LEONARD KHrzIS AXD ELSIEQULYAS
494
AS01243 values for reaction 4 were obtained from curve A. These values were combined with the AHo12d3 and ASOIZ~~ values for reaction 1 to obtain AHo12d3and ASo1243 values for reaction 6. The latter values are represented by curve B. The AH01243 and AS01243values for reactions 5 and 7 were obtained from curves C and D. The AC, values of Table IV were obtained from C, values estimated from values for similar halides given by Kelley,12 and the AH0298 and ASoaQ8values were calculated by assuming AC, t o be constant over the temperature raiige involved. TABLE 111
802
Obsd. total pressures,a atm. X 108
0.0175 IO88 .394 1.95 3.10 5.00
TABLE IV THERMODYNAMIC DATAFOR v.4PORlZATION REACTIONS Rh(s)
+ CL = RhCln(g)
AH'uta = +29.2 f 2.0
kcal./mole = +6.4 f 2.0 e.u. AC, = - 1.2 cal./mole "K. (estimated) AH02sg = +30.3 f 3.0 kcal./mole AS043s= +8.1 f 3.0 e.u.
AS01243
RhCls(s)
=
RhClz(g)
+ 1/2CIz
AH'im = +96.4 f 4.0
OBSERVED TOTALVAPOR PRESSURES RESOLVEDINTO INDIVIDUAL PARTIAL PRESSURES OF RhCh AND RhCls AT 1 ATM.CHLORINE PRESSURE Temp., OC.
Vol. 66
Resolved individual pressures, atm. X l o 3 PRhCIZb
PRhCl3
0.0004 .003 .018
0.0171 852 085 902 .376 956 .ll 1.84 1003 .25 2.85 1102 .57 4.43 7.8 1.20 6.6 1202 1301 11.4 2.3 9.1 1401 15 8 3.9 11.9 1504 21.3 6.5 14.8 5 Experimental vapor pressures, assuming one vapor molecule per rhodium atom condensed. The 956" value is the average of three experimental values-1.90, 1.96, atm. The 1003, 1202, and 1401" values and 1.99 X are from individual experiments. A slight correction was required to bring these values to 1 atm. chlorine pressure. The remaining values mrere taken from Figs. 2 and 3 . b From the RhClz curve of Fig. 4. CColumn 2 minus column 3.
kcal./mole = +60.5 =!= 4.0 e x . AC, = -5.7 cal./mole "K. (estimated) AHozga = +101.8 f 5.0 kcal /mole ASozss= 4-68.6 f 5.0 e.u.
.
Rh(s)
+ 3/2cIz
=
RhCls(g)
+14.9 f 1.0 kcal. /mole AS'i243 = +0.2 =k 1.0 e.u. AC, = - 1.1 cal./mole 'K. (estimated) AH'29s = +16.0 f 2.0 kcal./mole = +1.8 =k 2.0 e a .
AHOma
RhCla(s) = RhCla(g)
AHom, = f79.5 f 2.0 kcal. /mole ASnIz4~= +51.9 f 2.0 e.u. AC, = -5.6 cal./niolc OK. (estimated) AH02m = +84.7 f 3.0 kcaI./mole AXOpss = +59.8 f 3.0e.u.
-67.2 f 2.0 kcal./mole and AX01243 = -54.0 f 2.0 e.u. obtained from the dissociation pressure measurements. Combining ASo2g8 values for reactions 4 and 5 with standard entropies Xo298Rh(s) = 7.53 f 0.05 e.n. and So298C1, = 53.29 f 0.01 e.u. given by Kelley and King19we obtain SO298 RhClz(g) = 68.9 f 4.0 e.u. and SO298 RhC13(g) = 89.3 f 4.0 e.u. These values may be compared, respectively, with the estimated values of 79.4 and 83.1 e.u. calculated from an empirical equation given by Kubaschemki and Evans.8 They also may be compared with the following experimental values for analogous gaseous species: SO298 CrClz(g) = 76.0 e.u. and 8'298 CrC13(g) = 86.1 e.u. (found by DoerneP), and SOggr RuC13(g) = 95.1 e.11. (found by Bell, Garrison, and SIerter~'~). By combining the AH0m3and ASOIZGvalues for Acknowledgments.-The authors are indebted to reaction 5 with the respective AH01243 and AX0m3 R E. Inyard for performing part of the experinienvalues for reaction 7, we obtain AH0j243 = -64.6 tal work and to J. &I. Dixon for performing the f 3 kcal./mole and ASo1243= -51.7 f 3.0 e.u. for X-ray analyses. reaction 1. These values agree, within the un(13) H A. Doerner, U. S. Bur. hlines Tech. Paper 577, 1937. certainty of the data, with the values AHOW = (14) W, E. Bell, M. C . Garrison, and C. Merten, J . Phys. Chem., 65, 517 (1961).
