1704
ANALYTICAL CHEMISTRY
Growth is a function of the available precipitate surface and of the supersaturation-viz., dC/dt = k ( C , - C)"(C - Co)qthe surface exponent, u, represents, approximately, a complicated set of surface functions and is expected t o be a simple fraction. The supersaturation exponent indicates the size of the two dimensional growth nuclei ( 1 , 23). For q = 2, the dislocation theory of growth is also possible. A general chronometric integral (chronomal), derived by two independent methods on the basis of simultaneous nucleation and growth reactions, relates the experimental concentration to the constants and functions of those reactions. The chronoinal is limited to the induction period and the growth surge which terminates it. The curvature of the concentration-time curve a t the termination of the induction period is determined solely by the surface function of the growth reaction and is useful for determining this function. The effect of initial concentration on the length of the induction period is given by C,"t, = constant, in which x = mp
( 2 ) Bransom. S. H.. and Dunning. 1%'. J.. Discussions Faradau Sac.. 5 , 96 (1949). I
Bunn, C. W., and Emmett, H., Ibid., 5, 119 (1949). Christianson, J. A , Acta Chem. Scund., 8 , 909 (1954). Ibid., p. 1665. Davies, C. W., and Jones, --I.L.. Discussions Faraday
Davies, C. W., and Jones, h. L., Trans. Faraday Soc., 51, 812 (1985).
Davies, C. W., and Sancollas, G. H., Ibid., 51, 823 (1955). Duke, F. R., and Brown, L. lf,,J . Am. Chem. SOC.,76, 1443 (1954).
Dunning, W. J., Discussions Faraday SOC.,5 , 195 (1949) Fischer, R. B., and Rhinehammer, T. B., ANAL.CHEX.,25, 15.14 (1963).
Frank, F. C., Discussions Faraday Soc., 5 , 48 (1949). Frisch, H. L., and Collins, F. C., J . Chem. Phys., 21,2158 (1953). Johnson, R. A., and O'Rourke, J. D., J . Am. Chem. SOC., 76, 2124 (1954).
Kobayashi, K., J . Chem. Soc. J a p a n , 70, 125 (1949); Science Repts. TGhoku Unz'z'., 37, 125 (1953). LaMer, V. K., and Barnes, M. D., J . Colloid Sci., 1, 71 (1946). LaAler, V. K., and Dinegar, R . H., 6.Am. Chem. Soc., 73, 380
+
1
( 1 - m)p, rn being -. After the growth terms have been 2-u determined, the nucleation rate terms can be estimated from this relationship. The variation of particle count with initial supersaturation iq proportional t o the difference between the nucleation and growth order-i.e., ( p - q ) . Since p =p for barium sulfate the number of particles formed is independent of the initial concentration, lo9 particles per liter are formed if a n induction period precede8 nilpearance of precipitation.
(1951).
O'Rourke, J. D., Ph.D. thesis. Giiiversity of Illinois, Urbana, Ill,, 1953.
Rodebush, W H., Proc. .\-atl. &ad. Sci., U . S., 40, 739 (1954); Ind. Eng. Chem., 44, 1289 (19.52). Stranski, I. K., J . p h y s i k C'hevt. 1.. 155, 466 (1928) Turnbull, D., Acta N e t . , 1, 684 (1953). Turnbull, D., and Tonnegut. €3.. I n d . Eng. Chem., 44, 1292 (1952).
Volmer, AI., "KineLik der Phasenbildung," T. Steinkopf, Dresden and Leipzig, 1939. Zaiser, E. hl., and LalIer, V. K.. .J. C'olloid Sci., 3, 371 (1948).
LITERATURE CITED (1) Becker, 11 , and Doering, W , Ann. P h y s i k , 24, 719 (1935)
Soc.. 5,
103 (1949).
H E C E ~ for ~ Ereview D .kuanst 8, 105.5.
AccFPTED
Seutember 2 , 19%.
