R. A. ROBINSON, J. M. STOKES AND R. H. STOKES
542
Vol. 65
POTASSIUM HEXAFLUOROPHOSPHATE--AN ASSOCIATED ELECTROLYTE BY R. A. ROBINSON,* J. M. STOKES AND R. H. STOKES Chemistry Department of the Univwsity of New England, Armidale, N.S.W., Australia Received October SO8 1960
The densities, viscosities and conductances of aqueous solutions of potassium fluorophosphate have been determined a t 25 and 50'. Isopiestic vapor pressure measurements have been made a t 25' and the osmotic and activity coefficients computed. The equivalent conductances a t infinite dilution are 132.83 and 203.25 cm.2 int. ohm-' equiv.-' a t 25 and 50°, respectively, and the association constants are 2.42 and 1.43liter mole-'.
Our attention was drawn to the interesting salt, potassium hexafluorophosphate, KPFC, by the work of Randles' on the surface potent,ial of its solutions. 'We have studied some properties of aqueoiis solutions of the fluorophosphate, in particular the conductance and vapor pressure, and have concluded that it exhibits marked association to ion padrs and even higher aggregates.
and 0.1D potassium chloride standards; the equivalent conint. ohm-' ductances of Table I are therefore given in equiv.-'. Frequency-dependence in the range 500-2000 c./sec. was negligible. The conductivity-bridge was a Leeds and Northrup Jones bridge; the cells were immersed in oil thermostats held a t 25 and 50" within &0.002'. The temperatures were checked by a platinum resistance thermometer and may be taken as correct within 0.005'. Volume-concentrations of the solutions (c) were calculated using the above density data.
Experimental
TABLE I
Potassium fl.uorophosphate was obtained from the Ozark- EQUIVALENT COSDCCTASCE OF POTASSIUY FLCOROPHOSMahoning Company and recrystallized from water, using PIIATE AT 25 A S D 60" polythene vessels throughout; for most purposes one reA A crystallization sufficed, but for the conductance measurecm.2 int. x 103, em.* int. c x 103, mole 1.-1 ohm-'equiv.-' n1olc 1. -1 ohin-' equiv.-' ments three or even four recrystallizations were found necessary. In preliminary work, oven-drying of the re25" 25O crystallized material in glass weighing bottles resulted in 46.80 111.93 0.8123 130.04 slight etching of the glass, suggesting some decomposition of 49.86 111.38 1.3889 129.18 the moist mat'erial a t temperatures as low as 80"; this ovendried material gave considerable scatter of data in conduct55.04 110.40 2.5138 127.81 ance measurements. For all the measurements reported in 55.86 110.32 2.5192 127.81 this paper the recrystallized material was dried to constant 69.37 108.05 4.005 126.43 weight in vacuum desiccators over sodium hydroxide. 70.64 107.84 5.672 125.24 Density.-'The following densities of aqueous solutiondl were moasured at 25" 5.854 125.13 84.16 105.93 7.715 124.00 50" m 0.1010 0.1334 0.1901 0.2078 1.01217 1.01840 1.02048 d 1.00860 0.8049 198.81 10.642 122.44 0.3951 0.4121 m 0. :!SO6 1.3764 197.51 14.821 120.65 d 1.02830 1.04062 1.04211 3.969 193.38 14.964 120.57 These data can be represented by 5.621 191.56 15.940 120.24 d == 0.99707 0 . 1 1 5 3 ~-~ 0 . 0 1 3 9 ~ ~ ~ 5,801 191.35 18.292 119.32 7.645 189.73 20.438 118.62 where m is the molality of the solution. Densities were measured at three concentrations a t 50" 10.546 187.44 21.284 118.33 14,829 184.75 30.729 115.63 na 0.1862 0.3482 0.4479 d 1.00834 1.02512 1.03512 18.127 182.06 38.213 113.80 40.14 171.63 Viscosity.-Viscosities of aqueous solutions a t 25" were determined as Vapor Pressures.-Isopiestic vapor pressure measurem 0.11010 0.2033 0.2806 0.38T9 0.4459 mcnts were made a t 25', using sodium chloride as reference n/vO 0.998; 0.99G8 0.9952 0.9925 0.9918 electrolyte; the results are given in Table 11. Two measurements were made a t 50" TABLE I1 nl 0.1849 0,3151 ISOPIESTIC MEASUREXEXTS AT 25"" T h o 1.0019 1.0024 ml m2 mi m2 mi m 2 The saturated solutioii a t 25" was found to be 0.497 A I by 0 2781 0 3240 0 3730 0 4578 0 09001 0 09513 measuring the conductivity of a diluted aliquot and 0.501 M 2903 3426 3777 4651 1363 147'3 by the isopiestic method.* The saturated solution a t 25" has a refractive index identical wit,h that of water as closely 3261 3019 3087 5010 1'717 1055 as could be me:isured with an Abbe refractometer. 11ne 1153 52-40 lte Solutions," Second Edition. Hutterivorths Scientific Publications, London. 1950, p. Y i .
