a methane proportional a-counter.
Results and Discussion Defining the distribution coefficient in the absence of a complexing agent we have K = [MRl/[Ml
(1)
- u02
Time, min.
60 120 180 240
1.o
72.6 5 1 . 0 7 4 . 6 zk 0 . 1 7 4 . 3 =IC1 . 3 74.6 & 1 . 4
-
K NpOz
NpOz +z
+g
AND
p =
5 43 zt 0 . 0 4 8 . 6 5 zk .98 9 . 1 3 =t . l l 12.12 =t 1 . 0
5.40 i 1 . 3 8.61 0.50 9.72 f 1.15 14.03 zk .01
+
demonstrates the variation of the distribution coefficient as a function of bisulfate concentration a t constant ionic strength. The solid line is a theoretical curve with the values of the constants k1 and kz given in the defining equations below
Comparison with the previous values for the constants reported by other investigators5 indicates that the method yields the desired quantitative information.
I30
4
I20
."'I:/, 0 80
,
--.!__1-1_---~ ._ ----,.-l3
01
02
03
34
05
06
oa
07
09
1 0
1 1
82
1 3
1 4
, 5
~?
LCq
.tJS0iJ
Fig. 1.-Variation of the distribution coefficient of uranyl ion as a function of bisulfate ion a t 25.0" and p = 1.0.
where [MR]is the concentration of the metal in the resin phase per gram of air dried resin and [MI is the concentration of the metal ion in solution per ml. of solution a t equilibrium. Upon the introduction of a complexing agent ( I ) becomes
In an effort to extend the technique to a new system the distribution of Np02+2 between the perchloric acid and the resin was measured as a function of time. The data for this set of experiments are
(1) Work performed under the auspices of the U.S. Atomic Energy Commission. (2) See, for example, S. Fronaeus, Acta Chem. Scand., 6,859 (1951). (3) D.Cohen and J. C. Hindman, THISJOURNAL, 74, 4679 (1952).
(4) J. C. Sullivan and J. C. Hindman, ibid., 74, 6091 (1952). (5) R. A. Day, Jr., and R. M. Powers, ibid., 7 6 , 3895 (1954); S. Ahrland, Acta Chem. Scand., 6, 1151 (1951); R. H.Betts and R . K . Michels, J . Chcm. Sac., Supp. Issue #2,5286 (1949).
