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 TL = 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 quo0.5; these Q values are cortients Q1 to QS for I rected 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) < FZ < (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
EDWARD L. KINGAND PATRICK K. GALLAGHER
1074
4
I-
s x 2 R
0 2
0
x x 10-3.
4
Fig. 1.-The graphical evaluation of Qa which is the slope of this plot of
versus
X -
the method described in this paper are derived from the original data by a relatively laborious calculation, the advantages of the present method justify the labor. The principal advantage of the present method is simply that in each plot one uses only the data which are relevant to the establishment of the Qn under consideration. The stepwise reaction forming AlFZ3-" corresponds closely to the principal equilibrium in the solutions with a &%(a - 0.5) and thus it is obvious which of the data are relevant. I n Fig. 1 is presented a typical plot, the one having a slope which is the value of Q3 in potassium nitrate medium. I n Table I are presented the Qn values obtained by this treatment. The average difference between the observed values of ft and the values calculated using the Qn values obtained in this paper is 0.019 for the 16 points in potassium nitrate solution and 0.036 for the 19 points in ammonium nitrate solution.
2.37.
&I
&a &a Qd
3.7 X l o 3 4 . 4 X 10' 2 . 9 X 10'
1.46 X 1.13 X 8.2 X 5.1 X (2.9 X
lo6 lo5
lo3 lo*
Brosset and
Orring smoothed values'
1.36 X lo6 1.04 X lo6 7.17 X IOa 5.50 X 10' 4.26 X 101
QS will be a straight line if the third term on the right&e (1.1Y 2.94 hand side of the equation is negligible; the slope of These correspond to potassium nitrate solution. Very this line is the value of Qa. I n making such a plot, uncertain value. there is little point in using fi values less than -(a - 1.2) or greater than :(a - 0.1). If at the highThe Correction of Qn Values for their Dependest concentration of fluoride ionbeing considered,ie., ence upon I.-Latimer and Jolly4made calorimetric at Ei (a - O . l ) , the species of composition measurements upon solutions of ionic strength A~F,+:;", AlF;.,, ... are not present at significant ranging from -0.016 to -0.20. They used the Qn concentrations, the condition for linearity is satis- values derived by Brosset and Orring from smoothed fied. Although the value of is obtainable from data a t I S 0.5 without correction. Of the tacit asthe intercept in this plot, the experimental points sumptions in this procedure, (a) that the distribumost relevant to establishing the value of Q&l have tion of aluminum(II1)-fluoride species is not a funcnot been used; it is preferable to use a different plot tion of the ionic strength and (b) that the dependfor the evaluation of each Qn. ence of the AH values upon I is small compared to A number of methods have been proposed for the experimental uncertainty, certainly the first is the determination of Qn values given R ( [X]).6.7 not justified. It is difficult, of course, to predict Some of these have been reviewed and compared by the exact dependence of each Qn upon I. I n the Sullivan and HindmanGaand by Rossotti and Ros- present work it is assumed that the dependence of sotti.60 The latter authors have also proposed a log Qn upon I is a function of the value of (AZz)n, graphical procedure somewhat related to the present the difference between the square of the charges on one but which leads to values of the over-all equi- the products and reactants in the nth reaction. The librium quotients, @n = [MX,,]/[M] [XI". Such relationship equilibrium quotients correspond to reactions which are not, except for n = 1, the principal equilibria existing in any of the solutions. It is difficult, therefore, to decide which of the experimental with a = 6.80 nicely correlates the dependence of points are particularly relevant in the establishment Q = [CrNCSf+]/[Cr+++][SCN-] from I = 0.016 of a particular Qn. While the functions plotted in to O.Ba8 The Davies equationg
(6) (a) J. C. Sullivan and J. C. Hindman, J. Am. Cham. Soc., 74, 8091 (1952); (b) G . Scatchard, method presented in the paper: J. T. Edsall, G . Felsenfeld, D. 8. Goodman and F. R. N. Gurd, ibid.. 76,3054 (1954); (c) F.J. C. Rossotti and H. S. Rossotti, Acta Chem. Scand., 9, 1166 (1955). (7) J. 2. Hearon and J. B. Gilbert, J. Am. Chsm. Soc., 77, 2594 (1955).
