Sept., 1962
KINETICSOF THIG REVERSIBLE HYDRATION OF 2-HYDROXYPTERIDINE
tions or density data from which the rectilinear diameter equations were calculated. The agreement shown in Fig. 1 among the liquid metals is considered good since, with the single exception of mercury, the critica,l temperatures are estimated and evaluation of the critical densities involves extrapolations which are large compared with the temperature range over which experimental measurements were made. Two curves are shown in Fig. 1 since the behavior of the group I I B metals, although internally consistent, appears to he rather different from that of the other metals. The agreement in Fig. 2 is better since the critical temperatures and critical densities for these liquids have been experimentally determined. The correlation illustrated in Fig. 1 and 2 may be presumed valid for other metals and liquids in general, a t least in the absence of experimental evidence to the contrary. The Ared vs. Tred curve may be used to estimate critical densities for those metals and other substances for which adequate experimental data are not available. Since the curve for the group I I B metals is so distinct, it is considered reasonable not to refer to it in making the estimates. If the density of a liquid is known a t only a single point between its melting point and normal boiling point, its critical density may be determined to a first approximation from the average value of Ared a t T r e d corresponding to the temperature a t which the density is known. Knowledge of the two density values permits estimation of the slope of the rectilinear diameter and hence that of the density us. temperature line between the. melting point and the normal boiling point. As an example of the application of the method described herein, the critical densities, densities a t the normal boiling points, and slopes of the density us. temperature lines have been calculated for rubi-
1689
dium and cesium, two metals for which reliable density data are available only a t the melting points.' Results of experimental measurcments on the densities of liquid rubidium and cesium will be reported in a subsequent publication from this Institute. The calculated values, which agree rather closely with those predicted by GrosseZ2 on the basis of an average ratio of density a t the normal boiling point to critical density for several metalsJ3are shown in Table 111. The recent values of WeatherfordZ3in Table I11 mere taken from a density vs. temperature plot for the alkali metals, apparently constructed with the assumption that the slopes for rubidium and cesium would be quite similar to the slopes for sodium and potassium. The true situation is more complicated, however, since even in the case of elements in the same group of the periodic table, comparisons should be made only on the basis of reduced properties. TABLE I11 RUBIDIUM AND
1)ENSITY D A T A FOR
CESIUM
-dD/dT
x Dx,p., B.p., a K . g./cm.3 "K.
Kp.,
Metal
Rb Cs
DB.P., g./c~n.~
This Weather- To, Do, work ford CK. g./eni.a
104, g./
crn.3. OK.
312 1.475 974 1.16 1 . 3 3 2190 0.29 4 . 8 301 1.84 958 1.44 1.68 2150 0.36 6.0
Acknowledgment.-The aut,hor gratefully acknowledges the encouragement and guidance of Dr. A. V. Grosse. (22) A. V. Grosse, "The Liquid Range of Metals and Some of Their Physical Properties at High Temperatures," Paper No. 2159, A.R.S., Space Flight Report to the Nation, New York, N. Y., Oot. 9-15,
1961.
(23) W. D.Weatherford, Jr., paper presented a t the Symposium on High Temperature Properties and Applications of Liquid Metals, Fifty-fourth Annual Meeting, b.I.Ch.E., New York, N. Y., Dee. 2-7 1961.
KINETICS OF THE REVERSIBLE HYDRATION OF 2-I-IYDROXYPTERIDINE BY Y. INOUE' AND D. D. PERRIN Department of Afedical Chemistry, Institute of Advanced Studies, Australian Y'cctional University, Canberra, Australia Received Narch $0, 1068
Rapid-reaxtion methods have been used to study the kinetics of reversible hydration of 2-hydroxypteridine across the C(4), Nc3)double bond. The reaction is acid-base catalyzed and, over the pH range 4.55 to 12.4, times of half-completion a t 20' range from 0.5 to 375 see. A possible reaction mechanism is suggested.
Introduction Althoug,h reversible hydration across C=O bonds, for example in aldehydes and some ketones, is well known, similar reactions involving C-N bonds have been much less investigated. Known examples where such hydration occurs include pteridine (cation and neutral molecule), 2-hydroxyand 6-hydroxypterjdine (neutral molecule and anion),3-6 2-mercaptopteridine (neutral molecule (1) Australian National University Scholar. D.D. Perrin, J. Chem. Soc., 645 (196%). (3) A. Albert, i b i d . , 2690 (1955). (4) D. J. Brown a n d S. F. Mason, ibid., 3443 (1956). ( 5 ) D. D. Perrin a n d Y . Inoue, Proe. Chem. Soc., 342 (1960).