8th Annual Summer Symposium-Role of Reaction Rates
Slow Precipitation Processes Application of Precipitation from Homogeneous Solution to liquid-Solid Distribution Studies LOUIS GORDON Department
o f Chemistry,
Syracuse University, Syracuse
The direct addition of a precipitant to a solution results temporarily in a heterogeneity of conditions. In the vicinity where the precipitant has been introduced the formation of the solid phase takes place under conditions such that the solution concentrations vary between very wide limits. Therefore, results of coprecipitation studies obtained with conventional precipitation procedures may also vary markedly. Precipitation from homogeneous solution offers an ideal technique for controlling the rate and mode of addition of a precipitant. I t permits a slow precipitation process, which allows near equilibrium to be established between the surface of the solid and the solution. It is thereby possible to determine the nature and extent of coprecipitation. Applications of this technique are described in which Doerner-Hoskins' distribution coefficients have been obtained for systems containing barium-radium mixtures. Other coprecipitation studies are also described, particularly some which have revealed that the extent of coprecipitation is negligible except during the initial and final stages of the precipitation process.
IO, N. Y.
I
N 1937, Willard (45, 4 6 ) published the results of a n investiga-
tion illustrating the use of urea in a slow precipitation process. This study, in which the aluminum ion was slowly precipitated :is a basic salt, served as the stimulus for many subsequent papers describing applications of the technique now referred to as precipitation from homogeneous solution. The virtue of precipitation tiom homogeneous solution lies in the production of a very dense precipitate which minimizes coprecipitation. The principles of this technique and its merits have been reviewed in two papers ( Q ,38).
Either an anion or a cation can be generated homogeneously \+ithin a solution to serve as a precipitant. Urea (39, 41. 42. 14-46), hexamethylenetetiamine ( 2 5 ) , and acetamide (10, 38) have been used to release h v d r o u 1 ion. The sulfate ion can be produced from sulfamic acid ( 8 , 34) and either dimethyl ( 5 , 6) or diethyl sulfate ( 3 8 ) . Oxalate from dimethyl (11, 80, 4 1 ) or diethyl oxlate ( 1 , 4, 1 8 ) ; phosphate from metaphosphoric deid (43) or trimethyl or triethyl phosphate ( 4 0 ) ; carbonate from the trichloroacetate ion ( 3 0 ) : sulfide from thioacetamide ( 7 ) ; iodate from periodate (18); periodate from iodate ( 3 3 ) ; and chromate from dichromate ( I S ) are other examples. The generation of a cation in a solution may be effected b j one
1705
V O L U M E 2 7 , NO. 11, N O V E M B E R 1 9 5 5 or two methods. The cation may be released from a comples by removal of the ligand. This can be done either b y a change in pH, use of an oxidizing agent t.o destroy the complexing reagent, or by temperature. Ethylenediaminetetraacetic acid [(ethylenedinitri1o)tetraacetic acid] complexes have been thus utilized (f?, 24, 28). The silver-ammonia complex has been dissociated with hydrogen ion resulting frnm the slm- hydrolysis of an ester (143. By t,he other method, a wtioii niay be converted from one oxidation st,ate t o the desired oiie. Cerium(II1) iodate is soluble, whcwas cerium(1V) iodate is not. Thus, cerium(II1) may be oxitlizd in the presenccx of ioci:itci to produce ccrium(1V) i0dat.e (4Y 1. Precipitation from hoinog:t.neons solution has been used primaril?- in the development of improved gravimetric methods. Howel-c~,it has also been used as a method for the removal of a major caonstituent-e.g., iron ($4)from minor constituents-and in the wparation b y fractional precipitation of chemically similar pilirs such as zirconium-hafnium (40) and the rare earths (11, 17). Rerent studies ( 1 4 , 16,19. 26'. 