1070
EDWARD L. KING
controlled potential electrolyses. At higher currents where the output voltage of the potentiostat was inadequate a manually-operated auxiliary power supply was employed. The potential of the working electrode was maintained at 0.70 v. us. Ag, AgNOa. The electrode, which was rotated a t 600 r.p.m. in the Sargent Synchronous Rotator, was a spiral of platinum wire (B. & S. No. 22, apparent area, 6.0 cm.z) wound 1 mm. away from a 6 mm. glass tube. The auxiliary electrode, a mercury pool, was in a compartment separated from the sample compartment by two fritted discs. Resistance between the platinum and reference, and platinum and mercury electrodes, was 900 and 1300 ohms, respectively. Solutions were not thermostated. Current integration was done with the permanent magnet d.c. motor (Electro Methods, Ltd., Caxton Way, Stevenage, Herts, England) using the calibration technique developed by L i n g a ~ ~ eFor . ~ ~ electrolysis of solutions less concentrated than 1 mM a strip chart record of current was obtained and the current-time curve was integrated by weighing the paper. The absence of T P B at the completion of the electrolysis was verified by adding thallium perchlorate t o a small portion of solution. Electrolysis of the supporting electrolyte solution showed that no detectable hydrogen ion was generated by the small residual current -6 All electrodes were cleaned in nitric acid and then immersed in acidic ferrous ammonium sulfate solution to remove oxides. All sample solutions were degassed with nitrogen and nitrogen was passed over the solution during the electrolysis. Spectrophotometric measurements were made with a Cary model 11 recording spectrophotometer. Where necessary, spacers were used in 1 cm. cells so that path len ths of 0.1 and 0.005 cm. were also available. Ifinetic measurements were made by measuring the limiting current at the rotating platinum electrode (at +0.7 v.) as a function of time. Acetonitrile solutions of perchloric acid were freshly prepared for each run. Essentially anhydrous solutions were obtained by diluting anhydrous 1 M perchloric acid in acetic acid with acetonitrile.a4 Solution Analysis.-Two extraction procedures were used t o investigate the electrolyzed solutions. A 2-ml. aliquot portion was added to a saturated aqueous solution of mercuric chloride. This converted all the phenyl boron compounds into boric acid and phenylmercuric chloride,
Vol. G3
the latter being insoluble in water. This heterogeneous system was extracted with 10 ml. of cyclohexane. Biphenyl and benzene are quantitatively extracted under these conditions. Phenylmercuric chloride, while partially soluble in cyclohexane, has a molar absorbance index of only 288 at 258 mpa6and thus its absorption as well as that due to benzene (aa:""@ = 202) can be neglected in comparison with biphenyl (Fig. 7). The fact that biphenyl was the absorbing species in the cyclohexane extract was established by dividing the observed absorbances by the molar absorbance indices for biphenyl. The quotients, apparent concentrations of biphenyl, were constant within 5% over Bhe wave length region 230-270 mp. When a 2 4 . aliquot was treated with 1 M sodium hydroxide and extracted with cyclohexane, biphenyl was again the only strongly absorbing species in the cyclohexane. It was shown by experiment that under these conditions ghenyl diphenylborinate (from oxygenation of triphenyloron) hydrolyzed to diphenylboronite and phenolate ions and thus remained in the aqueous hase. Acidification of the aqueous portion was followed f y another cyclohexane extraction. The diphenylboronous acid quantitative1 extracted into the cyclohexane. The extraction of ptenol under these conditions is not complete. This is of no consequence since the weak phenol absorption in cyclohexane occurs at longer wave lengths than the diphenylboronous acid peak at 240 mp. The identity of the biphenyl and diphenylboronous acid absorption in the two cyclohexane extracts was established in the way described in the preceding paragraph. Benzene was estimated in acetonitrile by carrying out a reduced pressure distillation. The receiver was cooled in a Dry Ice-acetone mixture. After approximately one-half of the 1 5 4 . aliquot had distilled over the distillation was stopped and the volume of distillate was accurately measured. Since the benzeneacetonitrile azeotrope is more volatile than the biphenyl azeotrope it is possible to analyze for benzene spectrophotometrically using the base-line technique t o eliminate errors from background absorbance.
Acknowledgment.-The gift of a quantity of diphenylboron chloride from Prof. M. F. Lappert is gratefully acknowledged. This research was supported in part by the Higgins Fund. (36) G. Leandri and A. Tundo, J . Chem. Soc., 3377 (1954).
(35) J. J. Lingane, Anal. Chim. Acta, 18, 349 (1958).