(12) K. K. Kelley, U. S. Bur. Mines Bull. 584, 1960.
EFFECTS OF ELECTROLYTES ON ROTATORY DISPERSION OF AQUEOUS TARTRATE SOLUTIONS' B Y LEONARD I. KATZIK$ S D
ELSIE
GULYAS
The Chemistry Dzoision, Argonne Sational Laboratory, Argonne, Illinois Recezved September 27. 1961
Rotatory dispersion data over the range 6500-2650 8., for aqueous tartaric acid systems containing HC1 and chlorides of sodium, lithium, calcium, praseodymium, or thorium, and for alkaline tartrate, are fitted to a two-term Drude equation. The wave length parameters obtained are found t o be in fair agreement with the absorption spectra. The data are compatible with the hypothesis of direct interaction between the cations and the OH groups of the un-ionized tartaric acid.
One of the facts that continually has to be kept in mind in working with solutions of salts in water is that the ions formed interact with the water. (1) Based on work performed under the auspices of the U. S. Atomic Eneray Commission, Presented in part a t Smnrioan Chemical Society National Meeting, Chicago, September 3-8, 1961.
The type of interaction of most significance with regard to magnitude of energy effects, and influence on chemical behavior, is that of cations with the non-bonding electrons of the water OH groups. Such interaction may give a "ordinate bond Of varying degrees of strength. This mode is, in
March, 1962
ROTATORY DISPERSION OF AQKEOUS TARTRATE SOLCTIONS
495
.
aqueous medium, often the dominant one. Fre- procedures, a generalized least-squares program due to Dr James E. Monahan of this Laboratory was used. This inquently one deals with a donor which is not water volves refinement of preliminary guesses of the values of the but in which the electron-donating groups likewise parameters. The nature of the equation is such that the may be OH groups. It is most useful, therefore, usual least squares approach, in which preliminary values of if one can follow the effects of the cation on specific the parameters need not be specified, is not practical. Six significant figures in the parameters give the calculated hydroxyl groups, unperturbed by the over 55 moles rotation to about, 0.01" for most of the spectrtll range, but per liter of aqueous hydroxyls which are not in- at the shortest wave lengths one more significant figure may be needed. The parameters therefore are given to volved in the interaction. The device used in the work to be reported here 7 figures. As the dispersion curve is a smooth one, with a single is to label the hydroxyl groups of interest with broad maximum, more than one set of values of the paoptical activity. That is, use is made of hydroxylic rameters might be expected to reproduce the same calculated optically-active materials, in which the hydroxyl rotations to the second decimal place. We therefore inust group is attached to an asymmetric center. A analyze the computations more closely to appraise the of the particular parameters which result. cation influencing this hydroxyl group might be significance The two-term Drude equation in the form appropriate to expected to perturb the optical rotation of the sub- the tartrate specific rotation stance as a whole. Scattered prior observations [a] A/(X' - B ) - C/(Xz - D ) (1) of the effects of cationic complexing on the optical can be written in the equivalent form rotatioii of active substances support the feasibility of the approach. We ourselves have made similar [a]= ( ( A - C)X' - ( A D - BC))/(X4 (B+ D)X2 f BD) (2) studies.2 There is also a n older literature dealing with salt, effects on specific rotatory materials, as has been noted also by Lowry and Cutter.6 It is seen that, such as tartrate, which is too voluminous to cite. the direct parameters are now the complex ones, ( A - C), ( A D - BC), ( B -tD ) and B D . One may make the further There is, indeed, no logical restriction to hydroxylic substitutions, B = L -- A, D = L + A (i.e., 2L = (B+D)), reagents: the method can be extended to amino arid rearrange (2) to the form compounds, or to any substance containing donor [ a ] = [l/Xz((l - L/X2)' - (A/X')')][(A - C ) atoms. ( A - C)L/X2 - ( A C)A/Xz] ( 3 ) To be inaximally useful, such studies must relate As can be seen from the e q ~ a t i o n ,at ~ very long wave in some reasonable, quantitative way to concepts lengths the relation reduces essentially to ( A - C)/hZ, and quantities of theoretical significance. I n our Biot's relation, and the parameter ( A - C) therefore should ease, this linkage is furnished through the optical be obtainable readily with good precision. Let us now rotatory dispersion, and the Drude relation.3-5 assume that L>>A, as will be seen to fit the tartrate situaAs one moves to somewhat shorter wave lengths, This relation gives the optical rotatioii of a sub- tion. the ,parameter L should become determinable with fair stance as the sum of a series of terms precision. The parameter ( ( A - C ) L + (A+C)A) may 1