3 2 ) have been concerned with the ixiture and extent of copreripitittion. Precipitation from homogr.neous solution provides :in rscellent tool n-ith n-hich to study coprecipitation. For example, a precipitation rate can tw slo\ved down, so t h a t it will rcquire 8 days to precipitate 150 nig. of silver chloride. Thus. :I I)i,ecipitation process can be e l aniintd :at various stages and a study made of the distribution of tructe materials in solid-liquid sJ-stems analogous t o those of liquid-liquid distribution investigationp. This paper describes the utilization of the technique, of precipitation from homogencous solution in such studies. The latter have been divided into tu-o sections. One considem coprecipitation due to isomorphous mixed crystal formation and t,lic other to adsorption. (:OPRECIPITATIOTi €%I-ISOXiORPHOI S I l I X E D CRYSTAL FORRI ATION
Barium-Radium. Systems c.onsist,ing of radium and barium salts have been studied extensively : :in excellent review may he found in the text by Wahl and Honner ( 3 6 ) . The results h a w iisually been interpreted in term? of two distribution laws. Consider a system in which h:irium is precipitated as the sul~ of a niinutc~cjiiantity of radium. Thus fate in t l i presence
Ba++ (aq.) + SO;-
(:~q,) = BaS04(s)
-
Since the mole fraction of bai iiiin. S n u . is virtually 1. and sinct. B : ~ - * ) ~ ~ , then: ~t~i.
- Y R cmentially ~ equals ( R R
I +
(3
Rr:irrangement, and substitntion of
(E+) =
er)rl,,.
7)
'
D for K,/K?, gives:
(-R a--.) f' soliltion
Lquation 4 is known as t l x homogeneous distribution la\\ The equation describes a s j stem in n hich, a t equilibrium, thv microcomponent is homogeneously distributed throughout thv host crystal. Obviously, it niay take considerable time for the system to reach this equilibriuni state. Doerncr and Hoskins (3)considered that a more realistic approach assumed t h a t only the crl-stal surface would be in equilibrium with the solution Thus. Equation 4 becomes
From this equation, Doerner and Hoskins obtained:
In
Rainitial = Rarinai ~
Bainitiiil
Baiinat
(6)
The subscripts in Equation 6 refer to initial and final solution concentrations. Equation 6 is known as the logarithmic (or heterogeneous) distribution law and prescribes a nonuniform distribution of the microcomponent within the host crj-stal. The amount of microcomponent increases or decreases logarit,hmically from the center of the crystal outward depending on whether the value of the distribution coefficient is less than or greater than unity. The det,erminat,ion of the distribution coefficient is difficult when a conventional precipitation process is employed. The addition of one solution t o another results temporarily in a hoterogeneous mixture in which the solution concentrations of the ions may vary over a very x-ide range. For example, the radium and barium in the vicinity of a drop of added precipitant may be depleted in such a manner that the radium-barium ratio of the right-hand member of Equation 5 could assume almost any instantaneous value. I n 1927, Henderson and Krarek ( 2 2 )studied the radium-barium chromate system and concluded t,hat the system obeyed the homogeneous distribution law. Their results XTere obtained by precipitation of barium chromate in the presence of radium by :t ronventional precipitation procedure. Salutsky, Stites, and Martin ( 3 2 ) in 1953 used the technique of precipitation from homogeneous solution to re-esamine the radium-barium chromate system and ronclude that t'he system obeyed the logarithmic distribution law. The values of X, which Salutsky obtained, were not constant'with "fraction of barium precipitatrd" as Equation 6 predicts. These investigators proposed, as a result of t,heir work and their own survey of st,udies by others. t h a t the l-dues of the distribution coefficient he extrapolated to zero per cent precipitated and that X be reported as a limiting distribution coefficient. The question arises as to why X should vary. Salutsky ascribed this to recrystallization; the conditions