M. ANBARA N D S. GUTTMANN
1896
decrease in the concentration of H atoms in the flame front by the reactions (a) CzNz
Yol. 64
and
+ H -+ HCN + CN, (b) H + CN +HCN
which are similar to the effect found in halogenhydrogen reactions.21 The decrease in H atom concentration results in a decrease in the OH concentration, and subsequently in the decrease of the rate of reaction 13 and the flame velocity. The effect of halogens2*in reducing the flame velocity of wet CO-02 mixtures has already been observed. If the reaction between the OH radical and CO controls the flame propagation in moist CO-Oz mixtures, a difference in effect between hydrogen and deuterium additions may be expected in view of the difference in reactivity between the OH and OD radicals. The ratio of the reaction rate constants for OH and OD may be calculated from an expression derived by Biegelei~en~~ for the effect of isotope substitution on the rate of reaction. His theoretical relation for the ratio of the reaction rates i.
in which the indices 1 and 2 refer to the hydrogen and deuterium isotopes, respectively, to the reactants, and * t o the activated complex. K1*/Kzc 1 the ratio of the transmission coefficients effective mass of the activated complex along ,1.I the reaction coordinate (21) G . Hadman, H. K. Thompson and C. N. Hinshelwood, Proc. Roy. SOC.(London), 8137, 98 (1932). (22) E. Sterling and R. Arthur, “Third Symposium on Combustion, Flame, Explosion Phenomena,” The Williams & Wilkins Co., Baltimore, Md., 1949, p. 476. (23) J. Bigeleieen, Til18 JOURNAL, 66, 823 (1952).
In expression 1.5, S1/Szis the ratio of the symmetry numbers, and Ui = h c w i / k T , wi being the vibration frequency in cm.-l of the appropriate normal mode. The activated complex in the reaction between CO and OH was assumed to have the form [CO-0-HI. Values for the vibration frequency for OH and OD in the activated complex were taken as those of the corresponding groups in formic acid (3570 and 2666 cm.-l for OH and OD, respectivelyz4),yielding a value for f * of 1.07. The ratio of the partition functions of the OH and OD radicals was calculated to be 1.02 for vibration frequencies equal to 3735.21 and 2720.9 cm.-l for the respective species.25 The ratios of the symmetry numbers and the partition function for GO were both assumed to be unity. The introduction of these quantities into equation 14 gave a value for ~ O & O D = 1.33. In accordance with the square-root relation rate and burning velocity the ratio of the flame speeds of hydrogen to deuterium-containing mixtures may be expected t o equal 1.15. This ratio was observed for a mixture of 10% C2Nzplus 3% H2 or D Pand air. Acknowledgment.-The authors wish to express their appreciation to Dr. L. A. Wood for his helpful criticisms of this paper and to Dr. P. C. Colodnj7 for aid with the calculations. (24) G . Herzberg, “Infrared a n d Raman Spectra of Poly-atomic Molecules,” D. Van Nostrand Co., New York, K Y . , 1945, p . 321. (25) G . Hersberg, “Spectra of Diatomic Molecules,” D. Van Nostrand Co., New York, N. y., 1950, p. 560.
THE ISOTOPIC EXCHBNGE OF FLUOROBORIC ACID WITH HYDROFLUORIC ACID BY M. ANBARAND S. GUTTMAXN Isotope Department, WeizmannInstitute of Science, Rehoooth, Israel Received May S I , 1960
The rate of isotopic exchange of fluorine between fluoroboric and hydrofluoric acids has been investigated. The rate of exchange R = 4.5 X 104 e--24.7WlRT [BFI-) [Hf]. 1. mole-’ set.-'. The exchange was found to proceed oia HBF4 Ft H F HBF,OH followed by rapid isotopic equilibration between BF30H- and HF. The mechanism of exBF,, BF3 H,O change was found identical with the mechanism of hydrolysis in acid medium. The non-acid hydrolysis of BF4- proceedP by a S N 1 mechanism with a rate constant k = 8 X lo6 e-15J001RTsec.-l.
