SCsTCHARD RICHARD M. RUSHAND GEORGE
2240
However, the band at 1426 cm. -l is accompanied by another at 1388 cm.-'. These are similar to those which were assigned to the asymmetric and symmetric CHs deformations in the spectra of the cobalt and nickel complexes. Consequently, any other assignments would be very difficult to justify. The next band, at 1331 cm. -l has been listed as a C-N stretching frequency on the basis of its similarity to the corresponding band in the cobalt(I1) and nickel(I1) complexes. However, in the case of the iron(I1) complex, two distinct features are observed. The band is from 25-30 cm.-' higher than that found in either the cobalt(I1) or nickel(I1) complex. In addition, the band in the iron(I1) complex is of greater intensity, being the most intense in the spectrum. If, as has been suggested p r e v i ~ u s l y the , ~ structure involving double bonds with the iron(I1) ion (structure V) represents the predominate form of the iron(I1) methine type of complexes, the double bond character of the C==N function would be greatly reduced. In the extreme case, the chelate ring would form a
Vol. 65
completely conjugated five-membered ring with many of the characteristics of an aromatic ring. This is in agreement with the profound changes in the spectrum of the iron(I1) complex, as compared to those of cobalt(I1) and nickel(I1). The remainder of the bands in the spectra of the iron(II), cobalt(I1) and nickel(I1) complexes of biacetyl-bis-methylimine have not been assigned. However, it should be pointed out that the striking difference in the spectrum of the iron(I1) complex in the region 957-650 cm.-' also can be interpreted as indicative of radical changes taking place in the ligand. The vanishing or extreme alteration of the group frequencies expected for the ligand biacetyl-bis-methylimine upon coordination with iron(I1) provides a direct demonstration of the strong coupling between the n-electron system of the ligand and the t2gset of d-orbitals of the iron(I1) atom. This contention is supported by the appearance of strong absorptions assignable to the C=N groups in the spectra of the corresponding cobalt(I1) and nickel(I1) complexes.
MOLAL VOLUMES AND REFRACTIVE ISDEX INCREMENTS OF BaCI2-HCI SOLUTIONS. MIXTURE RULES1 BY
RICHARD M. RUSHA N D GEORGE SChTCHARD'
Chemistry Div., Oak Ridge National Lab., Oak Ridge, Tenn. Received J u l y 31 1961 ~
An equation for the apparent molal volumes of mixed electrolyte solutions in terms of the apparent molal volumes of the single electrolytes is derived from the excess free energy relationshi of Scatchard. This equation represents adequately the specific volumes of solutions containing both the 1-1electrolyte H81 and the 2-1 electrolyte BaC12. An equation which correlates empirically the solute refractive index increments also is given.
Young and Smith3 express the apparent molal volume and apparent molal enthalpy in a solution of two salts by an equation which in our symbols becomes @ = @AZA
+
*BZB
+ ~ABZAZBI (1)
additivity, B(OS1),which gives Harned's rule. For different valence types, however, B(Op1)leads to the equation @ = QAZA
+
@BZB
+
+m
~AB@~')ZAZB(VZA
~ (3) )
in which m.4 and mp, are the molalities of the two salts. The difference is not great, for the important thing is that the three apparent molal quantities are measured a t the same ionic strength. As part of an investigation of the behavior of three-component mixtures in the ultracentrifuge, the densities and refractive index increments of a @ = (v - nOvO)/(nA nB) (2) number of aqueous solutions containing hydroif V is the volume of the syst.em, Vo the molal chloric acid and barium chloride have been measvolume of the solvent, and no,n A and n B are t,he ured. The specific volumes u = l/d, are cornumbers of moles of solvent and solutes. For the related by equation 3 and the refractive index increpartial molal enthalpy, V and V oare replaced by ments, Anlc,by equation 4 the corresponding enthalpies H and Ho. An/c = (An/CA)' Z A $- ( h / C B ) O Z B f K 4 B Z A Z B C (4) For t,he solutions of 1-1 electrolytes to which CB) is the sum of the molar they applied it, equation 1 is identical with that in which c = (c.4 yielded by t'he equation for the free energy of mixed concentrations of the salts and (4n,lcA4)0and ( A n / salt solutions4 with only the first deviation from CB)O are the values of An/c for the two component systems a t the same c. (1) Work performed for the U. S. Atomic Energy Commission a t the Oak Ridge National Laboratory, operated by the Union Carbide Experimental Corporation, Oak Ridge, Tennessee.
in which XA and XB are t'he mole fractions of the solute components, nA/(nA n B > and ~ B / ( % A n ~ )and , +A and CPB are the apparent molal volumes (or enthalpies) in the two-component solutions a t the same ionic st'rength, I . For the apparent molal volume
+
+
+
+
(2) Department of Chemistry, Massachusetts Institute of Technology, Camhridgr, hlassachusetts; Consultant. Ctieroistry Division, Oak Ridge National Laboratory. (3) T. F. Young and h l . B. Smith, J. Phys. C h e n . . 58, 716 (195t). (4) G. Ecatclinrd, J . Ani. Chem. Soc.. 83,263fi (1961).