(2)
and anion),G 1,4,6-triazanaphthalene (cation and neutral m ~ l e c u l e ) ,and ~ ~ ~quinazoline (1,3-diazanaphthalene) (cation and newtral rnole~ule),*~V as well as some of their methyl and other derivatives. I n each case, the first of the forms given in parentheses exists mainly as the hydrate while the second form is mainly anhydrous. Covalent hydration and dehydration of 6-hydroxypteridine (across positions 7 and 8) proceeds (6) Y . Inoue a n d D. D.Perrin, J . Chem. Soc., 2600 (1962). (7) A. Albert and 0. Pedersen, i6id., 4683 (1956). (8) A. R. Osborn, K. Schofield, and L. N. Short, ibid., 4191 (1956). (9) A. Albert, W. L. F. Armarego, and E. Spinner, abid., 5267 (1961).
sufficiently slowly in neutral or weakly alkaline solutions that a hysteresis loop can be demonstrated by rapid potentiometric titration with alkali followed, after some minutes, by rapid back-titration with acid. 2-Hydroxypteridine behaves similarly,6 adding water across positions 3 and 4.4 Until now, the kinetics of such hydration reactions have not been studied except for qualitative observations that dehydration of the hydrated form of 6-hydroxypteridine is catalyzed by hydroxyl ion,6and hydration-dehydration of pteridine shows acid-base catalysis.2.11 The present paper describes the results of potentiometric and spectrophotometric studies at 20’ of the reversible hydration of 2-hydroxypteridine (which exists in solution predominantly as the amide (lactam) tautomer (I) rather than the enol (lactim) form4) to give 3,4dihydr0-2~4-dihydroxypteridine(11).
H OH
Experimental Materials.-Z-Hydroxypteridinele was generously provided by Professor A. Albert. All other reagents were of C.P. grade. Buffer solutions in the pH range 3.4-6.2 were prepared by mixing 0.05 M sodium borate and 0.05 M succinic acid solutions. Similarly, in the ranges pH 6.3-9.2 and 9.4-10.6, 0.05 M sodium borate was added to 0.1 M potassium dihydrogen phosphate and 0.1 M sodium carbonate, respectively. Above pH 10.6, 0.1 M sodium hydroxide was added to 0.1 M disodium hydrogen phosphate. Methods.-Potentiometric titrations were carried out under nitrogen in a magnetically-stirred, thermostated reaction vessel using a Vibron model 33B Electrometer pH meter (Electronic Industries Ltd.) fitted with a saturated calomel electrode and an internally shielded glass electrode. The output of the pH meter was applied directly to a Rectiriter recording milliammeter (Texas Instrument Co.). Standard 0.100 M acid or alkali (carbonate-free) wasadded by micrometer syringe. Ultraviolet spectra were recorded continuously on either a Perkin-Elmer Spectracord or a Shimadzu model RS 27 recording spectrophotometer, the optical density scales of which were calibrated against standard potassium chromate solutions. Into the cell compartment of each instrument, was fitted a 1-cm. silica cell attached to a modified Chancel3 rapid reaction apparatus which consisted essentially of two 10-ml. nylon syringes connected to a perspex tap, in the barrel of which a mixing chamber had been constructed. The syringes and cell were water-jacketed in metal blocks to maintain solutions at 20 I 0.05’. Each of the syringes could be filled independently of the other. One of them contained an approximately 9 X 10-6 M 2-hydroxypteridine solution in either 0.004 M hydrochloric acid or 0.008 M potassium hydroxide (depending on whether the initial species was to be mainly hydrated or anhydrous); the other syringe held a buffer solution to which the corresponding amount of alkali or acid, respectively, had been added. The barrels of the two syringes were depressed simultaneously by a metal plunger, so that the reactant solutions were mixed in (10) A. Albe+t, D.J. Brown, a n d G. Cheeseman, J . Chem. Soc., 1620 (1952). (11) J. Komenda a n d D. Laskafeld, Collection Czech. Cham. Commun., 27, 199 (1962). (12) A. Albert, D. J. Brown, and G. Cheeseman, J . Chem. Soc., 474 (1951). (13) E. Chance, “Rates and Meohanisms of Reactions,” “Technique of Organic Chemistry,” Vol. VIEI, Ed. S. L. Friess a n d A. Weissberger, Interscience Publishers, Inc., New York, N. Y.,1953, p. 690.