under which Equation 6 is obeyed n-ould, given sufficient time. revert to those under which Equation 6 would be obeyed. The radium-barium sulfate sJ-strnihas been studied by Doerner and Hoskins ( S ) , Marques ( 2 9 ) )and Gordon and Rowley ( I O , 16). Wherever conventional precipitation techniques were used, the values obtained for the logarithmic distribution coefficient have been somewhat erratic. However, where conditions conforming to or approaching precipitation from homogeneous solution Lvere employed, the results have indicated conformity to the logarithmic distribution law. \Then Doerner and Hoskins added sulfuric acid to "radiumbarium chloride solutions 'cvithout, regard to temperature or agitation." their values for X varied from 1.003 to 1.314. When "dilute sulfuric acid was added in vrr?- small portions to hot, agitated radium-barium chloridrl solution and the crystals were digested between each addition of arid" these authors obtained 1.568 to 1.686. K h e n these authors obtained mixed crystals by evaporation and cooling of :i sollition containing radium. barium, and sulfate, they obtained 1.713 to 1.893. Marques s l o ~ l yadded 0.01S sulfuric acid to radium-barium mixtures, a t 20" C.. and obtained values of X from 1.54 to 1.71 in the range of 5 to 96% barium precipitakd. By isothermal evaporation a t 20" C. of a dilut,e solution of the sulfates, she obtained 1.84 t o 2.01 in the range 67 t o 91% barium precipitated. Gordon and Rowley hJ-drolyzed snlfamic acid at, 90" C. to slowly precipitated barium sulfate in the presence of trace radium. In the range of 3 t o 96% of barium precipitated, X was virtually constant; the average value was 1.21. The calculated values of D varied continuously from 1.18 t o 1.92. Because the system obej-s the Doerner-Hoslcins equation. it s e e m reasonable to conrlude that the radium miis t he logarithmically distributed
ANALYTICAL CHEMISTRY
1706 within the carrier substance. Hom-ever, in a recent investigation by Jucker and Treadwell ( 2 6 ) in which sulfamic acid was also used to precipitate mixed crystals of barium and radium sulfates, i t was coiicluded on the basis of radio-autographs t h a t the radium is uniformly distributed. These conflicting views will have t o be eventually resolved. The distribution coefficient (cf. previous equations) is the ratio of the solubility products if t h e two compounds constituting the mixing crystal form a n ideal solid solution or nearly so. Thus, X is the ratio of the solubility products of barium sulfate and radium sulfate. A distribution experiment might then provide a potential means for determining the solubility of a trace substance since the experiment xould require only t h a t concentration of t,race ions required for radiochemical analysis. However, Hahn (21) has indicated t h a t a simple relationship betn-een solubility and distribution coefficient does not exist. Barium-Strontium. The barium-st,rontium sulfatc system has been studied b y Gordon, Reimer, and Burtt ( 1 6 ) . Barium and strontium were slon-ly precipitated with sulfate produced as a result of the hydrolysis of dimethyl sulfate ( 5 , 6). T h e system as studied in the range m-here 58 t o 95% of the barium was precipitated. The system apparently conforms t o the DoernerHoskins equation. Rare Earths. Weaver (36) precipitated pairs of rare earths with oxalate obtained by the hydrolysis of dimethyl oxalate. He concluded that these systems obeyed the homogeneous distribution law; the logarithmic distribution lam was apparently not considered. T h e conditions employed by Weaver in his investigation were those under which it might be expected t h a t the systems would have more closely obeyed the Iogarit,hmic distribution law. Weaver‘s conclusions have been discussed b y Callow ( 2 ) and by Salutsky and Gordon ( 3 1 ) . Hermann (23) investigated a system similar in many respects to those studied b y Weaver. Lanthanum was precipitated in t h e presence of actinium using dimethyl oxalate. The results indicated adherence t o t’he logarithmic dist’ributionlaw. COPRECIPITATION BY ADSORPTION