SOME COMMENTS ON THE VALUES OF ASo FOR IONIC REACTIONS AND THE VALUES OF THE ENTROPY OF SOLUTION OF IONS BY EDWARD L. KING' Contribution No. 2560 from the Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, CaE. Received August 1 1 , 1068
The values of AS0 for certain series of closely related acid dissociation reactions, with a correction applied for the difference of the symmetry numbers of the acid and conjugate base are correlated by equations of the form ASo,,, = a 6A.P. The entropies of solution of the gaseous ions Na+, K+, Rb'+, Cs+, Mg++, Ca++, S r + +and Ba++ are not, however, functions of 22. For the ions of each charge type the entropy of solution is consistent with an equation ASo.,l, = 01 p / r ; the value of p shows no stronger a dependence upon Z than first power.
+
I n seeking a correlation between the standard entropy changes in ionic reactions and some function of the charges 011 the reactants and products, one should consider only reactions with the same value of An, where An is the net increase in the number of solute species in the reaction. The relative values of AXo for reactions with different values of A n can be altered simply by a change in the con(1) John Rimon Guggenheim Foundation Fellow, 1957-1958; permanent address, Department of Chemistry, University of Wisconsin, Madison, Wisconsin. This study was supported in part by the Research Committee of the Graduate School, The University of Wisconsin.
centration scale (Le., by a change in the choice of standard state) .z Laidler3 has correlated the values of ASofor a large number of diverse reactions having variable values of A n with the values of AZ2 for the reaction, where AZ2 is the difference between the sum of the squares of the charges on (2) The failure to take this into account vitiates aome discussions of the values of AS0 in complex ion reactions (e.g., R. J. P. Williams, THIS'JOURNAL, 68, 121 (1954)) as has been pointed out by H. A. (See also A. W. Adamson, J . A m . Chem. Bent, ibid., 60, 123 (1956). Soc., 76, 1578 (1954)J (3) K. J. Laidler, Can. J . Chem., 84, 1107 (1056); J . Chem. Phga., 27, 1423 (1957).
VALUESOF ASo FOR IONIC REACTIONS
July, 1959
the products and the sum of the squares of the charges on the reactants. Scott and Hugus4 have pointed out, however, that the correlation is marred by the variation of An among the reactions considered. It is anticipated that factors other than charge also play a role in establishing the value of So for solute species in water6 and thus in the present paper a possible correlation with AZ2 of the values of ASo for only series of closely related reactions is investigated. Three series of acid dissociation reactions, all with An = 1, do, in fact, have values of ASocora t 25" which conform to the equation ASOoor = a
- bAZa
HnPOp-* = Hn-1P0,n-4 H+ H,Citn-3 = H.-1Citn-4 H+ (CHzNH2)1Hn" = (CH2NHa)zHn-In-'
n = 3,2,1 (A) n = 3,2,1 (B)S n = 2,1 H+ ( C) (CHzC02)zHnn-2= (CH~COz)zHn-l~-* H + n = 2,1
+
+
The values of the parameters a and b for each series as well as the observed and calculated values of AXocor are presented in Table I. The ions in each of these series are large and the total charge is undoubtedly distributed onto several of the peripheral atoms. The correlation of ASocor with AZ2 may be, therefore, somewhat fortuitous since nearby solvent molecules certainly do not see a localized charge of magnitude 2. It appears that there is some inconsistency between the observed correlation of AXOcor for the phosphoric acid dissociation reactions and the equation proposed by Connick and Powellg which correlates the conventional values of the entropies of oxy-anions (HO)mXO,-Z (Le., the values based upon So*+ = 0) with the equation 320
= 43.5
- 46.5(2
- 0.28~~)
I n the dissociation of any oxy-acid (HO)mXOn-'
+
= (HO),-IXO~,-''
+
(2)
+H+
with n' = n 1 and 2' = 2 1, the values of both n and Z increase by one unit. Thus equation 2 predicts a value of ASo = -33.5 e.u. for the acid dissociation reaction of all oxy-acids which are ions. Connick and Powell do not suggest that equation 2 is valid for species with 2 = 0. The observed values of this quantity for the limited number of oxy-acids which are ions (HCO3-, H2P04-, HSOa- and HPOI-) are riot constant but lie in the range -26 to -43 e.u.'O (4) P. C. Scott and Z Z. Hugus, ibid., 2T, 1421 (1957). (5) H. S. Frank and M. W. Evans. ibid., 13,507 (1945). (6) 8. N. Benson. J. Am. Chcm. Soc.. 80, 5151 (1958). (7) It is to be noted t h a t only a series of reactions consisting of three or more incrnbers provides a valid test of the form of equation 1. (8) I t is assumed t h a t , because of the presence of the adjacent hydroxyl group, the first acid dissociation of citric acid, HOC(C€IzC O ~ H ) ~ ( C O I Hinvolves ), the middle carboxyl group. This has relevance in making the symmetry number correction. (9) R. E. Connick and R. E. Powell, J . Chem. Phya., 21, 2200 (1953). (10) K.S. Pitzer, J . A m . Chem. Soc., 59, 2365 (1937).
