July, 193s
UNILATERAL TRIPLEI O N FORMATION I N AQUEOUS HYDROFLUORIC ACID [CONTRIBUTION FROM THE CHEMICAL
1609
LABORATORY OF BROWN UNIVERSITY ]
Unilateral Triple Ion Formation in Aqueous Hydrofluoric Acid BY CHARLES BUSHNELL WOOSTER ing conductivity of the triple ion. His conclusions were substantially verified by Davies and Huddlestone through a study of the anionic transference numbers.’ It is the purpose of this paper to present the results of applying equation 1 to the analysis of the conductance curves for aqueous hydrofluoric acid solutions and to compare them with the results which may be obtained by a substantially independent method from the transference data of Davies and Huddleston. The use of equation 1 involves the assumption that only the solute species H+, F-, H F and HF2- and the equilibria HF e H+ F- and HF2HF F- need be considered and that the species F2-- and HzF2 and this equation was applied successfully to the are present only in negligible proportions, if a t conductivity of dilute solutions of the metal all. Since it is probable that the hydrofluoride ketyl, sodium benzophenone, in liquid ammonia. ion owes its existence to hydrogen bridge formaBecause of the unusual character of this electro- tion,8 it is evident that there is no corresponding lyte and also due to the fact that additional justification for assuming the existence of F2---. equilibria must be considered in the analysis of The existence ?n the gaseous state9 of H6F6 sugthis conductance curve in the more concentrated gests the possible presence of H2F2 (or higher regions, it is very desirable to test equation 1 in- polymers) in solution, but the results of the present dependently by applying i t to another electrolyte. analysis decisively exclude this possibility in However, instances of unilateral triple ion forma- aqueous solutioiis of hydrofluoric acid a t contion are relatively rare since they may generally centrations 1 N and less. This result may be be expected t o occur only when some specific inter- interpreted as indicating that HzFz is a very action (formation of a chemical bond) between a strong acid or that the addition of a second proton simple ion and an ion pair is p ~ s s i b l e . ~The only to the hydrofluoride ion greatly weakens the well established instance seems to be in aqueous hydrogen bridge, or both. In Section I11 the hydrofluoric acid solutions where the equilibrium, results obtained from the data on hydrofluoric FHF H F c , was first suggested by Pickj5 acid are applied to the interpretation of the who carried out an analysis of the conductance conductivity of potassium hydrofluoride. data by assuming arbitrary values for the limitI. Analysis of the Conductance Curve
The phrase “unilateral triple ion formation” has been coined‘ to describe the situation in which a single ionic equilibrium of the type, BAB ABz-, is superposed on the customary binary ionization of the electrolyte, AB, and to distinguish this situation from that in which the corresponding equilibrium A+ AB e A2B+, is also involved.2 In a previous paper‘ it has been shown that with suitable approximations the conductance function for unilateral triple ion formation may be obtained in the linear form3
+
+
+
+
+
+
+
( I ) Wooster, THISJOURNAL, 69, 377 (1937). (2) Fuoss and Kraus, i b i d . , SS, 2387 (1933). (3) C is the total concentration in equivalents (as AB) per liter, A is the equivalent conductance, K = [A*][B-]/[AB], the constant for binary dissociation, k = [B-] [AB]/[AB-z], the dissociation constant for the triple ion equilibrium, do the limiting value of A , Xo the sum of the limiting values of the mobility of the triple ion and of the single ion with opposite charge, f the activity coefficient defined by -log f = , 5 ’ A o - ‘ ’ z G and m a mobility coefficient defined as 1 - (1Ao-~/1fi. The constants and ,5’ have the same significance a s i n the paper of Fuoss and Kraus [THISJOURNAL, S6, 47fl (1933)l. In water at 25’ (I = 0.228A.o 59.7 and ,5’ = 0 504; at Oo, (I = 0.22OAo 29.0 and L3 0.486. (4) I t is also conceivable, of course, that coulomb forces alone occasionally may give rise t o a situation which closely simulates unilateral triple ion formation in media of appropriate dielectric constant, if one of the simple ions is much larger than tho other and particularly if the larger ion is unsymmetrical. (6) Pick, Nernsl’s Festschrift, 360 (1912). (I
+
-
+
The conductance data of DeussenlO were chosen as the most reliable of those available and two series ,one a t 25’ and one of probably lesser accuracy a t 0’ were employed in the calculations. In order to apply equation 1 it is also necessary to have independent values of the limiting equivalent conductance, the dielectric constant and the (6) Davies and Huddleston, J . Chem. Soc., 146, 260 (1924). (7) The only other attempt at analysis of these conductance data is that of Kendall [THISJOURNAL, 89, 7 (1917)l on the basis of R more or less empirical equation for “transition electrolytes.” (8) Huggins, J. Org. Chem., 1, 409 (1936). 46, 2183 (1934). (9) Simons and Hildchrand, THISJOURNAL, (10) Deussen, Z . anorg. Chem., 44, 312 (1905).