Basic Stannic Sulfate. Precipitation from homogeneous solution has been used to determine the extent and nature of the coprecipitation of nianganese(I1) Tyith basic stannic sulfate (19). T h e latter was precipitated by t,he urea method ( 4 2 ) . I n experiments in which the tin and manganese concentrations n-ere approximately lo-* and lO-3JI, respectively, the results indicated t h a t the coprecipitation of manganese occurs primarily in the initial and final stages of precipitation of the carrier. Relatively little occlusion, defined as adsorption followed by covering over ix-ith subsequent layers, occurs during the intermediate precipitation stages. T h e coprecipitation occurring during the initial stages of carrier formation is apparently linked v-ith the supersaturation effect existing during nucleation (27). T h a t this may be the case was demonstrated in other experiments in which pure preformed basic stannic sulfate n-as initially present. I n these experiments, coprecipit,ation did not occur in the initial stage b u t only in the final stages. I n t,he final stages of precipitation, when the solution has been virtually depleted of carrier ions, t h e precipitate behaves as a n adsorbent for manganous ions. However, during t,he intermedia t e stages of Precipitation, i t is much more selective in its choice of cations as may be expected from the Paneth-Fajans-Hahn rule ( 3 7 ) . By using a slower precipitation rate, accomplished b y lowering temperature which reduces the rate of urea hydrolysis, i t vas possible t o minimize considerably the supersaturation effect and consequently the initial extent of coprecipitation. When t h e manganous ion concentration was reduced t o 10-6JI (and finally t o 10-llM) somewhat similar coprecipitation phenomena were observed. The fraction of manganese coprecipi-
tated increased slightly, b u t definitely, during the intermediate precipitation stages. For example, the manganese coprecipitated amounted t o 1 and 5% respectively, at 20 and 70% of tin precipitat’ed. I n the described experiments in which the initial concentration of manganese \\-as l O - 3 M , this increase in occlusion m s not evident, because the fraction of manganese absorbed a t any stage was so very small in terms of the amount initially added. An import,ant considerat,ion is t h a t occlusion can be reduced t o a minimal effect. This is accomplished by utilizing the technique of precipitation from homogeneous solution in order t o prevent the depletion of carrier ions in any portion of the solution. Such depletion allows the precipitate to adsorb other ions in its vicinity. This can occur repeatedly in a conventional precipitation process upon each addition of precipitant. If, on the other hand the precipitant is generated under controlled conditions depletion of the carrier ions occurs only a t the conclusion of the precipitation process; t,hus, adsorption-i.e., occlusion-during t,he intermediate stages of precipitation is minimized. However, adsorption by t,he quantitatively precipitated carrier poses a difficult problem with n-hich to cope, Killard and Sheldon ( 4 4 ) have proposed a simple but unique solution t o this problem. They utilize a two-stage process in which they initially remove the carrier by filtrat,ion when about, 95% has been precipitated. They then continue the prccipitation process and finally remove the residual carrier. The twostage process never permits more than a small fraction of the carrier to coexist in solution in the presence of contaminant only. T h e results obtained b y Killard and Sheldon bear out the efficacy of the procedure. Ferric Periodate. Acetamide was hydrolyzed a t 80” C. in a slightly acid solution containing iron(II1) and periodate (10). -4s the p H increased, iron periodate slowly precipitated over time intervals comprising many hours. Coprecipitation studies, utilizing aluminum and yttrium as contaminants, have confirm? 