Vol. 66
Y. INOUE AND D. D. PERRIN
1690
the mixing chamber and placed in the cell. Using a “stopped flow” technique, optical density readings at a selected wave length could be recorded continuously from about 1 sec. after mixing. The region near 370 mp was convenient because both anhydrous 2-hydroxypteridine and its anion absorbed strongly, whereas its hydrated species had negligible absorption. The pH’s of the final solutions were checked against the standards, freshly-prepared 0.05 M otassium hydrogen phthalate (pH 4.00 at 20”) and 0.05 sodium borate (pH 9.23 at 20”). Extinction coefficients and maxima of stable or only slowly changing species were checked on a Hilger Uvispeck spectrophotometer. Replicate kinetic experiments gave first-order rate constants agreeing within f5%. Calculation of Reaction Velocities.-The equilibria in 2hydroxypteridine solutions can be summarized by the schernc
LH++
x- -tH~O]
where HX is (anhydrous) 2-hydroxypteridine and HY is the hydrated form. (Lactam-lactim tautomerism, involving only a proton transfer between a nitrogen and an oxygen atom, is probably too fast to be detected by the methods used in this work.) A t any given pH the ratios [HX]/[X-] and [HY]/[Y-] are constant and equal to (aH+)/KaY, respectively, where KaX and K e y are “practical” acid dissociation constants. Also, X- and HX are in dynamic equilibrium, and so are Y- and HY. Under these conditions, the system can be treated as if it were kh
+ HzO I-B
A
kd
+
+
where [A] = [X-] [HX], and [B] = [Y-1 [HY]. Assuming that the forward- and back-reactions obey firstorder rate equations, the composite constants, k h and k d , in the equation
-d[A]/dt
=
h[A]
- kd[B]
==
d[B]/dt
(I)
can be evaluated as described below. Because [A] -k [B] = [AIesrn [BIeqm,eq. 1 can b e written as
+
- d[A]/dt
(kh
=
- d[B]/dt
=
kd)
+
[A] - h d ( [ A J e q n ~ kd)
(kh
[B]
[BIeqm)
h([B]eqm
f
[Alesm)
But, at constant wave length and constant pH, the optical density, D,of the system is given by D = a [ A ] @[B], where a and p are constants. Making use of the values of d[A]/dt and d[B]/dt given above, it may readily be deduced that
+
- dD/dt
+
=
kob,(D -
where k&s = kl, k d . Also, because k&h it can further be deduced that
Deqm)
=
[Aleqm/[Blesm,
where the constants K I = [Y’-1 e q m / l X - l eqm, Kz.= 1HYIeqm/ [HX],,,, and KaX = (a=+)[X-]/[HX]. As discussed elsewhere,E.6 these constants can be evaluated from rapid- and
Sept., 1962
KINETICSOF
THE
REVERSIBLE HYDRATION OF 2-HYDROXYPTERIDINE
1691
equilibriumtitration data (or, alternatively, they can be obtained from analysis of rapid-flow and equilibrium absorption spectra). Confirmation that the hydration-dehydration reaction of 2-hydroxypteridine obeys a first-order rate equation over at least the first nine-tenths of the reaction is provided by typical results shown in Fig. 1, where the plots oE log ((DDeqm)/Deqm) us. time are good straight lines.
Results Table I shows the pH-dependence of rates for the reversible hydration of 2-hydroxypteridine a t 20'. The primary salt effect on l ~ ~was t , small ~ and no attempt was made to extrapolate values to zero ionic strength. Thus, over the pH range 7.9 to 11.8, increasing the ionic strengths listed in Table I (0.054 to 0.087) to 0.100 by addition of sodium chloride gave no perceptible change in kobs. Between pH 6.4 and 7.6 log koba increased by about 0.05. Differences became greater a t lower pH values. The rate constants for hydration and dehydration, kh and k d , were obtained from koba by using eq. 2 and 3, respectively, and values of K1 = 0.14, K 2 = 320, Kax = 2.0 X 1.0-8, and K a y = 9.0 x 10-12.6
250
500 750 1000 Time, see. Fig. 1.-Representative plots of log ( ( D - Deq,,,)/DzqF) us. time for hydration of 2-hydroxypteridine a t 20 in buffers: 1, pH 7.58; 2, pH 8.43; 3, pH 9.25; 4, pH 10.19. Wave length, 370 mp. 0
(approximately) constant pH, kobs increases with the concentration of borax buffer. As discussed below, specific catalysis by boric acid is involved.