From the density data at 25", the partial molal volume of the salt at infinite dilution is calculated as 68.7 ml. mole-' and if the limiting partial molal volume of the potassium ion4 is 1.50 ml. mole-', that of the hexafluorophosphate ion is 67.2 ml. (4)
R II Stohes and R 4 Robinson
(1Q57).
rriiih
I ' a ~ a d o r /n o *
63, 301
March, 1961
POTASSIUM HEXAFLUOROPHOSPHATE-AN ASSOCIATED ELECTROLYTE
543
mole-I. With the same choice for the potassium ion, the partial molal volumes of the halide ions = are: Tc1-O = 25.31, 7 B r - O = 32.23 and PI-’ 43.S6 ml. mole-l. The PF6- ion is known from Xray studies5 to be octahedral, with a P-F internuclear distance of 1.73 f i . ; taking the vgn der Waals radius of the fluorine atom as 1.22 A., the maximum diameter of the PF6- ion is 5.9 8. h monovalent ion of this size is unlikely to cause appreciable electrostriction of water molecules in its vicinity, and its apparent volume in solution should be near to its actual physical volume. Spheres of 5.9 fi. diameter mould have a molal volume of 64.8 ml. The viscosity results a t 25” can be represented by n/no = 1
+ 0.0057dZ - 0.0286
0.0057 being the coefficient of the Falkenhagen and VernonG term calculated with the ion-mobilities given below. The linear coefficient, -0.028, includes a contribution of -0.007 for the potassium ion7; thus the PF6- ion, in spite of its large size, diminishes the viscosity of water. The small numerical value of the linear coefficient must represent a balance between the “obstruc tive” effect of the large anion and the “structure-breaking” effect on the solvent; that the former must be large can be argued by analogy with the effect of pentaerythritol, with a molar volume of 101 ml., on the viscosity of water, where it has been found8that the coefficient of the linear term is +0.353. The conductivity results (Fig. 1) are typical of an electrolyte showing pronounced ion-pair association, a conclusion which is supported by comparing the activity coefficients (Fig. 5 ) with those of normal 1-1 electrolytes. The method of Fuossg was therefore adapted to determine the values of Ao and the association constant, KA. The FuossOnsager equation for a completely dissociated 1: 1 electrolyte is A, = A’ - Sd/2 EC log c JC where X and E are parameters depending on iiu but not on the ion size and J depends on both R’ and the ion size. A,, is the experimental equivalent conductance corrected for the viscosity of the solution. In the case of very large ions, this correction takes the form of simple multiplication by the relative viscosity, but work in this LaboratorylU on the mobility of ions in solutions of non-electrolytes suggests thzt this is an over-correction for ions of less than 5 A. radius. In any event, it is doubtful if relative viscosities of less than unity can be appropriately used in this way since the argument depends on the u x of Einstein’s equation for the viscosity of a contiiiuum containing spherical obstructions. However, the maximum viscosity
+
0.1
0
0.2
0.3
di. Fig. 1.-Equivalent conductance of potassium fluorophosphate solution a t 25’ as B function of concentration.
+
( 5 ) H. Bode and G. Teufer, Acta Crust., 8, 611 (1955): H. Bode and H. Clausen, 2. anorg. Chem.. 266, 229 (1951); 268, 20 (1952). (6) H.Falkenhagrn and E. L. Vernon, Physik. Z.,SS, 140 (1932). (7) M. Kaminsky, Disc. Faraday SOC.,24, 71 (1957). (8) F. J. Kelly, R. lcIills and J . M. Stokes, J . Phys. Chern., 64, 1448 (1960). (9) R. M. Fuoss a n d F. Accascina, “Electrolytic Conductance.” Interscience Publishers, New York. N. Y., 1959, Chap. 16. (10) J n4. Stokes and R H. Stokes, J . Phys. Chern., 62, 497 (1958); B I. Steel, J &I. Stokes and R. €3. Stokes, ebrd., 62, 1514 (1958). (11) -4. Einstein. Ann. Phys. 19. 289 (1906)
L
0 Fig. 2.-Change
-
L
-
0.01 c, mole/l.
