NOTES
2292
Vol. 72
phenylhydrazone) in 100 ml. of dry chloroform was brom- tained in 85% yield; m. p. 238-239", "'"X'~:; 388 mp, inated with 2.00 ml. of 1.02 N bromine in chloroform. e = 30,900. After two minutes water was added. The aqueous phase MAYOCLINIC contained 10.7 ml. of 0.10 N Br-. A second wash with THE ROCHESTER, MINN. RECEIVED SEPTEMBER 20, 1949 water after five minutes contained 0.3 ml. of 0.10 N Br-. The chloroform phase was filtered through a pad of anhydrous sodium sulfate; X ; e f o r m 364 mp; e 23,600. Methyl 3,11-Diketo-12(~~)-brorno-A~-cholenate-3-(2,4Cation Exchange Equilibria at Constant Ionic dinitrophenylhydrazone) .-Chloroform was removed unStrength der reduced pressure from a half of the solution. The residue was dissolved in 10 ml. of acetic acid and 5 ml. of BY STANLEY W. MAYER acetic anhydride under carbon dioxide. Red crystals which separated within five minutes were filtered after The theory of cation exchange equilibria has three hours. This material (276 mg., 84% yield; m. p. been developed to the stage a t which activity 237-239') was identical with a sample of the A4-hydrazone. Admixture with this sample did not depress the melting quotient relationships have been formulated. point; Xohloroform Unfortunately, serious uncertainty with regard , 387 mp; e 30,200. Chloroform was removed from the remaining half of the to the mixed electrolyte activity coefficients in solution and the residue was dissolved in 15 ml. of acetic the resin, as well as in the aqueous phase,2 has acid under carbon dioxide. Yellow crystals which separated after twelve minutes were filtered after three hours. negated attempts to develop simple formulations The material weighed 298 mg. and was a mixture of the for the equilibrium concentrations of the elecA4-hydrazone and its hydrobromide salt; X~~::'"'" 387 trolytes in both phases. Extensive investigations have shown that very mp; E;?*, 402. Eighty-three per cent. of the theoretical amount of hydrogen bromide was present in the aqueous frequentlyla in a mixture of electrolytes a t conphase after distribution of 71 mg. of the crystals between stant total ionic strength, the logarithm of the water and chloroform. From the organic phase, after displacement with acetic acid, red crystals (43 mg., m. p. activity coefficient of an electrolyte varies linearly 237-238') of the A4-hydrazone were separated. Admix- with its ionic strength, even when the solvent is a ture with a sample of this hydrazone did not depress its mixture of organic and inorganic molecules. melting point; X;&joform 387 mp; e 30,100. When the ions involved in an exchange are of This hydrobromide was also prepared from 264 mg. of the A4-hydrazone in 1.60 ml. of chloroform with 0.40 ml. equal charge, the total ionic strength remains constant. For such exchanges, the principle of of 2.08 N hydrobromic acid in acetic acid and 16 ml. of acetic acid. After fifteen minutes the yellow crystals linear variation has been empirically applied in were filtered under carbon dioxide and placed in a vacuum this note to develop a simple relationship for desiccator over sodium hydroxide. The wet crystals turn red if exposed to moisture. After drying, the yellow the equilibrium concentrations in both phases. The exchange between two ions of equal charge, crystals (140 mg.) became red when heated to 130' and melted a t 241-242" ; X$~:jor0"" 387 mp; 417. After n, can be written as distribution between chloroform and water, the aqueous M+" [P*] = [M+"] P" (1) phase contained 85% of the theoretical amount of hydrowhere the bracket signifies that the ion is in the gen bromide. Methyl 3 , l l -Diketo-4,12 ( 0 1 ) -dibromocholanate-3 (2,4- resin phase. Following the development of dmitrophenylhydrazone) .-Bromination of 2 millimoles Connick and Mayer2 of methyl 3,ll-diketo-l2(or) -bromocholanate3 (2,4-dinitrophenylhydrazone) was carried out as described. The chloroform was removed under reduced pressure t o 10 ml., and 120 ml. of absolute ether was added. Canary yellow crystals separated, and three further crops were obtained by concentration of the mother liquor and the addition of (3) ether. The total yield was 80%. An analytic sample was prepared by recrystallization of the first crop from chlorofom-ether. When heated, the yellow crystals became where K , is the concentration quotient m [M+n]'red and melted a t 134-137'; X$~E~rorm 364 mfi, e = mppn/mM+ =am[ p n 1. 24,500. Calcd. for CslHt007N4Br: C, 50.28; H, 5.45; log K m = log K (a 1) (log Y*, log Y*[Zl - log Br, 21.59. Found: c, 50.07; H, 5.57; Br, 21.64; [a]D -169 =I 2' (29.6 mg. in 3 ml. CHCla). Y*;I1] 1% Y*Z) (4) With another sample [ a ] -181 ~ =t 2' (31.5 mg. in 3 ml. CHCla). After four hours and forty-fiv: minutes this where electrolyte 1 is MX,, electrolyte 2 is PXn. solution had become red, [ a ] ~-113 . * 2 This indiFor those electrolytes which follow the law of cates loss of hydrogen bromide in the chloroform solution. linear variation a t constant total ionic strength The crystals of the 4-bromohydrazone were converted (employing the notation of Harned and Owen,3 into the A4-hydrazone in two ways. A . The bromohydrazone (148 mg.) was dissolved in 20 ml. of acetic acid p. 459) a t room temperature in an atmosphere of carbon dioxide. (5) log Y i l = log Y(o)l all PI The yellow hydrobromide of the A4-hydrazone separated after ninety minutes. The hydrogen bromide was relog Y q z ] = log Y[nl(o) - %I] 4 1 1 (6) moved by solution of the crystals in acetic acid and chloro(7) --log 7*[1] = -1% 7(0)[11 "1121 %I form and concentration of the solvents under reduced -log Y*z = -1% Y2(o) 0121 PI pressure. The red A4-hydrazone separated in 80% yield; (8) m. p. 238-239'; X;:Efoform 387 mp; E = 29,400. B. (1) Boyd, Schubert and Adamson, THISJOURNAL, 69, 2836 One hundred ten milligrams of bromohydrazone was dissolved in 5 ml. of acetic anhydride and 10 ml. of acetic (1947). (2) Connick and Mayer, ibid., to be published. acid at room temperature in an atmosphere of carbon di(3) Harned and Owen, "The Physical Chemistry of Electrolytic oxide. After three hours the solution was concentrated under reduced pressure and the red A4-hydrazone was ob- Solutions," Reinbold Publ. Corp., New York, N. Y.,1943, p. 454 E.