TABLE I1 VARIATION OF VmocIw CONSTANT WITH COBCENTRATION VELOCITYCONSTANTS FOR HYDRATION AND DEKYDUTION OF BORAX BUFFER' O F %HYDROXYPTERIDINE I N BUFFERSOLUTIONS AT 20" Bb 0.01 0 02 0.03 0 04 0 06 0.07 0.09 Ionic strength kobaa khb PH kdb PH 9.16 9.20 9.21 9.23 9.27 9.29 9.34 0.017 I ,43 0,00447 4.55 1.43 103kObs, 1.01 1. .01 ,019 .00316 4.79 sec.-l 2.0 3.5 4 . 0 4 6 5.2 5 6 6 3 .021 .00218 4.93 0.700 0.696 a Ionic strength constant at 0.200 by addition of NaCl. .483 .481 .024 .00150 5.16 * Total concentration of boric acid and borax, expressed as .293 .028 .000913 5.39 .292 NazBa07,in moles/l. .189 .030 5.60 .000590 .188 Discussion .032 .108 5.89 .000343 .lo8 ,0532 The pH-dependence of k h and Jcd suggests that .038 6.18 .000171 .0530 they are composite constants for the folloiving .053 .0420 .000138 .0418 6.43 .0326 simultaneous reactions which represent catalysis of .0324 .059 .000110 6.62 .062 6.82 .0248 ,0000870 hydration of H X and X- and dehydration of HY .0246 .063 7.02 .0179 ,0000669 and Y - by solvent and by hydronium and hydroxyl .0177 .0124 ,0123 .067 7.23 .0000513 ions. .070 .00864 .00861 7.48 .0000432 IC1 ,071 7.63 .00682 .00676 .0000391 .00568 H20 1330 IIIY 4- IIAO + .075 7.89 .0000448 HX .00562 ----f .00342 .076 ,0000541 8.31 .00341 IC-1 .075 .00278 .00271 8.46 .0000572 .00265 .074 .0000661 8.56 .00257 162 .00228 .071 8.70 .00219 .0000751 H X HzO H,O -++ +H T 1120 .00235 .070 ,00225 8.84 .000104 k3 .00221 .066 .00208 8.98 .000130 XH20 H30+ +- YH30+ .060 .00216 9.16 .000183 .00198 .Ob4 .00185 9.29 ,00165 .000203 .056 .00376 .000967 9.76 .00280 HX+HzO+OH-+ + +HY+OH.00305 .059 10.32 .00145 ,00161 k: f- Y€120 .00241 .063 10.59 .00156 .000857 XH20 RzO --+ .00267 .077 .000722 10.84 .00195 .00354 .000647 11.28 .os0 .00289 ka 11.44 ,082 .00439 .000725 .00366 11.76 .087 ,00814 .00117 X- -t H20 OH- ZZ YOW.00697 .0122 12.01 ,093 "00164 .0105 IC-0 .044 12.38 .0293 ,00375 ,0256 The rate constants for reactions 2 and 3, and 4 and a koba = lirst-order velocity constant, in sec.-l, from rate of change of spectrum. kh, k d = composite rate constants 5 , cannot be evaluated separately because of the for hydration and dehydration reactions, respectively, in dynamic equilibrium between neutral species and sec .-l.