0.02
of h‘ (FA $- Ec log c) with concentration.
effect involved in the present work -vvould be only 0.05% a t c = 0.02, the highest concentration used in evaluating K A from the conductance data. For an associated electrolyte, we have
where CY is the fraction of free ions, c is the stoichiometric concentration, yi is the mean activity coefficient of the ions a t the ionic concentration, ac, and yu is the activity coefficient of the ion pairs (which for the present, we shall regard as unity). The denominator may more conveniently be replaced by c2y2where y is the stoichiometric activity Coefficient, known from the vapor pressure measurements. We then have
R. A. ROBINSON, J. M. STOKES AND R. H. STOKES
544
Vol. 65
suggested by FUOSS, is not in this instance linear at low concentrations. To overcome this difficulty, we write A' - JC = 11" - ( K A Y ~ C ~ ) so that, since J is known as a function of ion size, a plot of the left-hand side against y2cA should extrapolate to Ao with slope KA. In the cases of association discussed by FUOSS, who used the results of Mercier and Kraus12 on tetrabutylammonium bromide in water-dioxane mixtures, the ion size parameter, a, was determined by measurements in mixtures of low dielectric constant and the value so found used to determine J . In the present work we have calculated a from the potassium ion radius of 1.33 A. and the PF6- ion radius which we have taken as 2.67 A., (slightly less than the "maximum1) radius of 2.95 I A. on the grounds that some approaches of the ions 4 could be slightly closer because of the octahedral 129 shape of the PFe- ion). For the resulting ion size parameter, a = 4.0 A., we calculate J = 233 and 334 at 25 and 50") respectively. Values of A' and y2Ac are given in Table 111, which also includes values of hocalculated for each experimental point 128 \ e\ .-by the equation - - - _L __- L _ A" = A' - JC K&Ac 0 0.5 1.o 15 2.0 cy2A. The function (A'-Jc) is plotted against cyan in Fig. 3.-(A' - Jc) us. cy% Teyperature, 2.5'. Fig. 3, where it will be seen that the average deviaThe J function i s calculated with a = 4 A. (upper curve) tion of the points from the straight line does not and a = 5 A. (lower curve). exceed 0.03 A units. Thus me can with confidence use this plot to give Ao = 132.83 cm.2 int. ohm-' An improved equiv.-l and K A = 2.42 liter mole-'. approximation may be made by using this value of K A to calculate true ionic concentrations and reevaluating A', using these in place of the total con202 centrations, but this will not change the value of s K A by'more than 2% and leaves Ao unaffected. The value of K A is, however, quite sensitive to the choice of ion size parameter. Figure 3 includes a 1 201 plot which leads to K A = 3.02 liter mole-' with a u = 5 A., but the fit of this straight line is not quite so good at concentrations above 0.01 M . The value of a = 3 A. was also tried but gave deviations from the straight line several times larger. The same calculation was carried out with the 50" data (Fig. 4) where an ion size of 4 leads to Ao = 0 05 1.0 1.5 2.0 2.5 203.25 cme2int. ohm-' equiv.-l and K A = 1.43 cyzh. liter mole-'. The ratio K A , 5 / K A 5 0 is 1.69. Using I'ig. 4.---(~' - JC) us. C Y ~ Aat 50"; a = 4 A. an ion size of 5 A. at both temperatures the ratio is 1.51; thus there is no doubt that the ratio isclose a = 1 - KACY~ from bhich .ionic concentrations, q = ac, can be to 1.6 even if the correct value of a is somewhat unevaluated once K A is known. The Fuoss equation certain. Hence the mean enthalpy change on association is -4.0 cal. mole-'. Fuoss13 has pronow becomes posed the equation
-
+
>
- '
a.
A = a[AO - S d G
+ Ec, log + JCJ c1
In very dilute solutions where c, = c, this may be approxi mated by A = AD - S ~ CEC log c JC - KACY'A Following Fuoss, we first calculate A' (=A
+ + + Sd/G - Ec log
C)
using as preliminary values of Ao = 132.9 and 203.1 cm.2 ohm-' equiv.-' which give S = 91.22 and 149.47 and E = 49.79 and 83.55 at 25 and 50°, respectively. However, a plot of A' us. c (Fig. 2),
47r K A = -Naaeb 3000
where b = e2/(ekTa)for the molar scale association constant. With a = 4 A., this equation gives K A = 0.97 and 1.03 liter mole-' at 25 and 50", respectively, and the mean enthalpy change would be +0.46 kcal. mole-'. Thus the experimental enthalpy change is not only of different magnitude (12) P.L. Meroier and C. A. Kraus, Proc. Nail. Arad. Sei.. 41, 1033 (1955). (13) R. M. Fuosa, J . Am. Chsm. Soc.,[SO, 5059 (1958).