*
Ii 20 . 5 Y C a l c d . in this paper----. NHdNOa KNOI soh. aoln.
- %)IF-]
The values of Q1and Q2 have been obtained previously from analogous plots. The points shown in this figure are, from left to right, for 5 values of 2.94, 2.80, 2.66, 2.58, 2.49 and
.
TABLE I THEVALUESOF THE EQUILIBRIUM QUOTIENTS FOR ALUMINUM(III) FLUORIDE COMPLEX ION FORMATION REACTIONS AT 25"
(3 - ii) (4
Vol. 63
has also been much used, although generally only to ( 8 ) C. Postmus and E. L. King, THIE JOURNAL, 69, 1208 (1966). (9) C. W. Davies, J. Chem. Soc.; 2093 (1938).
*
&
July, 1959
THERMODYNAMICS OF ALUMINUM(III) FLUORIDE COMPLEX IONREACTIONS
a lower maximum value of I . The values of (Q/ K o ) l / A zazt I = 0.5 calculated by each of these two equations differ by a factor of two. The plot of log y* for sodium chloride versus I lies between the plots of ( 1/AZ2) log &/KO versus I calculated using each of the two equations. This plot of log (Y&)NaCl versus I is assumed to give the ionic strength dependence of (l/AZ2)log Qnfor each of the aluminum(111) fluoride reactions. The Calorimetric Evaluation of AH,.-Each Qn value was corrected by the means just outlined to the ionic strength of the final solution in each of the calorimetric runs; these Qn values were used to evaluate the distribution of aluminum among the several forms. The QI values from the potassium nitrate series were used for the calorimetric runs carried out in sodium fluoride solution and the Qn values from the ammonium nitrate series were used for the runs carried out in ammonium fluoride solution. Latimer and Jolly reported the results of eleven calorimetric experiments for which the values of of the final solutions, calculated using the corrected Q n values, were 0.217, 0.738, 1.34, 1.91, 2.96, 3.16, 3.58, 4.05, 4.67, 4.93 and 4.94. In the last two solutions, the calculated extent of formation of AlF6-3 is approximately 10%. Certainly little confidence can be placed in any value of AH6 obtained from considering the results of these two experiments. Whether one considers the eleven experiments and six unknowns, AH1 through AH6, or the nine experiments (with Q 4.67) and five unknowns, AH1through AHs. has little effect on the calculated values of AH1 through AHs. The value of AH6,which is the most affected, differs by 0.3 kcnl. in the two treatments. The simultaneous equations have been treated by the method of averages; in this treatment, it is assumed, of course, that the value of AH, for each n is independent of the ionic strength. The values of AH1 through AH5 derived in this manner from Latimer and Jolly's calorimetric work are presented in Table 11. Using these AH, values and the corrected Qn values, one calculates values of the net heat absorbed per mole of aluminum(II1) which differ from the observed values by an average of 36 cal. These values of AHB do not differ greatly from those reported by Latimer and Jolly; the largest difference is 390 cal. in the case of n = 5 . Results and Discussion The calculated AH, values have been coupled with AF; values calculated from the Qn values corrected to I = 0.07, a value in the middle of the ionic strength range of the calorimetric studies, to allow the calculation of AS; values; these AS: values are assumed to be appropriate for an aqueous solution with I = 0.07. The Qn values from Table I which were corrected to I = 0.07 were for n = 1,2, and 3, the values obtained from the studies on potassiuni nitrate solution, for n = 4, the average of the values obtained in the two different media and for n = 5, the value obtained from the studies on ammonium nitrate solution. A list of the derived thermodynamic quantities is given in Table 11. Before scrutinizing the values of ASo for a possible dependence upon the value of AZ2, it is necessary that they be corrected for the symmetry
1075
TABLE I1 THERMODYNAMIC QUANTITIES FOR THE REACTIONS AlF22-4;" . - + F- = AlF.+'-" (A@ + Calcd. T-25O
n
AFo,
kcal.