+
RA = Z In/(X2
- An2)
The constants An in the denominators, with the dimensions of wave length, refer to energy level differences in the molecule and, therefore, to part of its absorption spectrum. Not all absorption peaks are optically actire, and maximal optical activity inay be associated with a rather weak absorption peak. I n the form given, the equation is valid at a distance from an optically active absorption peak. The region of the peak itself constitutes a siiigular point in the mathematical description. In this paper we shall shos17 that a two-term Drude eqiiation is adequate to describe the results of a precise determination of the rotatory dispersion of tartrate ion and of undissociated tartaric acid in various chloride salt solutions. The wave length range is 650-265 my. As 4 parameters are required, two for each Drude term, maximum precision ,and widest possible spectral range (without intruding into the region of the absorption band) are required to yield significant values of the parameters. I n the case of the tartaric acid system above, agreement is found with the absorption spectrum. Experimental Computations.-The experimental data were fitted to a two-term Drude equation, containing 4 parameters, with the aid of the I B N 704 computer. After trials of numerous (2) L. I. Kiltzin and E. Gulyas, J . Phys Chem., 64, 1347 (1960). (3) I-'. Drude, Gottinge? Sachrzchten (1892). (4) E. U. Condon. Re$. M o d . Phys., 9 , 432 (1937). (5) I \'. Moffitt and A. Mosoowitz, J . Chem.. Phys., 30, 648 (1959).
be obtained with comparable ease, depending on the exact numerical relations for the given system. The parameter A will require a further extension toward the shorter wave length region, and rather more precise data, to be obtained with reliability. This means that the absolute magnitudes of the Drude parameters A and C will be even less reliable: they are obtained from the compound parameter above after first subtracting the product ( A - C ) L , with its precision probably limited by that of L, and then dividing the residual by the less precise factor A. The (A+C)A value may be expected to be much more accurately determined than any of its components. These considerations will be illustrated in the following. Dispersion data were obtained in the standard way for an alkaline (pH 7 ) solution of commercial sodium tartrate, not specially purified. I n alkaline solution, the rotation is still highly positive even a t 265 mp; acid solutions show large negative rotation at this wave length. Tmro different computations with the same data gave the respective equations [ a ] = 651.9583/(h2 -- 0.03921965) - 637.2467/ (A* - 0.03979033), and [ a ] = 395.4362/(h2 -- 0.03902518) - 381.6248/ (Az 0,03997448) The rotations computed from the two equations for each of the 58 experimental wave lengths differ from each other by more than 0.01" only for the extreme point a t 265 mp. The differences in A and in C between the two equations are obvious, and the respective A values are 0.000285 and 0.000473, yet the (A-l-C)A values are 0.3676 and 0.3677, respectively. This agreement is fortuitously close, as the L values differ by 1 part per 1000, but the principle is illustrated. It also should be pointed out that even a-ith this large perrentage uncertainty in A, the difference between the B values for theJwo equations amounts to that between 1980.4 and 1975.6 A . for thep,bsorption peak, and for D , betwen 1994.7 and 1999.4 A. In general the computer
-
(6) T BI. Lowry and J. 0. Cutter, J. Chem. Soc., 127, 604 (1925). (7) Bnalogoos relations, in increasing numbers of parameters, can be obbained with more than two Drude ternis.