+
The chemistry of fluoroboric acid HBF4 has been extensively studied by Ryss, et aL,l and by WamserZJ who have determined the equilibrium constants for the formation of HBF4, HBF30H, HBF2(OH)zas well as the rates of formation and hydrolysis of HBF4 at room temperature. Wamser has pointed out that the rate of HBF, formation is affected by acidity though he did not present a rate law including hydrogen ion concentration. The purpose of this study was to investigate the rate of (1) I. ( 2 . Ryss, M. M. Slutskaya a n d S D Palevskaya. Dokl. S.S.S.R., 62, 417 (1946); 67, 689 (1947); Zhur. Obshchei KhLm., 19, 1827, 1838 (1949); 26, 19 (1955). 12) C . A. Wamser, J. Ana. Chem. Sac., 70, 1209 (1948). (3) C . A, Wamser. ibid., 73,409 (1951).
+
isotopic exchange of fluorine between fluoroboric and hydrofluoric acids over a range of hydrogen ion concentration and to compare it with the rates of formation and hydrolysis of fluoroboric acid over a similar range of acidity. Quantitative data on the rates of exchange and hydrolysis of fluoroborates are of importance in applying KBF418as a tracer in biological systems.4 Experimental A. Materials.-Potassium fluoroborate commercially available was three times recrystallized from water. Technical sodium fluorohorate was first purified from insoluble (4) M. Anbar, 9. Guttmann a n d Z. Lewitus. Endocrinolopy. 66, 888 (1960),
Dec., 1960
ISOTOPIC EXCHANGE OF FLUOROBORIC ACIDWITH HYDROFLUORIC ACID
matter by dissolving i t in a minimum amount of water, then concentrated lanthanum nitrate was added in excess to remove the fluoride ions; lanthanum fluoride was separated by centrifugation and the supernatant was passed through a cation exchange column (Dowex 50, sodium form 50 mesh). The solution was next tested for traces of lanthanum by increasing the alkalinity to pH 9. The solution which was fluoride and lanthanum free was gravimetrically assayed for fluoroborate by precipitating both as potassium fluoroborate and nitron Auoroborate. The amount of fluoride ions present in the purified fluoroborate salts was estimated by the zirconium-aliaarin6 and ferrithiocyanatee methods. The amount of fluorine found in our purified KBF, and NaBF4 in any other form than BFI-, was below 0.2YC. This value was confirmed when KBF4 was prepared and the amount of fluoride was determined by isotopic dilution analysis. Carrier-free fluoride 18 was prepared by bombarding LizCO31stargets with 3.2 MeV. protons (20-30 microamperes) from an electrostatic Van de Grrqaff accelerator. The LizCOa18 was prepared by the equdibration of LizC03 with HzO1*(92-96 atom Yo 0l8)in a slightly acidic medium. ilfter irradiation the targets were dissolved in 0.5 ml. of 0.1 N HC1. Labelled BF4- was obtained by adding a weighed amount of pure KBF4 (50-200 .mg.) to the acid solution of carrier-free LiF18. The solution was heated to 100' and kept at this temperature for 2-5 minutes in order to undergo exchange. It was cooled in ice and the labelled KBF4 was precipitated and recrystallized three times from neutral aqueous solution; then i t owas washed with ethanol and dried in a vacuum oven a t 70 . Five to 10 mg. of the labelled KBF4 was weighed and dissolved in 100 ml. of water and an aliquot of 1 ml. was taken for radioassay. To another aliquot of 1 ml., 0.5 ml. of 0.1N NaF was added and the fluoride ions were precipitated by Pb(N03)2 in presence of 0.2 N NaC1. The PbClF precipitate was washed with 90% ethanol and radioassayed. The activity of the PbClF never exceeded 0.5% of the total activity present; this value may be considered as the upper limit of fluoride impurity in the KBF418 preparations, as any exchange, hydrolysis or incomplete separation would contribute to the fluoride activity. All other reagents used were of analytical grade. B. Methods of Analysis. Hydrolysis of BF4-.