The solutions were prepared by weighing solid BaC12. 2H20, a stock solution of HC1 standardized by rn-eight titrations and water into a volumetric flask. The densities were measured at 25.0" with a 24-ml. pycnometer. The precision of these mpasutements is about 3
MOLALVOLUMES AND REFRACTIVE INDEXINCREMENTS OF BARIUM CHLORIDE
Dec., 1961
parts in lo5. There may, however, be a systematic error of 0.2% in the concentrations. The refractive indices were measured a t 25' with a BricePhoenix differential refractometer using light of 436, 546 and 589 mp wave length. The mixtures were measured vs. various HCl solutions to keep the measured refractive index difference within the range of the instrument. The HC1 solutions were measured stepwise vs. each other and water so that the refractive index of the mixtures v8. water, An, could be obtained directly. The refractometer was calibrated with KCl solutions from the data of Kruis.5 The precision of the measurement of An/c is about 1 part in los.
Molal Volumes.-To determine the volume of a ternary solution, we rearrange equation 13 of reference 4 to
a*
a
2241
df- 0.032751)~~ di+ 0.07841)y~
= (18.026 + 0.9181 f (8.109 1.0315
+
+ 0 . 1 0 ~ ~(14)~ ~ 1
= (18.026 + 0.9181 d f - 0.032751)~* + (24.328 + 3.0945 df + 0 . 2 3 5 3 1 ) ~ ~ + 0.30xAZB(mA +
VLB)
(15)
I t follows that the partial molal volumes are VHCI~= (18.026 + 1.3772 V? - 0.0655OZ)y~
+ (18.026 + 1.4338 dj + 0 . 1 4 5 7 1 ) ~ ~
(16)
V B ~ =C (24.328 ~ ~ + 4.4717 fl+ 0.43711)~~
+
+
+
(24.328 4.6418 dl 0 . 4 7 0 6 1 ) ~ ~ (17) Ge = RT[Aana* A B ~ B * B A B ( ~ ) ~ A * ~ B f *nB*) /(~A* Young and Smith3 obtained from the data of B A B ( ' ) ~ A * ~ B* (?ZB*)/(nA* ~A* nB*)'] (5) Wirths for HC1 the equation
+
+
+
+
in which nnA*= n ~ Z i v i ~ 2 , ~=/ 2I A ~ O Wand O , w o is 0.001 times the molecular weight of the solvent. Then ve =
-
ac+/ap
+
uAnA*
+
CLBTZB*
ba~(')na*fla*(na* -
nB*)/(nA*
%There aA = RTdA-i/dP, AB") etc. The ideal volume V'
=
+
Vono +
+ %B*)+ + nB*)' (6)
~AB(')~A*~B*/(~A*
VBnB =
VOnO
=
+
RT bBAB'"/~P, VA*nA*
+
vB*nB*
(VB* - Vono
+
+
+ + +fma*)* [(VA* + + (VB*+ + + (8)
+ ( n ~+*
%B*)
U.4)nA*
UA)~A
bAB("yAYB
in lyhich
+
aB)nB* bAB(')n.4*nB*/(nA* nB*) b.kB(')nA*nB*(nA* nB*)/(nA*
YA
+
~B)YB
bAB(')YAYB(YA
YB)]
is the ionic strength fraction of A , I J I . If we define a* analo-
na4*/(nA* n B * ) =
gously to a ip*
= (V
+
- Vono)/(n~* + n ~ *=) O ( ~ A
so a* = @A*YA =
*A*TJA
~B)/(%A*
+ (9)
%B*)
+ %*YB+ + (10) + + ( d ~ ~ ( ~ +. ' ) 1 + .. + (daB(',2)12 +. . .)YAYB(YA - YB) (11) ~AB("YAYB
~AB(')YAYB(YA
dAB(0s2)12
@B*~B
YB)
.)YAYB
in which the d A B ) s are independent of I . If we drop the terms in I 2 and higher powers of I , we may write @AZA
+
aBSB
$- (dAB(o'1)nAnB/1ZA*71B*)SASB(~A
+
mB)
(12)
which is identical with equation 3 if kAB(O,')
= dAB(Os')nA?lB/nA*nB*
(13)
=
18.052
+ 1.00096 di - 0.067361
(18)
TABLE I DEVIATIONS FROM MIXTURE RULES A refers to the observed minus the calculated value X 10-
-A(An/c)
Au X mHcl
(7)
and the total volume V = v' + v" = To' no f ( V A *
ip
and from the measurements of Palitzsch,' Kohner18
0.5070 1.5450 2.4033 3.5248 4.3586 4.9446 0 0 0 0 0 0.5119 0.3078 0.5172 0.7238 0.5162 1.5610 1.3561 1.5812 1,7910 1.5763 0.4180 1.0393 0.2098 0.8420 1.0589 0.4206 0.6343 1.2720 0.4222 1.0550