LEONARD KATZIN AXD ELSIEGULYAS
496
would throw up parameters differing in this way only when one or two very bad points would give a local minimum in the least squares sums. When this occurred, the rotations computed by the two equations would not agree as well as in the case used for illustration, and choice between them could readily be made by observing the error distribution pattern. One of the two generally had a non-Gaussian error distribution, all points in essence being equally poorly fitted, to compensate for improved fit at the one or two very bad points. il'e are indebted to Dr. Gordon Goodman for stimulating discussions on some of these points. Polarimetry .-The rotatory dispersion measurements were made with a Rudolph photoelectric spectropolarimeter, Model ZOOS, and a xenon compact arc lamp. The 100 mm. polarimeter tube was jacketed, and had quartz end plates. Temperature was controlled by circulating water at 25 i 0.1' through the jacket. Optical rotations were measured a t 10 mp interval3 in the wave length region 650 to 300 mp, and a t 5 mp intervals a t wave lengths below 300 mp. With PrC4 solutions, interference from absorption peaks a t some points in the visible necessitated variations in this program. At each wave length, a minimum of four instrument settings were read and averaged to give the rotation. The average deviation of the readings was 0.0020.003' in the wave length region 650-300 mp, and 0.0060.04' below 300 mp. A good over-all average in this latter region is about 3Z0.01'. For our tartaric acid solutions (0.2 iM) a measured 0.003' corresponds to 0.1" in [CY]. As a blank reading must be subtracted, the statistical expectation is about 3Z0.15 pH Measurement.-A Beckman Model G pH meter giving a precision of f0.02 p H unit was used to determine the pH values of the solutions. Purification of Materials.-The analyzed reagent grade of d-tartaric acid (2-5 p.p.m. iron) shows a small absorption peak a t about 265 mp. The acid mas purified twice by ether extraction of the solid by the Soxhlet procedure. The 2G5 mp absorption was no longer present in the repurified acid, and with it disappeared a marked irregularity in the rotatory dispersion below 300 mp. Sodium chloride was recrystallized by proloneed boiling of excess salt with G N HC1, to remove any Iron. The crystals were washed with ethyl alcohol and dried a t about 100'. An approximately 4 M solution of the purified salt showed no absorption at wave lengths greater than 215 mp. PrC&.zH,O obtained from Lindsay Light and Chemical Co. showed a small foreign absorption peak around 270 mp, in aqueous solution. A 1 M solution of the salt in 6 N HC1 was passed through a Dowex-1 anion exchange column. After the anion-exchange process was repeated, the eluate was reduced in volume to about one-half the original in a vacuum desiccator. A solution of the product crystals showed no ultraviolet absorption down to 235mp. A 2 M solution of ThC& in 3 N HC1 was twice passed through a Dowex-1 anion resin column. Crystals obtained by partial evaporation of the eluate were filtered off, washed with ether, and stored in a desiccator over sulfuric acid to dry. A broad absorption peak centering a t about 290 mp in the starting material was reduced to a small absorption at approximately 255 mp. Lithium chloride and calcium chloride dihydrate, analyzed reagent grade, were not further purified. We are indebted to Miss Gail Norman for technical assistance in the purifications. Preparation of Solutions.-All solutions contained 0.2000 mole per liter of d-tartaric acid (HPT). On the basis of previous data,* pH 0.3 was chosen as a suitable compromise between an acidity at which the ionization of HzT is less than O.1y0, and one in which the HCl concentration might be so high as to introduce complications. In general, solutions were made from a stock solution 0.4000 M in H,T by dissolving the salt to be tested in a small volume of 0.8 N HC1, adding the appropriate amount of the tartaric acid stock, and making up to volume with 0.8 Ar HCl. Highervalent salts (CaC12, PrC4, and ThCh) gave a slightly lower final pH, as noted in the data. I n some instances, the pH was altered deliberately through the addition of an appropriate amount of HCl. The alkaline tartrate solution was prepared by the addition of 10 ill NaOH to the H2T.