-Tenml. of solutions of KBF4l8 or N a B F P were adjusted to a certain pH by nitric acid, sodium acetate or sodium hydroxide, and placed in a thermostat at 25, 37, 60 or 100". At intervals aliquotes of 1 ml. were taken, cooled and neutralized. One ml. of a solution 0.1 N in NaF and 0.2 N in NaCl was added to the solution at pH 3-5 and 1 ml. of 1 N Pb(NO& was introduced to precipitate PbClF. The precipitate was centrifuged, washed with 90% ethanol and counted. When solutions of BF4- below 0.01 N were studied, one ml. of KBF4 0.05 N was added as a "hold back carrier," to prevent undue adsorption of BF4'8- on the precipitate. Samples were counted in a 2 inch well type NaI scintillation counter; the discriminator level was held a t 400 Kev. I n experiments where the effect of fluoride ion concentration on the rate of hydrolysis was studied, the initial concentration of fluoride ions was kept low in comparison with that of BF4-. The rate of hydrolysis was calculated according to firstorder kinetics, by plotting log a / ( a - 2) US. t , where a is the initial concentration of BR-. Exchange of BF4--F-. 1. Labelled BF4-.-Solutions of KBF4,or NaBF4were prepared containing known amounts of fluoride ions. The fluoride concentration chosen in these experiments was high compared with that of BFd-, thus there was little net change in the BF4- concentration due to hydrolysis.'S2 The pH was adjusted and the solution was thermostated. Next a known amount of fluoride-free KBF418 was added. At intervals fluoride ions were precipitated and radioassayed by the method described above. 2 . Labelled Fluoride.-Carrier-free LiF18 was added to solutions containing known concentrations of BF4- and Fof a known pH, which have attained hydrolytic equilibrium. Aliquots of 1 ml. were introduced into 2 ml. of 10% nitron solution. The nitron fluoroborate was separated by centrifuge, washed with 70ycethanol and counted. The rate of exchange was calculated from (5) F. D. Snell and C. T. Snell, "Colorimetric Methods of Analysis," D. Van Nostrand, New York, N. Y.,1959, p . 638. (6) R. S. Ingole, e t al., Anal. Chem., 22, 799 (1950).
1897
4[BF,-][F-] A m - Ao 4[SF4-j [F-1 log A x where A is the activity of F18 a t the different phases of reaction, or
Rt
where
+
=
-
was derived graphically by plotting log A
A t
US. t .
Results Isotopic Exchange of BF4--F-.-The rate of fluorine exchange between fluoroborate and fluoride ions was studied in solutions 0.01-1.0 molar in hydrogen ions. The concentrations of BF4- and of H F were changed in range 0.005-0.5 and 0.020.2 M , respectively. A selection of results at various temperatures is presented in Table I. TABLE I ISOTOPIC EXCHANGE OF FLUORIXE BETWEEN BF4-
0 0 0 0 25 25 25 2.5 25 25 25 37 37 37 60 60 60
1.30 1.20 1.34 1.25 0.28
.70 .87 .95 1.10 1.54 1.88 1.08
1.30 1.35 0.88 1.1 1.3
0,093 .099 ,035 ,020 .10 .10 .50 .2 ,088 .42 .1
.37 .1 .09 ,087 ,005 .094
0.017
1650 5700 ,015 3250 16400 .20 .07 35 72 .07 33 .07 75 .07 ,022 50 1.034 60 0.07 1340 5.0 .03 .1 46 .2 16 0.7 ,033 .045 12 ,106 4.0 ,101
6.8 9.5 2.8 2.4 1.15 5.6
1.4 5.9 2.9 3.9 3.0 4.2 1.2 7.8 3.0 7.7 1.4
10-6
AND
1.4
10-0 1 . 4 10-6 1 . 7 5 10-6 2 . 1