the dielectric constant of the medium reduces the interionic (coulomb) forces so much that the approximate forms of the Debye-Hiickel--Onsager equativns employed serve adequately to calculate the effective values of the activity and mobility ieficirtits. The applicability of equation 1 t o unilateral triple ion equilibria is also determined by the degree to which the ratio X O ~ A Oapproximates uiiity, siiice this approximation was used to clispose of a second order term in the derivation of the equation. In general, this ratio may not . -" be obtained directly from the conductance data and , X I I the sole available test of 4 4 Ithe validity of this approxii mation may often be the extent to which the linear A . form of equation 1 is satisfied by the data. 111 the 1 present instance, however, additional information is 1 available from two sources. First, the difference be/. . II l I , I tween Xo and .io IS deter01 02 03 0.4 (I t3 00 0i 08 0 c, mined entirely by the difC(1 - A/.io) ference in the limiting moFig l.-Cnilateral triple ion formation in aqueous hydrofluoric acid bilities of the simple anion of least squares to the ten points covering the (F-) and the triple anion (HFB-) which is doubtdilution range 1-512 liters a t 23' the values less so small in comparison with the high mobility 351.5 for the slope and 112.4 for the intercept of the hydrogen ion (351 a t 25' and 229 a t 0') that were obtained and in a similar way a slope of the ratio XO/.\O cannot differ widely from unity. 201.1 and intercept of 71.2 were obtained from Second, the value for the limiting mobility of the nine points a t 0' over the dilution range 1-256 triple anion which may be obtained from the transliters. The lines iii Fig. 1 are drawn in accord- ference data (see Section 11) yields the value ance with these values from which the equilibrium XO = 437 a t 25' so that a t this temperature constants are found to be K = 6.89 X 10 at X g / r \ ~ = 1.08. The maximum alteration in the slope of the plot due to neglect of the second order 25" and 10.95 X 10 at O", k = 0.:320(2 AO/.\o-1) a t !Goand 0.354 ( B X O / A O - 1) a t 0". The term in deriving equation 1 is given in percentage ionization constant obtained a t 2.i' differs very- by 100(1 - X O / A O ) ~ / [ ( " X ~ / A O- 1) (1 - X ~ / A i O ) y / little from that (6.9 X 10- I) obtained by other which on substituting 1.08 for X0/.lo becomes b u t the value at 0' is somewhat O.SjL;.;, and is well within the limits of the experimental errors involved in Deussen's measurehigher than that in the literature" ('3 X 10The excellent agreement with equation 1 at ments. I t may also be noted a t this point that evaluasuch high total concentrations requires some esplanation which is afforded by the facts that due tion of the ratio XO/& permits the calculation o f to the low value of the ionization constants and the k = 0.371 a t 2 5 O and (assuming ho/Ao independent high values of the triple ion dissociation constants12 of temperature as it would be if Walden's rule applies) 0.4 11 at 0'. ( 1 1 ) "International Cntical Tables, ' McCraw-Hill Book Co , Using the slopes and intercepts given above Inc , New York, N . Y , 1829, Vol VI,p. 260 (12) The order of magaitude of k is given by 0.320 a t 25' rrnd 0 354 the conductance curve (A against log V) has been at 0" since the coefficient (PAo/Ao - 1) does not differ widely from calculated as previously described' and the reunitv
Yiscosity. 'Thc values which were used, .io 404, and ,io = 2 3 , i> = ~ h 9, = ~).Oli'Mat 0' , were obtained from a vaof sources h i rlii not differ iri any important respect from the values given 111 thP Interriational Critical Tabies. Hots of f2C.\2/nz2(1 -.\, ,io) against C( i appear in Fig. I where curve I represents values based on the rneasureinents a t 2 3 ' and curve I1 at 0". It i s evident that, in accordance with the requirements of equation i , the points fall very iiearly on a straight line. By applying the method : I
r
-*-
-1-1
( bc
. p l l l l l l l l ~
L.