.
(8) L. I. Katzin and E. Culyas, J . Phys. Cham., 64, 1739 (1960).
~701.
66
Absorption spectra were obtained through 0.1-mm. path lengths with the Cary spectrophotometer.
Results The full data are given as two-term Drude equations, together with plots of the deviations of the experimental values of the rotation from the rotation calculated by the equation given (open circles). At several wave lengths, for orientation, the experimental rotation is written in. (Fig. 1-6). Many of the error plots show systematic drifts suggesting lack of optimum match of the equation with the data, owing to difficulties a t the short wave lengths. Since the data below 300 mp already were considered less reliable than the rest, the computation was repeated using only the data through 300 mp. Rotations were computed from the parameters so derived for the wave lengths below 300 mp. The deviation plots for these equations also are included in the figures as solid circles. The root mean square deviations for the 36 out of 40-43 original points retained were considerably improved, often by about a factor of 2, to a modal value of ca. *0.25'. (If one used only the data through 350 mp, the error function was *O.l0.2', verifying that the experimental precision in the measurements was about that stated earlier.) The compound parameters discussed above were taken from the Drude equation constants for the data through 300 mp, and are listed in Table I. The parameters having to do with peak wave lengths (L, L+A(&Q) and 2A(=XZ2 are essentially indistinguishable for the pH 0.29 HC1, and the solutions with 0.5 &I LiCl and 0.5 M XaC1. The two more dilute CaClz solutions, and the PrC4 solution, show essentially the same values for 2A, but the CaC12solutions show a consistent though small change in L, and the PrCI3 solution a larger change in this parameter. The two ThC14 solutions are consistent with each other, but show both L and 2A sharply altered from the standard pH 0.29 solution. The 1 M CaClZ parameters indicate some marked alteration in the solution, possibly formation of a complex between the cation and bitartrate ion. Alkaline tartrate ion, in addition to the marked shift of L to shorter wave lengths, has a smaller value for 28, though this parameter is larger than the corresponding one for the solutions containing thorium. The absorption spectrum of the aqueous tartaric acid a t pH 0.29 shoys a broad peak (width a t halfmaximum ea. 300 A.), wi$h extinction about 225 a t its maximum (ca. 2116 A.))set on the slope of a much more intense peak whose maximum lies below 1950 A. (Hereafter these will be designated P and S, respectively.) The spectrum is not changed significantly in the presence of 0.5 M LiC1, 0.5 &f NaCl, or 0.2 M CaClZ, though the first seems to give perhaps 3Oj, lower, and the last, 3% higher absorption a t the P maximum. The solution 1.0 ill in CaClz shows a definite shift of the S absorption to longer wave lengths, so that the P absorption becomes a shoulder on it, essentially flat from 2965 to 2110 B.,with the same height as the 2116 A. peak of the 0.2 M CaClz solution. The 6 N HC1 solution also shows a displacement of the S absorption to longer wave
ROTATORY DISPERSION OF AQUEOCS TARTRATE SOLUTIOSS
March, 1962
HIT-
0.2
1
CaC12,
-
821.2640
'
t10.0 t 5.0 0 A -0.04397951
A'-0.04295956
0.21
:
416.4696
A' -0.04260136
A'-0.04370431
I t 10.0 t 5.0 0 -5.0 -10.0
t 0.5 0 -0.5
-5.0 -10.0
-
468.3990
[.I
n
pH
497
d JI
0
I
HCI
H2T-SY
H2T- 0.51
i
[.I
d
3 4 6.6926
~2-0.0414060Y
&-
CoC12,
pH
I
:0.26'
416.4915
X L
c Y
t 10.0
t 5.0 0
t 0.5 0 -0.5
-5.0
-10.0
-
1
I
I
I
l
l
I
650 600 550 500 450 400 350 300 250 650 600 550 500 450 400 350 300 250 WAVELENGTH,
I
HpT-0.5
A'-
-0.5
4
c.3
:
r l
P
t10.0 t 5.0 0 5.0 - 10.0
-
A -0.04214337
H2T- 1.0
M
HpT- 0.5 400.5104
M
0.04407020
-
'499.9294
mp.