+
+
+ +
+
-
.
+
-
+
NOTES
May, 1950 Noting that the first term of each of the right hand members of equations (5)-(8) is constant
+ +
log K , = log K (E 1)kl (n 1)(Ly[21] 'y[12])P[1] (a
+
+
+ + 1 ) ( q 2+ a*,)!+
(9)
The a's of equation (9) are constant a t any given total ionic strength. Combining the constants of equation (9) log K , = k?
+ k a ~ ~ +i l
k4P1
(10)
2293
containing p1 and [PI] become negligible. Accordingly, log K , must be constant in the range below m cerous perchlorate. CHEMISTRY DIVISION NAVAL RADIOLOGICAL DEFENSELABORATORY MARCH14, 1949 SANFRANCISCO, CALIFORNIARECEIVED
Precise Measurement of Polarographic HalfWave Potentials
Noting that the ionic strength of an electrolyte is proportional to its molality
+ k,m[,] + k p ,
BY LOUISMEITES
The recent polarographic literature contains many examples of half-wave potential measureThe concentration of electrolyte 1 in the resin ments apparently accurate to * 5 'mv. or better. phase is proportional to the quantity that has been Because of the increasing interest in refined polaroabsorbed from the solution. Or graphic measurements, a method has been developed which yields values with a probable error of mt1] = W(m! - m l ) / R = W m z / R (12) about f 0 . 2 mv. where m! is the concentration of electrolyte 1 The residual current is measured a t 10-mv. inin the aqueous phase before equilibration; W = tervals over a range including the previously degrams of water involved in the equilibration; R = termined approximate value of the half-wave pograms of resin involved in the equilibration. tential in question, and also a t several points corConsequently responding to the plateau of the wave. The reducible material is added and its diffusion current log K , = k 2 + kSWmP/Rf ksml (13) secured from the average of several measurements Equation (13) can be tested by using the data on the plateau. The applied potential is then adof Boyd, Schubert and Adamson' (Table IV) justed so that the measured diffusion current is for sodium-hydrogen equilibrations a t constant roughly half that on the plateau, and the current total ionic strength. It was found that the is measured a t 1-mv. intervals on either side of this equation potential. After correction for the (interpolated) log K , = 0.413 - O.llOWmat/R (14) residual current a t this potential, the half-wave fits the data for samples 7-9 within an average potential (including, of course, the I R drop in the deviation of 0.3%. The data for samples 1-5 cell circuit) is most easily found by a short linear show an average deviation of 1.3% from the interpolation. The application of the method is illustrated by equation the data on the tetrammino-cadmium(I1) comlog K , = 0.137 + 0 . 1 1 4 W m ~ , + / R (15) plex given in Table I. The ammonia solution was If sample 4 were omitted from consideration, the standardized against recrystallized sodium tetraaverage deviation would be 0.2Oj,. (The average borate decahydrate v i a perchloric acid. Volumetdeviation obtained by Boyd, et aL,l without equipment was calibrated by standard methmaking the complete correction for mixed elec- ric ods. Polarographic measurements were made with trolyte activity coefficients, was 4.4%.) I t is known that (a12 a21) for sodium chloride TABLE I and hydrochloric acid mixtures is mall.^ When HALF-WAVEPOTESTIALOF CADMIUMIN 0.812 F AMthe concentrations of sodium chloride and hydroM O N I A - ~ . ~F ~POTASSIUM NITRATE chloric acid are not high, the product (a12 The cadmium concentration was 0.65 millimolar, Measazl)ml, does not vary sufficiently to cause sigurements were made a t 25.00 * 0.01' E d . e . US. nificant change in the calculated values of K,. S. C. E., Microamperes For that reason, equations (14) and (15) are volt ir i l + ir accurate, notwithstanding the omission of the ml -0.770 0.522 variable. - .775 2.458 The observation of Tompkins and Mayer4 - .776 2.546 2.020 that K , is constant for exchange between < low4 - ,777 (0'526) 2.641 2.115 m cerous ion and 0.5 M ammonium ion can be - .778 2,727 explained on the basis of the considerations in this - .780 ,528 note. The concentration of cerous ion varied .950 .653 4.738 4.085} 4,086 m; however, through the range of 10-lo m to -1.000 .688 4.776 4.088 the total ionic strength of the solution did not - 2'020) 2.020 (0.001) = -0.7762 v. vary significantly. Accordingly, equation (9) E:/2 = -0.776 can be applied, with Ce(C104)3as electrolyte 1. idR = -0.7762 (2.034 X 10-6)(210) Because FI and [PI] are very small, the terms El/, = E ; / 2 2 log Km = k,
(11)
+
+
(i:;::
+
(4) Tompkins and Mayer, THISJOURNAL, 89, 2859 (1947).
+
= -0.7758 V.