FOR
TABLEI ACID DISSOCIATION REACTIONS --AS%or
Reactions
a
b
A
-5.5
5.9
B
+0.1
4.9
C
-6.6
4.1
n
Obsd."
3 2 1 3 2 1 2* 1b 2C
-16.8 -29.5 -40.2 - 9.6 -19.8 -29.2 1.5 - 6.6 -17.0 -22.7
l c
(1)
(The ASOcor values being considered are corrected for any difference in the symmetry numbers of acid and conjugate base;6 this correction must be made before the values of ASo are scrutinized for a possible dependence upon AZ2.) The three series of reactions are7
+ +
VALUESOF ASO,,,
1071
valuesCalcd.
-17.3 -29.1 -40.9 - 9.8 -19.6 -29.4 1.6 - 6.6 -14.8 -23.0
Values of ASo,,, are calculated from experimental values of AX0 reported in the papers: phosphoric acid, K. S. Pitaer, J. Am. Chem. Soc., 59, 2365 (1937); citric acid, R. G. Bates and G. D. Pinching, ibid., 71, 1274 (1949); ethylenediammonium ion, D. H. Everett and B. R. W. Pinsent, Proc. Roy. Soc. (London), 215A, 416 (1952); succinic acid, T. L. Cottrell and J. H. Wolfenden, J . Chem. Soc., 1019 (1948). The correction factor to be subtracted from the value of AS0 to obtain ASOoor is R In UA/UB, where UA and U B are the symmetry numbers of the acid and conjugate base.6 These correction factors for the successive reactions in each series are: A, 0.8, -0.8 and -2.8 e.u.; B, -1.4, 0.0 and -2.8 e.u.; C, 3.6, 0.8, 0.0 and -2.8 e.u. Ethylenediammonium ion. Succinic acid.
I n connection with this correlation of values of ASo for the dissociation reactions of phosphoric acid with the value of AZ2, it is of interest to note that Altshullerll has found the values of the entropy of solution of gaseous oxy-anions are a function of Z 2 and not 2.12Couture and Laidlerls have also correlated the "absolute" values of So for oxyanions with an equation involving Z2. The dependence of the values of So for monatomic cations (or the values of ASo for the process M+(g) = M + ( a q . ) ) upon the value of 2 is open to some question and appears to be u n ~ e t t l e d . ~ ~ ~ While Laidler3 is correct in pointing out that, i_n general, a physically meaningful correlation of So u on 2 should involve the "absolute" values of the form qf the equations which have been used to correlate So (or ASOsoln) with 2 and r are such that the use of the conventional ionic entropies (based upon SOH+ = 0) is appropriate in discerning the p-ower to which Z is raised in the correlation of So or ASoso~,, with Z. The various equations which have been suggested for this correlation have in common the incorporation of the dependences upon Z and r in the same term
3
(3)
The value of p ( 2 ) obtained from the correlation with T of ASOsoln for ions of a particular charge does not depend upon the origin with respect to which the values of Soare reckoned. The value of p ( 2 ) which correlates the dependence of ASOaoln of ions of a particular charge upon the radius depends in a critical way upon the choice of radius values (11) A. P. Altshuller, J. Chem. Phys., 24, 642 (1956). (12) Altshullerl' used zzo values based upon &to = 0. If one uses &to = -5 e.u.lsb instead, the correlation of ASosoln with D i s not marred. For the isoelectronic sequence Clod-, so4-2and P O P , the "absolute" value of A ( A S 0 8 0 ~ n ) / A ( Z ~ = ) -10.5 f 0.5 e.u. (13) A. M. Couture and IC. J. Laidler, Can. J . Chem., 35, 202 (1957).
I
20 --
-/ 0
;
second power dependence expected on the basis of the Born equation under the assumption that r is not a function of T.” The approximately first power dependence of 0 upon 2, obtained if the univalent radius values are used, is viewed as fortuitous. The corresponding values of a are
-
July, 1959
THERMODYNAMICS OF ALUMINUM(III) FLUORIDE COMPLEX IONREACTIONS
1073
THE THERMODYNAMICS O F ALUMINUM(II1) FLUORIDE COMPLEX ION REACTIONS. THE GRAPHICAL EVALUATION OF EQUILIBRIUM QUOTIENTS FROM E( [XI) BY EDWARD L. KINGAND PATRICK K. GALLAGHER Contribution from the Department of Chemistry, University of Wisconsin, Madison, Wisconsin Received November 88, 1869
The existing data, Ti( p-]), of Brosset and Orring on the stability of aluminum(II1) fluoride complexes are treated by a newly devised graphical procedure to obtain values of Q. = [AlF~3-"]/[AlF~~~"] [F-1, for 12 = 1 to 5. These Q. values valid for I Y 0.5 are corrected to the ionic strength values of the calorimetric work of Latimer and Jolly and used in interpreting this work to give values of AH, and AS:. These values of AS: corrected for the symmetry numbers of the reactant and products species agree with the values calculated by the equation AS,,, = 12.8 - 2.9A.P with an average difference of 0.4 e.u.