P
NaCI, pH 0.28
A' - 0 . 0 4 2 0 6 3 6 6
n
WAVELENGTH,
mp.
A -0.043431
CaC12,
pH
3
0.25
t0.5 0 d -0.5 0
57
H p T - 0.5
1
LICI,
PH
i
4
0.30
E I
t 10.0 t 5.0 0 5.0
lUI I'[
416 6700
'
413.1815
= A'-
Y X
PrCI3, pH
-
0.04119655
* 0.22
367.2120
A1-0.04237178
' 1
I
1
rn
a t0.5 0 -0.5
-xz351198
At-0.04226190 I
- 10.0
i n
-10.0 I
I
WAVELENGTH,
I
I
I
,
mp -
A
I
I
I
I
j50 600 550 500 450 400 350 300 r
HpT' 0.5' p?
1
p H 1: 0.23
ThC14, I
l
tiO.0
I 1
t 0.5
403.5635 )11-0.04260136
410.2062
'
a
J
A'-0.04220254
250
'WAVELENGTH, m p .
1
*
409.6836
a
tlO.O t 5.0
4'
0
d
- 5.0
J
I
l
I
I
l
Hel't WOH,
pH
l
l
I
:8.0
418.3800
-10.0
r-l
23
H2T-O.SM
I A I-
[a]
x P
pH:0.02
ThCI4,
-
421.1099
417.9597 A2-0.04402643
A1-0.04424622
I
0
t 10.0 t 5.0 0
- 5.0 ~
L. 650
I
I
600 550
I
,
500 450
- 1
400 350
WAVELENGTH,
mp.
300 25C
10.0
[.I
: -a%P.s!E-
A'-
0.03906400
650 600 5 5 0
-
500
417.2616
A'-
0.03961633
450 400
WAVELENGTH,
350 300
250
mp.
Fig. 1-6.-0.200 M tartaric acid in various aqueous solutions. Differences between experimental specific rotations and those calculated from two-term Drude equations: 0, equation parameters based on full data; e, equation parameters based on data from 650-300 mp only. Vertical numbers illustrate actual rotations, [a], a t wave length indicated. (Note change in error scale at 300 mp.)
498
Vol. 66
LEONARD KATZIPU' AKD ELSIEGULYAS TABLE I COMPARATIVE FUNCTIONS O F DRUDEEQUATION PARAMETERS FOR System
HCI, pH 0.29 6 M HC1 0 . 5 M LiC1, pH 0.30 . 5 M NaCl, pH 0.28 . 2 A f CaCls, pH 0.25 . 5 A4 CaC12, pH 0.25 1.O M CaC12, pH 0.25 0 . 5 M PrC13, p H 0.22 . 5 M ThCh, pH 0.23 .5 M ThCld, pH 0 02 NaOH, pH 8
ha
420.7252 421.2715 422.9479 420.3014 421.2641 420.2866 420.7703 400.5104 416.3732 421.1099 433.0330
II
+ I2
5.669 4.379 5.614 5.061 4.794 3.789 1.926 3.298 6.489 3.150 13.652
A2
+ D);A
THROUGH 300 mp
=
a.04408398
0.0434898 ,0420622 ,0434628 .0434770 ,0431923 ,0431585 .0441845 .0417851 .0446349 ,0445373 .0396317 '/2(€3
length, slightly less marked than for the 1.0 M CaCL A similar alteration is seen for the pH 0.02 solution containing 0.5 ill ThCl,, but accompanying it is a definite movement of the P absorption to shorter wave lengths. At pH 0.23 the P shift seems the same, but the S contribution a t ca. 2100 A. is more marked. I n spite of interference from the 2135 8. peak of Pr+3(cf. Stewart and Katog), which is of comparable intensity, the absorption above 2225-2250 8. is decreased from the standard, indicating a probable shift to shorter wave length in the P absorption. I n the alkaline tartrate, finally, although the S absorption completely obscures the P absorption to 2160 8.,from 2175 k. the absorption falls well below that expected for the P absorption, which would be consistent with a strong movement of the P absorption to shorter wave lengths.