10-3 2 . 2 10-4 2 . 8 io-4 2.1 10-4 2 . 6 10-4 4 . 1 10 1 3 . 4 10-6 2 . 3 10-8 1 . 4 10-3 2 . 4 10-4 1 . 9 10-2 2 . 6 10-4 1 . 9 10-9 3 . 0
HF
10-3 10 8 10-8 10 -3
10-2 10 - 2 10 - 9 10-2
10 - 2 10-2 10 - 2
10-1 10 -1 10 -1 100 100 100
Within the range of concentrations investigated the rate of exchange was found proportional t o BF4- and H+ concentrations and independent of of H F R = kl[H+] [BF4-]. From average specific rate constants at 0, 25, 37 and 60" the activation energy of the exchange reactions was calculated A E = 24.7 kcal./mole. The average specific rate constant in the given range of temperature is therefore k = 4.5 x 1014 e-24700/RT1. mole-' see.-'. Hydrolysis of BF4-.-The rate of hydrolysis of fluoborate ions was found to be first order in BF4- and first order in hydrogen ion concentration in the acid region Rate = k [H+][BF4-] as may be seen from Table 11. HYDROLYSIS OF BF4IBF4-I, mole 1.-1
0.015
,017 .14
W+I,
mole I.-'
2.0 1.0 1.0 0.5
,019 ,019 .2 .I4 .1 k = 7.1 f 0.5 X e X 1 0 - 4 m ~ l -ll.sec,-l,
TABLE I1 IN ACID SOLUTIONS AT 25'" tl(2,
min.
I?-",
1u-3,
min.-l
min. -1
52 13.3 6.7 98 7.1 7.1 95 7.3 7.3 20 1 3.45 6.9 490 1.41 7.0 870 0.8 8.0 mole-' 1, m h - 1 = 1.18 =t0.08
M. ANBARAND S. GUTTMANN
1898
There was found no catalytic effect of H F initially present on the rate of hydrolysis. This result is confirmed by the fact that no autocatalytic deviation from first rate law was observed. In another series of experiments bisulfate ions were added up to 0.9 M keeping the pH constant, no appreciable change of the rate of hydrolysis could be detected. Activation energy A E = 25.1 kcal./mole-', was derived from data at 25, 37", (1.23 f 0.05 X mole-' 1. set.-'), 60" (IC = 1.33 f 0.05 X mole-' 1. see.-') and a t 100" (IC = 1.10 X 10" mole-' 1. set.-'). The specific rate constant of fluoborate hydrolysis in acid solution is therefore k = 2.3 X 10'4 e-25,100'RTmole-' 1. sec.-l
In neutral and basic solutions the rateof hydrolysis is much lower and no effect of alkalinity on the rate of hydrolysis could be detected as it is shown in Table 111.
Vol. 64
not necessarily appear in the rate expression because its concentration remains essentially constant. It has been shown that hydrofluoric acid as well as bisulfate ions failed to show any catalytic effect on the rate of hydrolysis: these results make a general acid catalysis rather unlikely and suggest that reaction 1 is a fast pre-equilibrium rather than a rate determining step. This assumption is supported by the relatively high energy of activation of the acid hydrolysis (-25 kcal./mole). The available experimental data on the hydrolysis of B E - are insufficient to decide between reaction paths (2) and (3), but some information may be gained by comparison with the reaction of fluoroborate formation. As the equilibrium constant of BF4- hydrolysis is unaffected by acidity,2 the reaction of HBF4 formation, namely BFIOH-
+ H F +BF4- + HzO
(4)
must be acid catalyzed as well. It should be noted TABLEI11 that throughout the whole range of acidities conHYDROLYSIS OF FLUOROBORATE IN NEUTRAL AND ALKALINE sidered in this work there is no appreciable change SOLUTIONS AT loooa in the concentration of H F and there are practically tl( 0.693/tifr X IOH-I, IBF4-I, no fluoride ions present, therefore it is the concen10-1, mtn.-' mole 1.-1 mole 1. -1 min. tration of HBF30H which increases with acidity, 2.0 0.016 167 4.2 and reaction 5 is probably involved in the sequence 1.0 .016 167 4.2 of fluoroborate formation. 0.1 .020 156 4.4 ¶I
.010 160 4.3 = 4 . 3 XO.l X10-3min.-1=7.2f0.210-4sec.-*.