I
I
l l l l . L l l _ I
1 ~
c
/------
~
1
+
July, 1938
UNILATERAL TRIPLE IONPORMATION IN AQUEOUSHYDROFLUORIC ACID
sults appear in Fig. 2 where the smooth curves represent the calculated values and the circles represent the experimental points. The arrows indicate the limits beyond which the smooth curve represents an extrapolation, the experimental points in these regions not having been used in determiiiirig the slopes and intercepts given. The experimental points lie very close to the calculated curve except in the most dilute region. Due to experimental difficulties in maintaining a constant temperature a t 0” under the conditions of Deussen’s measurements, the data a t this temperature, particularly in the more dilute region, are less reliable than that a t 25’.
11. Analysis of Transference Data By combining values for the anionic transference numbers with those for the equivalent conductances a t various concentrations, Davies and Huddlestonti have calculated the values for the triple ioii dissociation constant and the mobility, L7, of the triple ion which appear in the second and third rows of Table I.
1.o
0.0 Fig. 2.-Conductance
16iI
2.0 3.0 Log curves for aqueous hydrofluoric acid.
v.
Huddleston’s equations13 with the following substitutions: K / f 2 for K114;351 ma for a, and 53 f l z b for b. The figures 351 and 53 represent the limiting mobilities of the hydrogen and the fluoride ions and the m’s are mobility coefficients calculated by the use of the following form of Onsager’s equation for the mobility of an ion of the type j .
TABLE I V
CONSTANTS FROM TRANSFERENCE DATA AT 1 2 4 8 16
k U k corr.
uo
0.212 73.0 0.338 85.6
0.215 68.3 0.338 83.6
0.210 64.9 0.324 83.5
0.199 61.0 0.356 89.C
25”
0.165 53.4 0.340 89.3
32
0.137 47.3 0.288 84.3
It may be observed that Davies and Huddleston’s values of k show an average deviation of 13.7Yu from the mean 0.190 which, itself, is much lower than the figure 0.371 obtained in the previous section. The two values are not strictly comparable, however, since these authors introduced no corrections for the effect of interionic forces on the activities and mobilities of the ions. The effect of this omission is particularly evident in their values for the mobility of the triple ion, which show a lZ.lyoaverage deviation from the mean and a pronounced trend toward decreasing values of 11 with decreasing concentration, whereas the true mobilities of iotis should increase with decreasiiig concc~itratioii. 111 the fourth mid fifth rows o f the table are giveii values of h aiid of the limiting mobility of the triple i o t i , (-’,,, which have heel1 obtained from the Same data by introducing activity and tnohility coefficients. This method of calculatioii uses Davies and
In the present instance this reduced to the following values for the mobility coefficients, ma = 1 - 0.01562/C~andmb= 1 - O.O395-\/Ci. The values for the limiting mobility of the triple ion were obtained from the values, U , of the mobility a t various concentrations also by the use of equation 2 in the reduced form Uo
=
L‘ 1
+ 1.49 6
(3)
- 0.0113-
I t is evident on inspection of Table I that the “corrected” calculations give more consistent values of k (0.331 * 4.9%) and of UO(85.9 * 2.6%) which, unlike U, should be independent of concentration. It is further noteworthy that the value of k from transference data now agrees reasonably well with that obtained substantially inde~endently‘~from conductance data. Al(13) Equation 9 of Davies and Huddlestone (p. 267) is i n error due t o a misprint and should read [I“] =
e- V’(P-
1.)*
-
86K1(aC
-P)
2h Zb ( 1 4 ) Yor the sake of cousistency t h e value 6.89 X 1U 4 was usrtl lor K inctead of t h r figure 7 . 4 X 1 0 - 4 employed hy I>avirs and 11tirI. dleston. I t map also tic noted t h a t their Kz = 1 ‘k (15) I t is true t h a t 1Uo from transfrrence (lata was iised to ohtniil k = 0 371 from conductance d a t a . but thie a p p a r r n t d e p m d e n r r rotild br avoided easily by romparing k = 0.320 ( 2 h o ‘An 1 ) fiom conductance d a t a alone with k = 0 286 (2A0,’Ao -. I ) from transfer^ ence d a t a by t h e “corrected” method of Davies and Huddleston; the direct comparison of t h e k values is more convenient, however.