TARTRATE D A T A
Lb
,04271845 ,04405376 .04407025 ,04378431 .04376052 .04474886 ,04237178 ,04491277 -04482643 ,04005734 '/21
B
ha2
- Xi2
0.001188 .001312 .001182 .001186 .001183 .001204 ,001129 .001173 ,000556 .000578 .0008513
- D 1.
Possible error in calibration of the instrumental rotation scale or wave length setting inaccuracies where the rotatioq may be changing by as much as 100-120° in 50 A. cannot explain the behavior. There is, as might be anticipated, some correlation with the statistical fit to the points above 3000 A. The pH 0.29 HC1, and the alkaline tartrate, for which the root mean square deviations in the 6500-3000 A. region most closely approach the experimental precision, deviate only Eome 3' or so from the experimental points at 2650 A. The two solutions indicated above as having large deviations show relatively large values of the root mean square deviation even above 3000 k., a n i the distribution of deviations in the 6500-3000 A region is non-Gaussian. The implication is strong that the factors involved are related to some (probably minor) species for which at least one more Drude term would be involved. The deviaDiscussion tion from the Drude relation due to the Cotton From the above it is seen that a two-term Drude effect region would seem to be much less significant, equation can fit the dat? quite well. With read- inasmuch as the alkaline tartrate for which the ings from 6500 to 3000 A. the differences between absorption wave length is more remote than for the experimental rotations and calculated approach acid solutions also shows the effect. the reproducibility of the oexperimental rotations. All the dispersion curves show positive rotation With data down to 2650 A. included, Drude con- a t the longest wave lengths, which passes through stants are modified somewhat, and the root mean a maximum as the wave length decreases. Below square deviation may double. Less homogeneity some wave length the rotation is negative. Alkaand reproducibility of the data are indicated. A line tartrate has a rotation maximum of 130.76' number of factors contribute to this: decreased at about 3050 k.,and the rotation is still +61.76' precision in the data, effects of minor impurities, at 2650 k. Thorium chloride a t pH 0.23 gives possible contributions of more than the two ab- the maximum tartrate rotation of 45.70' a t 3400 sorption peaks implied, and possible deviations A., and shows negative rotations below 2830 A. from the Drude relation itself as one gets nearer The more acid ThC1, solution shows a maximum to the absorption wave length, and into the rotation of 10.43' at 4500 k., the sign becomes inCotton effect region. verted below 3500 8.)and a t 2800 A. the rotation A significant datum is the difference bet\yeen the is -109'. Tartrate in HC1 at pH 0.29 has its rotations calculated for the 3000-2650 A. wave rotation maximum of 16.26' between 4600 and 47QO length region via the parameters deduced from the 8.,and turns negative between 3600 and 3700 A. data for the 6500-3000 8. span, and the experi- The rotation is -380.7' at 2700 8. The extreme mental rotations. In all cases, the computed ro- of the solutions seen is that 1.0 in CaC12, with tation is increasingly more negative in the shorter the maximum positivejotation of 1.60' a t 6400 k . , wave length region than is the corresponding ex- sign inversion a t 5400 A., and a rotation of -481.6' perimental value. This difference raqges from 2' or so for the pH 0.29 HC1 a t 2700 A. (rotation, at 2700 A. This rather marked difference in gross -380.70') t o 20' for the pH 0.23 ThC1, solution features, as indicated in the figures and in Table I, involves relatively small alterations in the Drude at 2650 A. (rotation, -77.14') and 26' a t 2700 parameters. k . for the 1 M CaC12solution (rotation, -481.60'). The most marked gross characteristic of the dispersion curres, the rapidity with which the rota(9) D. C. Stewart and D. I