TABLE I
+
+
+ +
+ +
+
+
z-
I:;[+] ]+[:I *
+
From results in Table 11,the reaction is catalyzed by borax buffer: at constant ionic strength and
+ +
+
+
their anions. Further reactions can be written to take account of catalysis by other species such as buffer ions. Thus, a t very low reaction rates, ca-
Vol. 66
Y. INOUE AND D. D. PERRIS
1692
+
3 X lo6& = 27. Hence, at 20°, the rate constants for the hydration of 2-hydroxypteridine and its anion are given by
5
kh =
h
6.3
x
1O4(aHt)f 1 2
4
x
10-4[Hz0] f
5 1 . 5 X 103(aoH-)
v
(for IIX)
+ 5 9 X lO-'[HzO] +
+ 7
1 5 . 5 X 106(aH+)
2
(for X-)
0.22(a0~-)
v
&$ w
The corresponding constants for the dehydration reaction are obtained by dividing by 320 and multiplying by 7.1, respectively. Because the pyrimidine portion of the nucleus appears in 2-hydroxypteridine, as in pteridine itself,2 to have little aromatic character, considerable 11 charge localization is likely in the bond joining llrT(3), and C(4).2 It is known that C(4) has a suffiPH. ciently large net positive charge to facilitate attack ) pH for hydration of by nucleophilic reagents (so that 2-hydroxypteriFig. 2.-Log kh(Kaz + ( a H + )vs. 2-hydroxypteridine: solid curve, eq. 5 ; dashed line, eq. 5 dine readily undergoes Nichael addition reactions14) 4.3 X 10-1"[H3BOa]. whereas N(3)can add electrophilic reagents. A comtalysis by boric acid and bicarbonate ion is signifi- parable situation exists for the carbon and oxygen cant. atoms of the carbonyl group in acetaldehyde and, Rearranging the equation for k h , and substituting as a tentative hypothesis, we suggest that the acidbase catalyzed hydration of 2-hydroxypteridine [X-] = K a x ( ( X - ] [HX])/'(KaX ( a H + ) ) proceeds by a mechanism similar to that for acet[HX] ( a ~ t ) ( I X - l [ ~ ~ X l ) / (3.~ (~aa~ xt ) ) Acid-catalyzed reaction gives - 9 I
+
+
+ +
h ( K a X f ( a H + ) ) = kl(aH+)' (k2 k3KaX)(aH+) ( I C ~ K I~ C ~ [KH~~ o~] ) kcKaXKw/(aII+) (4) Values of log Ich(KaX (arr+))from the results in Table I are plotted against pH in Fig. 2 . Over the p€I ranges 4.5 to 8.5, 10.6 to 12.4, klI(KaX3. (oat)), which varies by a factor of 3 X lo6, can be well represented by the equation lzh(Kax ( a ~ t ) = ) 6.3 X l O 4 ( a ~ t )4-* 1.1 x 10-*(aH*) f 1.0 x lo-'' 3.0 x 10-23/(aH (5)
+
+
+
+
+
Iy
N
+ k)
The deviatioris between pH 8.5 and 10.6 can be explained quantitatively if the additional terms, 4.3 X 10-10[H3B03] 2.8 X 10-9[HC03-], are included in eq. 5. That specific catalysis by boric acid, and not borate ion, is involved in the reaction is supported by the absence of any correlation between the extent of the deviation and the borate concentration of the buffer solutions used. Similarly, for solutions where bicarbonate ion 1s present (pH 9.8 to 10.6 in Fig. a),deviations correlate with bicarbonate, but not with carbonate, concentration. Below about pH 8.5 the effect of boric acid is swanaped by hydrogen ion catalysis, and above pI-1 10 boric acid is largely ionized to borate (pK, = 9.2). The highest point for the borax buffers in Table 11 gives kh(KaX f ( a H + ) ) = 1.15 X lo-'', in fair agreement with the value calculated from eq. 5 only if the term for boric acid is included (7.8 x as against 1.6 x By equating coefficients in eq. 4 and 5 , and taking [HZO] = 55.5 M , we obtain (in sec.-l), 1t.1 = 6.3 X io4, k 6 = 0.22, k2 2 x 10-8k3 = 1.1 x k4
H
activated complex
+
+
Ba?e-ctlta!vzd reac'ti
H,
0-
H\
0
in
'0
I H
H\
I
0-
H hydrated
H activated complex (14) A. Albert and C. F. Howell,
J. Chsm. Soc., 1591 (1962).
Sept., 19621
TEMPERATURE DEPENDENCE OF KSIGHT SHIFTOF SODIUM-XMMOSIA SYSTEM
aldehyde,ltk and also that the structures of the activated complexes from 2-hydroxypteridine are analogous to those postulated16 for the acid-base catalyzed hydrolysis of esters and amides. Thus, the reactions for the neutral molecule with hydronium and hydroxyl ions would be as set out below. The steps (iij and (ivj involve simple proton trans(15) R. P. Eiell and W. C. E. Higginson, Proe. Roy. SOC.(London), 8197,141 (1949). (16) K. J. Laidler and P. A. Landskroener, Trans. Faraday Soc., 62, 200 (1956).
1693
fers to and from oxygen atoms and would be very fast, so that the steps (i) and (iii), which require more extensive structural rearrangements, would become rate-determining. The reversible acidbase catalyzed hydration of pteridine2t1l and 2hydroxypteridine across their 3 :4 double bonds would be expected to involve similar mechanisms and analogous activated complexes. This accords with the view that the oxygen atom of 2-hydroxypteridine is not directly involved in the formation of the activated complex.