-
tcltal coticelitration aiid the coiiceIitraticms o f thr several i o i ~ cspecies (iitdicated 1 x 7 the terms in pareiiihesesi hy cquatioii $ I f - 7 4 ~ 1 , (hl - -)
X : $ ~ j f r b ~ -(HF?
-).OwJF-)
111. The Conductivity of Potassium Hydrofluoride Data for the conductivity of potassium hydrofluoride over the dilution range tjO-lOOO liters based 011 the measurements of WaldenL7are given 111 the "International Critical 'Tables'' (p. 251). Since the conductivity of this electrolyte exceeds that of potassium fluoride at correspondiiig coiicentrations, W-aldeii coiicluded that the salt decomposed iiito potassium fluoride and hydrofluoric acid. Although his conclusion appears to he substantially correct a t low concentrations, it was based partly o n the erroiieous assumption that the mobility of the hydrofluoride ioii could not exceed that of the fluoride ioii. In view of the results obtained with hydrofluoric acid in .Sections I and I1 and the fact that potassium fluoride is a strong electrolyte, it is likely that only the following sohate species : E: 1 , H -, F-, FIE'S--, HF and equilibria: HF €I+ 14' -,IiFz-+ H F F-need be considered it1 interpreting the conductivity of potassium Iiytlrofluoride, but this restriction is iiisufficient to permit direct analysis of the data. It is possible, however, to use the equilibrium constarits and mobilities which have been obtained for independent calculations of the equivalent con ductance a t various concentrations. The equivalent conductal ice is related to the
+
+
(18) i n fact, it is probable that B part of the self-eonsiutency of fhr results from transference datnis due to the fact that Davies and Huddleston used values interpolated from a smoothed curve and not the direct experimental measnrztrwnts. T h e Tame values were used in tlle above calrulaiioos it] order t o o b t s i i n results comparable with those of Davie.; and HuiJdleatuii. Sinw the conducttinre data are much more precise than the tran5slerence dnt;i, and since a satisfactory equation for the rondurtaxice c u r v e is n m available, it wonld seem a more advisable prociidure tu use the experimentally rletarmined transference data in couhiriatiou with interpolated (aud where nrcessvry io the concentrated 1-egiun,eutrapolalrd) couduci. ance data. 'l'llia rnetliud applied to the t e n transference measurements in the coilcentration mngt 2 . 3 3 t o 0 327 moles per liter yielded .k = 0.3%; * 5.Y%, LTo = 53 0 * O . l % , irom which it is evident that the results are less self consistent. although the agreement of the mean with the results from the conductance equation is substantially unchanged: k from conductance equation using Ca = 83.0 to calctilate L o i s 0.368. The difference from 0.327 is ll,8Y0 oi the mean. i17) W'llldi-Il, x b/-)' + k [ i i f ' - C](F-) - 2 C k K / j 2 = 0 (9) ( 1 3
by the usual methods, and the other two ionic concentrations by successive substitution in equations 10 and 11 (HY?)