The correlation with AZ2 of the corrected entropy changes in series of closely related acid dissociation reactions presented in the companion paper2 suggests that such a correlation may also exist in complex ion formation reactions. The aluminum(II1)-fluoride complex ion formation reactions
are a n ideal series in which to seek such a correlation for there are equilibrium data by Brosset and Orring3providing AF'n values for the reactions with n = 1 to 5 in solutions of ionic strength 0.5 which can be coupled with the calorimetric data of Latimer and Jolly4to give AH, and AS', value^.^ With n varying from 1 to 5, AZ2 varies from -6 to +2. The calculation of the values of AS', has, of course, been carried out already by Latimer and It is possible, however, to subject the equilibrium dataa to a more careful analysis than has been done. The variation in ionic strength existing in the solutions used in the calorimetric work also makes desirable certain corrections which were not applied in the original paper.4 The present paper deals with a reinterpretation of the equilibrium and calorimetric data to yield values of the equilibrium quotients Q1 to QS for I 0.5; these Q values are corrected to values appropriate for the ionic strength of each calorimetric run before being used to calculate the concentrations of the several aluminum(111) fluoride species present. The values of ASOcor, the entropy change corrected for the change in symmetry number, obtained from this treatment of the data do fit the equation
=
ASo,,,
=
a - bAZz
function of the concentration of fluoride ion in media of ionic strength -0.5 a t 25". With potassium nitrate as the principal electrolyte present, the range of a was 0.49 to 3.29; with ammonium nitrate present, the range of a was 2.23 to 4.65. It is to be noted that with a maximum observed value of fi of 4.65, the value of Q 6 cannot possibly be established with much certainty. The data indicate that different sets of Qn values are appropriate for each of the two media, potassium nitrate solution and ammonium nitrate solution. I n the calculation of the Qn values, Brosset and Orring used six points from the smooth curve of a versus -log [F-] for the potassium nitrate solutions. Use can be made of all the appropriate experimental points in the evaluation of each Qn by a newly devised graphical procedure. The experimental points most appropriate for the evaluation of a particular equilibrium quotient Qa ,are those with (a - 0.9) < fi < (a - 0.1). If such points do not establish the value of Q a , none will, This graphical procedure is suggested by a derivation given below. The general equation for a as a function of [F-] is n=N
( n - E ) [ F - ] " QoQI.. .Qn = 0 n=O
with Qo give
( 1 ) Supported in part by a grant from the U. S. Atomic Energy Commission (Contract A T ( l l - 1 ) - 6 4 , Project No. 3). (2) E. L. King, THISJOURNAL, 63, 1070 (1959). ( 3 ) C . Brosset and J. Orring, Svenslc hem. Tid.,66, 101 (1943). (4) W . M . Latimer and W. L. Jolly, J . A m . Chem. Soc., T 6 , 1548 (1953). ( 5 ) The standard values of A S and AJ', indicated in the present work with the usual zero superscript. correspond to the standard state for solute species being a hypothetical one molar solution of the species in an aqueous solution of ionic strength under consideration.
This equation can be rearranged to
n=a-1
(G n=O
(a
- ) ~ ) [ F - ] ~ - ~ - l & o. Q. n.
+ 1 - Z)QoQi. . . Qn-I
-
(a - Z)Qa
(a
(1)
which has the same form as that which correlates the values of AS',,, for the acid dissociation reactions. The Evaluation of the Equilibrium Quotients.Brosset and Orring3obtained a, the average number of fluoride ions bound per aluminum(II1) ion, as a
= 1.
+ 1 - Z)[F-] + n=N
+
(n - Ti)[F-]"-a-lQoQ1..
n=a+2
(a
.Q,&
+ 1 - Z)QDQI... Q ~ - I
which is the form suggesting the plot for the evaluation of Qa, the values o f Qo, &I! . . and Q a F 1 having already been determined by similar plots. A plot of n=a-1
(Z n=O
(a
- n)[B"-ln-a-'Qo...Qn __
+ 1 - E)QoQI..
.Qa-l
versus (a
(a
-E)
+ 1 -E)[FT