A H , bI = 0.07aA S 0 , C
kcal.
e.u.
R UR).d In UP/ ea.
Avalue s o (COP.) of
ea.
-9.02 S1.06 33.8 30.2 30.2 -7.32 0.92 25.8 24.4 27.6 .I8 19.2 18.6 18.6 -5.54 .04 -3.66 12.4 13.0 12.8 -1.82 -36 4.9 6.7 7.0 See text for discussion of the as~umeddependence of &, values upon I . b The values of AH presented by Latimer and Jolly4 for n = 1 to 5 are 1.15, 0.78, 0.19, 0.28 and -0.75 kcal., respectively. The values of A S " presented by Latimer and Jolly4 for n = 1 to 5 are 32,26, 18, 13 and 5 e.u., respectively. The entropy change corrected for the change of symmetry numbers of the reactant ( U R ) and product ( U P ) . 1 2 3 4 5
-
number factor in the value of ASo; this is equivalent to considering the so-called intrinsic value of the equilibrium quotient. lo In. making this correction, it was assumed that all of the aluminum species are octahedral AI(OH2)B-n F,f3-n,with the relative amounts of any geometrical isomers being dictated solely by statistical considerations.l' These values of AS",,,are nicely correlated with equation 1 with a = 12.8 and 2, = 2.9. For reactions with n = 1 to 5, the average difference between the observed and calculated values is 0.4 e.u. (There is very poor agreement in the case of the reaction with n = 6 but, as has been stated, the experimental data tell us very little about this reaction.) The observed correlation of A S " c o r with AZ2 neither confirms nor denies that a contribution to the value of ASo is that due to the replacement of tl water molecule by a fluoride ion as suggested by 15.6 Latimer and This contribution, e.u., is the same for each step and thus does not influence the value of b. .It is to be noted that the approximate symmetry in the residual charge effect upon ASo, as calculated by Latimer and Jolly, is somewhat fortuitous since these reactions are ones in which An # 0; the actual values of ASo for such reactions depend upon the arbitrary choice of standard state. This correlation of AS",,, with the value of AZ2, like t,he similar correlation in the companion paper, is somewhat surprising since the net charge on the
+
(10) S. W. Benson, J . A m . Ckem. SOC.,80, 5151 (1958). (11) I n the cases of cis- and ~ r a n s - C r ( O I ~ z ) , ( ~ C Sand ) z + Cr(OI1a)dCln+, the trans isomer is present in an amount -2 times that expected statistically (J. T. Hougen, K. Schug and E. L. King, ibid., 79, 519 (1957); E. L. King, Sr. M. J. RI. Woods, 0. P. and H. S. Gates, ibid.. 80, 5015 (1958)). In the case of cis- and trans-Cr(OHz)dFz+, the Ivanisomer is present at a relative concentration - 1 . 6 times that expected statistically (E. L. King and Y. T. Chia, forthcoming publication). The nuclear magnetic resonance study on aluminum(II1)-fluoride complexes suggests that one or the other of the two isomers of difluoroaluminum(II1) ion is present predominantly (R. E. Connick and R . E. Poulsen, ibid., 79, 5153 (1957)). If the predominant isomer of diRuoroaluminum(II1) ion is the cis isomer, the appropriate correction for the symmetry number change is very similar to the value given above. For R = 2. the correction would be - 1.4 e a . rather than the - 1.8 e.u. calculated under the assumption of statistical distribution. On the other hand if the predominant isomer is the trans isomer, the correction would be f1.4 e.u.: if this were the true nituation, the correlation of ASooor with AZS would be less striking. The question of the distribution of bomers also exists for trifluoroaluminum(II1) and the correlation of all of the reactions would necessitate information regarding its isomeric composition.