=
(11 )
2
(F-)[2C' - (I: )]'[k f 2 ( l ? , (17 j (w2-) -
+
(10) (1 1)
Using the values K = 6.89 X k = 0.368, the following results were obtained a t C = 0.0200: (F-) = 0.1~2007, (HF2-) = O.OO098, (H+)= 0 00103, (HI') = 0.01797 and -2 = 136.0; the observed value o€ .I is l 3 q At lower concentrations decompositioii of the hydrofluoride ion is so great that the solution of the cubic equation becomes too sensitive to the value of k to be useful. X better approximate calculation of A is then obtained by setting (HIT2--) = 0, so that the other ion concentrations are given by equations 12 and 13 if
= (
+ + (Fr
- _.___-___
+
1
K,'f2j*
+ 4RC/J? (12)
(13)
The complete results are given in 'Table 11. It is unfortunate that data are not available a t higher concentrations where the triple ion equilibrium plays a inore important part, although it is true that at much Q h e s ion EOUceutratioiis the interioiiic coulomb forces will
July, 1988
INFLUENCE OF DIELECTRXC CONSTANT ON IONICREACTIONS
TABLE I1 THE CONDUCTIVITY OF AQUEOUS POTASSIUM HYDROFLUORIDE AT 25 '
c A exptl. A calcd.
yo Dev.
0.020 0.006 0 . m 5 0.002 0.001 138 150 167 217 270 136.0 163.3 169.fi 217.7 265.5 1.45 8.87 1.56 0.32 1.67
complicate the analysis. The relatively large deviation at C = 0.006 is, of course, due to the error introduced by neglecting the concentration of the hydrofluoride ion; at lower concentrations this error becomes of less importance.
JOINT
CONTRIBUTION FROM
THE
1618
Summary It has been shown that the conductance function for unilateral triple ion formation applies satisfactorily to the conductance data for squeous hydrofluoric acid a t 25 and a t 0'. The constants determined in this way are consistent with the substantially independent values which may be obtained from transference measurements and they may be employed successfully to calculate the conductivity of potassium hydrofluoride solutions. PROVIDENCE,
RECEIVED APRIL20, 1938
R. I.
CHEMISTRY LABORATORIES OF CANISIUSCOLLEGE AND MARYLAND]
OF THE
UNZVERSITY OF
The Critical Increment of Ionic Reactions. 111. The Influence of Dielectric Constant and Ionic Strength BY JAMES LANDER'AND W. J. SVIRBELY KecentlyJ2 equations were derived which predicted the influence of dielectric constant and ionic strength upon the critical increments of ionic reactions. The critical increments obtained by means of the theoretical equations were then compared with the experimental critical increments obtained for the reaction between ammonium and cyanate ions in methanol-water mixtures of constant dielectric constants. In the present investigation, the same reaction was studied over a temperature range of 30 to 60' in mixtures of water with ethylene glycol a t the fixed dielectric constants of 63.5, 60, 55, 50, 45 and 40 in order to observe if there would be any specific medium effects due to the use of a different solvent. The experimental critical increments were then compared with the values obtained by means of the theoretical equations.* Experimental The ethylene glycol used was Eastman Best Grade (Highest Purity). The glycol was distilled and the fraction boiling sharply a t 197' (uncorr.) was used. All other materials were prepared or purified as described in previous papers3 which also describe the procedure used in this investigation. ,411 temperatures were checked (1) From the thesis presented to the Graduate Committee of Canisius College by James Lander in partial fulfilment of the requirements for the degree of Master of Science, June, 1938. (2) (a) Svirbely and Warner, THIS JOURNAL, 87, 1883 (1935); (b) Svirbely and Schramm, i b i d . , 50, 330 (1938). (3) (a) Warner and Stitt, i b i d . , 65, 4807 (1933); (b) Warner and Warrick, i b i d . , 57, 1491 (1935).
against a thermometer calibrated by the Bureau of Standards. Thermostat temperatures were maintained constant within f 0.01'. Dielectric constants for glycol-water mixtures were taken from the work of Akerlof.4 Average values of the limiting velocity constants were determined by means of the equation3b,2 k a t = { 1+4A