nlBdlz
10'
436ma
0 0 0 0 0 0 0.3037 0.6108 0.9249 1.2436 1.5792 0.4090 0.5116 0.5176 0.5166 0.6186 0.4184 0.5221 0.5271 0.5274 0.6315 1.0432 0.8379 1.2566 1.0534 1.0603 1.2611 1.2677 1,0607 1.3731 1.1691
0 - 1 0 2 0 0 0 - 2 2 1 - 1 1 3 3
8 10 0 4 - 1 - 1 - 3 2 1 9 1 - 6 - 2 - 1 -8 - 6 -4
5 -10 - 2 8 4
- 7 - 6 12 - 5 - 2 1 - 4 - 2 16 13 13 12 12 15 7 11 -23 - 8 -38 3 2 - 4 - 5 -10 1 -15
546 m p
3 - 4 - 1 3 3 - 4 2 - 6 5 2 - 3 24 14 27 20 17 14 16 9 - 7 1 8 7 - 24 - 9
- 13 - 3 16 34 - 15 33
-
589 ma
4 - 6 0 5 4 - 4 1 - 3 0 5 - 3 25 11 30 25 25 13 16 11 - 5 3 12 5 - 31 - 8 - 12 - 5 -18 48 -18 33
-
The extension to higher terms is so much simpler for a* than for that it is convenient to calculate a* in terms of ionic strengths from equation 10, Shibata and Holeman,g and Jones and Dolelo on then calculate 6,from equation 9. The extension to BaClz solutions we calculate more complicated solutions from equation 4 of referip = 24.08 + 3.36 d j+ 0.1251 (19) ence 4 is direct though complex. The application from Both equations for BaCL are very different to enthalpies differs from that to volumes only in replacing dG/bP by b(G/T)/b(1/ 5"). (6) H. E. Wirth. J . A m . Chem. Soc., 6 2 , 1128 (1940). (7) 9. Palitaach, Z. physik. Chem., A136 379 (1928). For the hydrochloric acid-barium chloride-water (8) H. Xohner. ibid., B1,427 (1928). system we obtain (9) Z. Shibats. and P. Holeman, ibid., B13,347 (1931). ( 5 ) A. Kruip, Z. physik. Chem., BS4, 13 (1936).
(10) G . Jones and M. Dole, J . A m . Chem. Soc., 52,2245 (1930)
2242
L. S. BARTELLAND D. CHURCHILL
that of Gucker,I1 copied by Harned and Owen,12 which is in error because Gucker interpreted the symbol C, in Geffcken’s review13 as moles per liter rather than equivalents per liter. The differences between the equations for the two-component systems determined from our measurements and those from the results of ot,her observers may be caused by systematic errors in our concentrations. For comparison with the three component systems, w have preferred to use our own results, measured over the same concentration range and under the same conditions. The deviations, Av, of the measured specific volumes from those calculated by equation 15 are shown in Table I. (11) F. T. Gucker, Chem. ZZeus., 13, 111 (1933). (121 H. S. Harned a n d B. B. Owen, “Physical Chemistry of Eleotrolytic Solutions,” Third Edition, Reinhold Publ. Carp., New York, N. Y., 1958, p. 361. (13) W.Geffcken, 2. p h y s t k . Chem.. AMs, 1 (1931).
Vol. 65
Refractive Index Increments.-The equations for the refractive index increments are
-
Anqae/c = (0.0090667 (0.0318274
+ +
0.0002273~ 0 . 0 0 0 0 1 5 8 ~ ~ ) ~ ~ 0.0017776~ 0.0002335~~)~~ 0.0002682~S~C( 2 0 ) Ansr6/c = (0.0086264 - 0.0001911C 0.0000112C2)2A (0.0309489 0.0018557~ 0 . 0 0 0 2 8 7 8 ~ ~ ) ~ ~ 0.000252~A~Bc( 2 1 ) anbs9/c = (0.0085450 - 0.0002054~ 0 . 0 0 0 0 1 3 5 ~ ~ ) ~ ~ (0.0307106 - 0.0018172~ 0 . 0 0 0 2 9 2 4 ~ ~ ) ~ ~ 0 . 0 0 0 2 2 ~ ~ A ~ B( 2c 2 )
+
+
-
-
+
+ + +
+
+ +
+
The deviations of the measured refractive index increments A(An/c), from those calculated by equations 20,21 and 22 are shown in Table I. Acknowledgment.-The authors express their appreciation to Drs. J. S. Johnson, I