POTASSIUM HEXAFLUOROPHOSPHATE-AN ASSOCIATED ELECTROLYTE
March, 1961
545
TABLE I11 CALCULATION OF Ao AND K A = AQ - K A ~ p c - = A 4-SdC - EClog c
i';
50'
s = 140.47 E = 83.55 J = 354 ( a = 4 K A = 1.43
0 8123 1 3889 2 5135 2.5192 4 005 5 672 5 854 7 715 10 642 14 821 14 DG4 15 940 18 292
132.77 0.0983 .I63 132.78 132 71 .282 132 71 .282 132.68 ,430 132 74 .585 132 713 .601 132 82 .766 132 92 1.001 133 10 1.322 1.328 133 OD 133.18 1.398 133.24 1.558 hlean Ao = 132.83 f 0.03
132.82 132.85 132.81 132.81 132.79 132.84 132.85 132.87 132,86 132.85 132.81 132.85 132.75
0.8049 1,3761 3.969 5.621 5.801 7.645 10.546 14 829 18.127
A.)
A'
Ay%
n
203.26 203.38 203.59 203.82 203.82 204.15 204.53 205.22 205.72
0.151 ,251 . G68 ,912 ,936 I . 207 1.581 2.099 2.471
203.21 203.28 203.23 203.24 203.23 203.32 203.28 203.27 203.20
103~
Q
Mean ha = 203.25 f 0 . 0 3
but of different sign; this discrepancy may perhaps be due to the neglect of entropy terms in the derivation of FUOSS' equation. The limiting ionic mobilities of the PFs- ion are 59.28 and 91.85 cm.2 int. ohm-' equiv.-' at 25 and 50°, respectively. The (XOvo) product therefore changes from 0.5278 at 25" to 0.5021 at 50": in this respect the ion is intermediate in behavior between the halide ions for which the (Ao vo) product diminishes more rapidly with temperature and the calcium ion for which the product decreases by about 1%. From the isopiestic vapor pressure measurements, the osmotic and activity coefficientsgiven in Table IV were calculated. Figure 5 compares these activity coefficients with those of potassium chlo\ \ 1.7 1 ride and potassium nitrate, and shows that the data b for the fiuorophosphate conform with the limiting \ Debye-Huckel equation up to saturation! In con\ trast with normal salts such as potassium chloride \ and iodide and with the somewhat less associated \ L L 1.6 L ' ' potassium nitrate, the association is so marked that 0 0.2 0.4 0.G it should be possible t o calculate the association VGl. constant from the thermodynamic data alone. For Fig. 5.-The activity coefficient of potassium fluomthis purpose we use the equation phosphate compared with those of potaesium chloride and Y
1
potassium nitrate and with the values computed by the limiting Debye-Huckel equation. TABLE IV OSMOTIC ASD ACTIVITY COEFFICIENTS OF POTASSIUM TABLE VI FLUOROPHOSPHATE AT 25' CALCULATION OF KQ AT 25' Usrsci K A = 2.09 LITER m 0.1 0.2 0.3 0.4 0.5 MOLE-] $ .878 ,829 .795 .763 .735 "Apparent" Y .693 .507 .535 .486 .447 8' m a' KQ K.4
TABLE V CALCULATION OF K A AT 25" FROM ACTIVITY COEFFICIENT DATA kOK
m
Y
Y l
a
(KA/vJ)
0 1 .2 .3
0.6'33 ,597 .535 .486 447
0.774 ,728 ,700 ,681 ,667
0.895 ,820 .764 .714 .670
0.340 .402 .439
.4 .5
.481 ,519
0.1 .2 .3 .4
.5
2.19 2.52 2.75 3.03 3.30
0.0024 ,015 ,028 .044 ,061 UICPF~
K~
=
= (1
~K+~PFC
0.900 .850 .820 .802 ,791
2.4 3.3 2.6 2.8 2.8
- CU)WY~ azrnzyiz
where now we are calculating a molality scale K A . As above, we can reduce this to
E. J. SMUTNY AND A. BONDI
546
log yu = -0.1789m~ci
0.6 -I-
Fig. ~.--KI/-,c
Vol. 65
(omitting higher terms in 1 1 ~ ~ ~ 1 ) . Assuming that quadruple ions are formed, let the concentrations of ion pairs and quadruple ions be denoted by mu and mQ, respectively; then a t a stoichiometric molality m, the concentrations of 0 0.1 0.2 0.3 0.4 0.5 potassium and fluorophosphate ions are each [m 11%. mu - 2 m ~ ] .The relation y = Q: yi,used above, JS. m and the extrapolation t o obtain K A . now becomes y = “,i[cu’ - a@’] Kdrc
=
(1 - a ) / ( m r 2 )