10-8 a k
From measurements at 60 and at 100' the following rate constant for non acid hydrolysis of fluoroborate ion was found k = 8 x 106 e-166m/RT sec.-l
Discussion Both reactions investigated, namely, the isotopic exchange between BF4- and H F and the hydrolysis of fluoroborate ions in acid medium, follow the same rate law
HsO+
+ BFaOH-
HBFsOH
+ H2O
(5)
Once HBFQOHhas been formed the two alternatives are a bimolecular reaction 6 HF
+ HBFsOH Jr HBF4 + HsO
(6)
or a fast predissociation of HBFsOH
followed by BFs
H20
+ BFI
+ H F +HBF,
(7 ) (8)
The existence of hydrated BF3 in aqueous solution as assumed in reactions 2 and 7 and its nonequivalent with the HBFaOH molecule has been R k[H+][BFd-] demonstrated by Ryss.' Assuming an effective nucleophilic attack of HF It may be suggested that the isotopic exchange proceeds via the hydrolytic dissociation of fluoroboric on HBFaOH (reaction 6) a similar interaction beacid. Consequently the acid-catalyzed hydrolysis tween H F and HBF4 could be expected, leading of BF4- will be discussed fist. to a bimolecular isotopic exchange. There is no The rate of hydrolysis of BF4- may be expressed experimental indication of an isotopic exchange by the rate law Rhydrolyeis = k h [H+][BR-1. This depending on H F concentration, thus we may rate law implies the reaction followed by a second suggest that a bimolecular reaction between H F and HBF3OH is rather unlikely. Now, if a BFd- + HoO J_ HBF4 + HzO (1) nucleophilic attack of H F and HBF4 or HBF30H step in which H F is formed. H F may be formed seems improbable, the analogous reaction between from H B R either by a dissociative process (SN1) HzO and HBF4 may be considered unlikely as well. The bimolecular reactions both with HBF4, and HBFr If BFa + H F ( 2) IIBF30H involve a five coordinated boron atom in followed by the transition state; although such a transition BF3 + HzO J_ HBFaOH state cannot be excluded, it would hardly be (2a) favored by a small boron atom shielded by negaor by a nucleophilic attack of HzOon fluoroboric acid tively polarized large fluorine atoms. It is sug(SN2) gested, therefore, that the ratedetermining step HBFi + H10 J_ HBFsOH + H F (3) of fluoroborate hydrolysis involves a monomolecular dissociation. followed by The specific rate constant for the HBF4-+ BF3 HBF80H + HzO BFsOH- + HIO+ ( 3 4 H F reaction can only be roughly estimated. WamAny of these reactions may be the ratedetermining (7) J. G. Rysa a n d M. M. Slutakaya, Zhur. Obshchei Khim., 22, 41 step; the participation of water in reaction 3 does (1952).
+
MISCIBILITY OF RUBIDIUM WITH RUBIDIUM HALIDES
Dec., 1960
ser found that the dissociation constant of HBF, is comparable with that of hydrochloric acid.8 The dissociation constant of HC1 in aqueous solution is approximately8 lo7, thus the specific rate constant of HB F4 monomolecular dissociation is of the order of magnitude of lo5 min.-' a t 25". The BF3 which is formed in the dissociative step is immediately hydrolyzed and the equilibrium BF3 HzO i f HBFSOH is established. The equilibrium constant of this reaction ( K = 5 X lo6) may be calculated from the free energies of BR-, HzO and HF9 and from the equilibrium constant of the BF; HzO BF30HH F reacmole l.-I). tione2 ( K = 2.3 X A specific rate constant a t 25" for the reaction
+
+
HF
-+ BFs -+
*
+
1899
= 6.9 X 10-8 1. mole-' min.-I for the specific rate constants of the exchange and hydrolysis reactions, respectively. The energies of activation of the two reactions, on the other hand, are equal within the experimental error. The factor four between the two specific rate constants: kex/kh = 4,may be accounted for if the fast isotopic equilibration HOBF3HF* e HOBF3-* H F is ~onsidered.~Thus for each molecule of HBF4 undergoing hydrolysis another HBFI molecule i s formed in which all four fluorine atoms are exchanged. This isotopic equilibration between BF3OH- and H F may be attained by successive dissociations of the type