1 the general conclusions reached in the described studies iyith basic stannic sulfate. Silver Chloride. Silver ions were slowly released, in the presence of chloride ions, from the silver-ammonia complex lvhich was dissociated with hydrogen ions generated b y the hydrolysis of P-hydroxyethyl acetate ( 1 4 ) . This process produced large crystals of silver chloride. Because the cation in t,liis case is de:ived from a complex ion and because its concentration is determined by the amount of chloride, the Concentration of free silver ion can actually increase during the precipitation process. This is in contrast to the radium-barium sulfate case-for example. \There the barium concentration is st,eadily decreased with the formation of barium sulfate. T h e investigation v i t h silver chloride as carrier utilized tballium(1) a t approximately 10-6M in the coprecipitat’ion study. T h e free silver ion concentration was smaller than this in many instances, although the total silver concentration was initially 10-2M. The initial concentration of chloride was varied from 0.01 to 1.00M. -4lthough thallium( I ) chloride does not mix isomorphously with silver chloride, the coprecipitation of thallium could have conceivab!y obeyed one of the t x o distribution laws. Cases of anomalous mixed crystal formation have been noted b y Hahn ( 2 1 ) n-ho refers to these as “isodimorphism.” I n the application of either Equation 4 or 5 t o the thalliumsilver system, account must, be taken of the fact t h a t i t is the silver ion which is involved. Thus, for esample, integration of Equation 5 results in a different equation ( 1 4 ) from Equation 6. The data did not fit either Equation 4 or 5, as modified, under the experimental conditions which were employed. Thus, the system under the conditions investigated is not a case of Hahn’s isodimorphism. The thallium-silver ratio in the crystal, under any given set of conditions, remained constant throughout the precipit’ation
V O L U M E 2 7 , NO. 1 1 N O V E M B E R 1 9 5 5
1’107
process; the mole ratio, thallium t o silver in the precipitate, was of the order of lo-’. So little of the initial thallium added was coprecipitated. about 1 p a i t per 1000. t h a t the solution concentration of thallium remained essentially unchanged during the precipitation process. Other experiments indicated t h a t the thallium-silver ratio in the crystal 17-as dependent on the solution concentration of thallium. Thus, the system was one in nhich
Flaschka, H., Chemist Analyst, 44, 2 (1955). Freund, H . , dissertation, University of Michigan, Ann Arbor, AIich., 1945. Gordon, L., h A L . CHEM., 24, 459 (1952). Gordon, L., “Annual Progress Report,” U. S. Atomic Energy Commission, NYO-3558 (1955). Gordon, L., Brandt, R. H., Quill, L. L., and Salutsky, 31. L., ANAL. C H E M . , 23, 1811 (1951). Gordon, L., and Caley, C. R., Ibid., 20, 560 (1948). Gordon, L.. and Firsching, F. H., Ibid., 26, 759 (1954). Gordon, L., Peterson, J. I., and Burtt, B. P.. Ibid., in press. Gordon, L., Reimer, C. C., and Burtt, B. P., Ibid., 26, 842
for a given initial concentration of thallium. .ipparently, what happens is t h a t each layer of silver chloride adsorbs essentially the same small amount of thallium from the solution 8-hich contains a n essentiallj- constant thallium concentration. Thus, a n apparent1)- homogcneous distribution results even though the data do not fit the homogeneous (or logarithmic) distribution lan-.
Gordon, L., and Rowley, K., unpublished research. Gcrdon, L., and Shavei, K. J., ANAL.CHEV.,25, 784 (1953). Gordon, L., and Stine, C. R., Ibid., 25, 1519 (1953). Gordon, L., Teicher, H . , and Burtt, B. P., Ibid., 26, 992 (1954). Gordon. L.. and Wrocxvnski. A. F.. Ibid.. 24. 896 (1952). Hahn, O., “Applied Rakochemistry,” Cornel1 University Press, Ithaca, S . Y., 1936. Henderson, L., and Kracek, F., J . Am. Chem. Soc., 49, 735
(1954).