where y is the stoichiometric activity coefficient of where Table IT. Also y = a yi where y1is the mean ionic activity coefficient of the unassociated part,14 which we shall take as given by
a’ == m - mu ~
m
@’=
and
nt,/m
Hence, if quadruple ions are formed, the quantity LY should be replaced by (a’ - 28’) with A == 0.511 liter”? mole-’/2, B = 0.328 liter’/% and 1 - CY‘ 2p‘ mole-‘/7 :md a = 4 A., ie., a fully dissociated but K A (apparent) = my2 uiihydrated electrolyte with an ion size consistent with the physical dimensions of the ions. The details of the calculation are shown in Table V in which only the final stages in the successive approxi- and the equilibrium constant for quadruple ion mations for LY and yI are given. A plot (Fig. 6) of formation is log K-4 YL- against m is a straight line and, since yu -+ 1 as m -+ 0, Fig. 6 gives the limiting value of K.4 as 2.09which is in reasonable agreement with the value of 2.42 from conductanre data. However, assuming that the activity coefficients of both unthe slope of the line implies that log yu = -0.4m. charged species are unity. At first sight, this means a surprisingly rapid Thus 6’ can be calculated from the variation in decrease in the activity coefficient of the ion pairs the “apparent” K A with concentration. These but itornust be remembered that an ion pair with a values of p’ can then be substituted to give KQ. The results of this calculation are given in Table VI. = 4 A. constitutes a dipole of moment 19D which d l interact strongly with both neighboring ions It is evident that the lack of constancy in KA caland neighboriig ion pairs leading to the formation culated from the activity coefficient data by the of triple and quadruple ions. In this connection first method can be explained by assuming a small amount of quadruple ion formation. Similar calwe niighi note that Roberts and K i r k ~ o o d found l~ that the artiyity coefficient of glycine in potassium culations showed that the assumption of triple ions chloride wlution is given by formation was inadequate. We thank the Ozark-Mahoning Company of (14) Ref. 3 p 3 i . Tulsa, Oklahoma, for providing potassium fluoro(15) R &I Roberts a n d J. G. Kirkwood, J . Am. Chem. Sac., 63, 1373 phosphate. (1911).
+
DI-t-BUTYL ETHER : STRAIN ENERGY AXD PHYSICAL PROPERTIES BYE. J. SMGTNY AND A. BOSDI Shell Development Go., Emeryville, California Recezaed October 84, 1966
IX-t-but yl ether was synthesized and several physical properties recorded: the heat of formation, the heat of vaporization, the vapor pressure, density and viscosity. The strain of di-t-butyl ether, consequent to the crowding of the opposed methyl groups, wzts deterniined as q~proximately7.6 kcal./mole.
The synthesis of di-t-butyl ether has remained for several years a vexing and frustrating problem. Many futile attempts have been made. Reboul’ observed that the conventional Williamson technique gave only isobutylene and t-butyl alcohol. Henry2 was no more successful. These early failures led some authors3to point out that it would be (1) E. Rcboul, Compt. Tend., 108, 162 (1888) (2) L Hcnry, R e “ . Irau. chzm , 23, 324 (1904) ( 3 ) W. A Hare and E Mach J A m . Chem SOC. 64, 4272 (1932)
impossible to plac,e two tertiary butyl groups on the same oxygen atom. It was not until the relat,ively unusual met,hods of Erickson and Ashton4 and more recently of Homer5 and of Lamesson and Yang6 that authors claimed success. (4) J. L. E. Erickson and W. Bshton, ibid,, 63, 1769 (1941). ( 5 ) L. Homer, Ann., 691, 138 (1955). ( 6 ) S. Laweswn and N. C. Yang, J . .4m. Chenk. Soc., 81, 4230 ( 1959).