k
+
+
HBFiOH
HBF, (1014 1. mole-' min.-l)
HBF20H
+ HF
(9)
It may be concluded, therefore, that isotopic exchange proceeds via two processes; the slow hydrolysis of HBF4 and the fast isotopic equilibrium of BFaOH--HF. Considering the non-acid hydrolysis of BF,one encounters a typical S N (lim) ~ mechanismlo; there is little evidence available for the existence of a five coordinated boron atom and on the other hand both BFs and F- are well established chemical Rsrohvnge = kex[H+][BFd-] species. The specific rate constants of the monothus it may be suggested that the exchange pro- molecular dissociation of BF4- a t 25" is slower by ceeds via reactions 1 and 2. Yet there is an ap- a factor of about 1Olo from that of HBB, although parent discrepancy between the rate constants of its energy of activation is lower by about 9.6 the isotopic exchange and the hydrolysis reactions. kcal./mole. This points to a spectacular increase At 25" we derive the values k = 2.7 X low2and in the entrorw of activation of the dissociation (8) T.Moeller, "Inorganic Chemistry," John Wiley and Sons, Inc., process on &ition of a proton to the BF4- ion. can be estimated from the specific rate constant of HBFd hydrolysis and the equilibrium constants of the BF4HzO BFZOHHF, BF3 HzO HBFSOH and IlBFaOH H+ BF30H- reactions; it is then assumed that the dissociation constants of HBF30H and HBF, are comparable. The rate of isotopic exchange between BF4- and H F follons the same rate law
+
+
+
+
*
New York, N . Y., 1952, p. 314. (9) W. M . Liltimor, "The Oxidation States of the Elements," Prentice-Hall, Inc., New York, N. Y., 1'262.
( 1 0 ) F. Basolo and R. G. Pearson, "Mechanisms of Inorganic Reactions," John Wiley and Sons. Inc., New York, N. Y., 1958,p. 97.
MISCIBILITY OF METALS WITH SALTS. V. THE RUBIDIUM-RUBIDIUM HALIDE SYSTEMS BY M. A. BREDIGAND J. W. JOHNSON Oak Ridge National Laboratory,I Chemistry Diwision, Oak Ridge, Tennessee Received M a y Si, 1960
The miscibility of rubidium metal with its molten halides is found to be large and, as expected, intermeaiate between that of potassium and cesium with their halides. A miscibility gap is absent in the RbBr-Rb system; like the other alkali metalbromide systems, it thus deviates less from ideality than the corresponding chloride and iodide systems.
in the potassium3 and sodium systems would in Introduction The miscibility of the alkali metals with their the case of rubidium lead to the absence of a halides in the molten state was shown to increase miscibility gap in the RbBr-Rb phase diagram. rapidly in going from the sodium systems to the Experimental potassium and cesium systems.2 The present Of the rubidium halides used, RbBr and RbI were prereport covers the rubidium systems which were pared from the sulfate by double decomposition with the expected to exhibit a behavior intermediate be- barium halides, recrystallization from the aqueous solution tween that of the potassium and cesium systems. and final crystallization from the melt. The chloride was from the bromide and iodide by anion exchange. One of the objectives of the present investigation prepared The very hygroscopic fluoride was not charged to the capsule was to verify the prediction that slightly smaller used for the thermal analysis, but was produced in situ departure from ideality in the bromide compared by the reaction of rubidium metal with chromium difluoride. with the chloride and iodide systems, as observed Small amounts of potassium and cesium, of a few tenths of (1) Operated for the U. S. Atomic Energy Commission by the Union Carbide Corporation. (2) M. A. Bredig and H. R. Bronatein, THIS JOURNAL, 64, 64 (1960), and e.wIlier papera from this Lahoratory.
one mole per cent., were found spectrographically to be present, but because of the similarity of these elements with rubidium are not believed to produce significant effects. (3) J . W. Johnson and M. A. Rredig,