TEJIPERATURE DEPENDENCE OF THE KNIGHT SHIFT OF THE SODIUilrC-A;?~MONI~4SYSTEM BY J. V. ACRIVOS Laurence Radiation Laboratory, Berkeley 4, California AND
K. S . PITZER
Department of Chemistry, Rice University, Houston 1, Texas Received March $9,1962
The Knight shift of NaZ3and "4 in sodium-ammonia solution was measured over the temperature interval -33 to +22" and in the concentration range corresponding to mole ratio 5.7 to 700 (NH,/Na). The results in the dilute region, R 2 300, were interpreted in terms of the equilibrium constants K1 and K z for the reactions Na(am) = Na+(am) 4. e-(am) and Na(am) = '/ZNa?(am). The effective Knight shifts, k~ for Na23 in Na(am) andkl' for W4in e-(am) were found to be ko = (0.034 f 0.005)T+ and kl' = (13.5 f 1)T-I. The measured standard enthalpy and entropy of reaction for the dissociation and the dimerization equilibria are, respectively, AHlo (298') G -6.6 and AH20 = -7.3 f 1 lwal./mole and Aslo (298") E -34 and ASZO = -24.1 f 3 cal./deg. mole. The change in enthalpy for the dissociation equilibrium was temperature dependent and indicated that a large negative change in heat capacity accompanied the reaction. The electron densities a t the Na23 nucleus were pl(NaZ3)= 0,071 a ~ and - ~ 0.00098 ao-a for the concentrated ( R % 5.7) and dilute solutions ( R 5 300), respectively.
The study of the electromagnetic properties of the alkali snd alkaline earth me-tals in liquid ammonia has supplied a great deal of information about the chemical nature of these solutions. As a result of conductivity measurerrrents, Krausl ha.s proposed that there exist, present in solution, solvated atoms, positive ions, and electrons. The presence of paramagnetic species was indeed verified by Huster2and Freed and Sugarman3from the static magnetic susceptibility, x, and by Hutchison and Pastor" from the paramagnetic absorption by means of e.s.r. The main conclusions to be drawn from these measurements are: (a) the magnetic susceptibility of the metal in ammonia solution always lies below the expected Curie d u e , which is approached asymptotically only as the dilution increases to infinity, and (b) tlhe l / T t'emperature dependence of x is not obeyed. Elecker, Lindquist, a,nd Alder5 oxplained these result's by assuming the existmeliceof four differen.t species, solvat'ed metal dimers, atoms, and positive ions and electrons in the dilute solutions, and t,hen proceeded to evaluate the chemical equilibrium coiista,nts for the dissociation and dimerization of the solvated m e h l (1) C. A. Kraus, J. Am. Chsm. Soc.. 43, 749 (1921); for review work also see J . Chem. Educ., 30, 83 (1953). (2) E. Huster, Ann. P h w i k , 33, 477 (1938). (3) S. Freed a,nd N. Sugarman, J . Chem. Phys., 11, 351 (1943). (4) C. A. Hutohison, Jr., a n d R. C. Pastor, ibid., 21, 1959 (1953). ( 5 ) E. Becker, R. H. Lindquist, a n d E. J. Alder, ebid., 26, 971
(1956).
atoms or monomers from the e.s.r. data.4 These reactions may be written Sa(am)
=
Na+(amj
+ e-(am)
Na(amj = '/2Naz(am)
(1) (2)
with the combined reaction 1/z;2;a2(am) = Sa+(am) f e-(am) ( 3 ) where the respectiye equilibrium constants are K1, Kz, and Ka. The Knight shift (KS) data of McConnell and Holm6for the YaZ3-W4H8solutions at room temperature in the concentration range R = 5-500 supported these views. Pitzer' and Blumberg and Das8 were able to explain some of the features of the KS data6 by calculating the distribution of electron densities in the solvated paramagnetic species. Moreover, both Dye, Smith, and Sankuerg and Evers and Franklo derivecl sets of rquilibrium constants from conductance measurements of Krausl at t = -33" together with transference number data. Their respective results are in fair agreement. (6) H. M. McConnell and C. H. Holm, zbzd., 26, 1517 (1957). (7) K. S.Pitzer, zbid., 29, 453 (1958). ( 8 ) W. D. Blumberg a n d T. P. Das, pbzd., 30, 251 (1959) (9) J. L. Dye, R. F. Sankuer, and G. E. Smith, J . A m . Chem. Soc., 82, 4797, 4803 (1960). ( I O ) E. C. Evers and P. W. Frank, J . Chem. Phys., 30, 61 11959).