I
Hermann, J. A, “Separation of Americium from Lanthanum by Fractional Oxalate Precipitation from Homogeneous Solution,” U. S. -4tomic Energy Commission, AECD-3637 (1953). Heyn, A. H. A., and Schupak, E., ANAL.Cmhr., 26,1243 (1954). Ismail, A. N., and Harwood, H. F., Analyst, 62, 185 (1939). Jucker, H., and Treadwell, W.D., Help. Chim. Acta, 37, 113
I n 1950 Willard (38) wrote as follon-s: “The n-ork on precipitation from homogeneous solution n-as begun at, this university (Michigan) over 20 years ago and is still continuing. The advantages of this method are beginning t o b e realized, as evidenced by t h e n.ork of other authors. There are many different ways of applying this principle. Some have been described and others are being investigated.” Today, five years later. precipitation from homogeneous solution is widely recognized as a n important technique 13-hich can be used t o develop new methods of analysis and t o improve existing ones. It can also b e used to increase the efficiency of separation methods xvliich utilize fractional precipitation. Some of its most useful applications are in coprecipitation studies n-here it can b e used nnder near equilibrium conditions t o determine t h e true nature and extent of coprecipitation. I n particular i t facilitates the measurements of distribution coefficients in heterogeneous systems in n-hich a solid carrier phase is precipitated.
(1954).
LalIer, Sr. K., and Dinegar, R. H., J . Am. Chem. Soc., 72, 4847 (1950).
RIacSevin, W.PI., and Dunton, 31. L., -4n-a~. CHEII.,26, 1246 (1954).
Marques, B. E., Compt. rend., 198, 1765 (1934). Quill, L. L., and Salutsky, 31. L., J . Am. Chem. Soc., 72, 3306 (1950).
Salutsky, 11. L., and Gordon, L., communication submitted t o ANAL.CHEM. Ibid., 25, 1677 Salutsky, 11.L., Stites, J. G., and Martin, A . W., (1953).
Tanselow, C. H., N.S.thesis, Syracuse University, Syracuse, K. Y., 1951. Kapner, W. F., and Wuellner, J. A, ANAL.C m x . , 24, 1031 (1952).
Wahl, A. C., and Bonner, S . A., “Radioactivity Applied t o Chemistry,” Kiley, iiew York, 1951. Weax-er, B., ASAL. CHEM.,26, 479 (1954). TT’eiser, H. B., “Colloid Chemistry,” 2nd ed., p. 112, Wiley, Sew l o r k , 1949. Willard, H. H., *&N.iL. CHEY., 22, 1372 (1950). Willard, H. H., and Fogg, H. C., J . Am. Chem. Soc.. 59, 1107
ACKNOWLEDGMEKT
T h e author wishes t o thank Thomas Walnut of the Department of Chemistry of Syracuse Univeisity for his suggestions during the preparation of this paper. Some of the researches described were supported in p a r t b y the Atomic Energv Commission and t h e Research Corp.
(193i).
Willard, H. H., and Freund, H., IKD.ESG. CHEM.,Ax.iL. ED., 18, 195 (1946).
LITERATURE CITED
Caley, E. R., Gordon, L., and Simmons, G. d.,Jr., .IXAL. CHEM.,
22, 1060 (1950).
(1925).
Elving, P. J., and Chao, P. C., Ass. CHEM.,21, 507 (1949). Elring, P. J., and S‘anAtta, R. E., Ibad., 22, 1375 (1950). Elving, P. J., and Zook, W.C . , Ibzd., 25, 502 (1953).
,
(1927).
SU-MMARY
CalloTv, R . J., Research, 7, S o . 9, 549 (1954). Doerner, H., and Hoskins, IT.,J . Am. Chem. Soc., 47, 662
.
Willard, H . H., and Gordon, L., AxaL. CHEhi., 20, 165 (1948). Ihid., 25, 170 (1953). Willard, H. H., and Hahn, R. B., Ibid., 21, 293 (1949). Killard, H. H., and Sheldon, J. L., Ibid., 22, 1162 (1950). Willard, H. II., and Tang, S . K., IXD.ENG.CHEX.,XXAL.En., 9, 357 (1937).
Killard, H. H., and Tang, N. K., J . Am. Chem. Soc., 59, 1190 (1937).
Willard, H. II.,and Yu, S. T., ANAL.CHEM.,25, 1754 (1953). RECEIVED for review June 28, 1955.
Accepted August 4 , 1955.