.
CONWAY PIERCE
1076
polyatomic aquofluoroaluminum(II1) species is undoubtedly spread out over the peripheral atoms. Whatever the cause of the correlation, its existence is unmistakable. The validity of equation 1 does raise a question regarding the proposed correlation
of
Vol. 63
Sovalues of complex ions with the first power of
z.12,13
(12) J. W. Cobble, J. Chem. Phys., 21, 1446 (1953). (13) P. George, G. I. H. Hanania and D. H. Irvine, ibid., 22, 1616 (1954).
EFFECTS OF INTERPARTICLE CONDENSATION ON HEATS OF ADSORPTION AND ISOTHERMS OF POWDER SAMPLES BY CONWAY PIERCE Department of Chemistry, University of California, Riverside, California Received November I , I968
Additional heat of immersion measurements for graphite in benzene confirm a previous conclusion that there is extensive capillary condensation in voids between particles when powder samples adsorb vapor at high relative pressure, Heats of adsorption, computed from heats of immersion, show that beyond the first 2-3 layers practically all the net heat is due to destruction of film surface as the interparticle spaces fill. The contribution of capillary condensation to nitrogen adsorption isotherms for powders is measured by comparing isotherms with an ideal isotherm which gives that part of the adsorption 130 due to multilayers on the free surface. The ideal isotherm follows the equation ( V/Vm)2.76= -a t all relative pres10gPolP sures above 0.2. The ideal isotherm is applied to experimental data to ( I ) determine surface area, independently of a BET plot, ( 2 ) evaluate the contribution of inter article condensation to the isotherm, (3) measure the adsorption in small pores that fill at low relative pressure and (4)expfain abnormalities in isotherms of graphite samples whose surfaces are exceptionally homogeneous. Studies of many powder sample isotherms show that interparticle condensation normally occurs, to an extent determined by the size and shape of particles and their tightness of packing.
It was shown in a preceding publication2 that when a powdered graphite sample is equilibrated with benzene vapor there is capillary condensation in the voids between particles. The evidence for this is that the area of the liquid film surface adsorbed on the particles is only 15% the area of the dry powder. The powder used in the preceding study had been prepared by grinding and nothing was known about the particle size distribution. It was felt desirable, therefore] t o repeat the measurements using a sample of known particle size. The one selected was a graphitized carbon black prepared by the Cabot laboratories,*designated as Elf 4(2700°). Electron microscope studies4on the original black have shown that the particles are spherical and quite uniform in size, with an arithmetic mean diameter of 260 A. The nitrogen area before heating is 120 m.2/g. After heating the area is 85-100 m.2/g. Details of the calorimetric measurements have been described.2 Results are shown in Fig. lA, which gives the heat of immersion per gram as a function of the weight of benzene preadsorbed. These data show that for this sample also there is capillary condensation between particles, as previously observed for two other powder samples. It appears, therefore, that such condensation is normal for adsorption by powder samples. Effects of Interparticle Condensation on Heat of Adsorption.-As discussed in the preceding paper2 the heat of immersion for a dry sample is the sum of three effects, first noted by Harkins and Jura.6 (1) Presented at Symposium on Energetics of Surfaces and Interfaces, 134th National Meeting, American Chemical Soaiety. (2) C. Pierce, J. Mooi and R. E. Harris, THISJOURNAL, 69, 655 (1958). (3) Provided through courteay of Drs.
W. R. Smith and W. B. Spencer, Godfrey L. Cabot, Inc., Cambridge, Masaacliusetts. (4) “Cabot Carbon Blacks Under the Electron Microscope,” Godfrey L. Cabot, Ina., 1953.
H,
=
E
- EL +-
He
(1)
where H , is the heat of immersion, E - EL is. the integral net heat of adsorption and H , is the heat due to destruction of the adsorbed film when immersed in bulk liquid. H , is the product of the film area by the unit enthalpy of the surface. It follows from (1) that H , for a sample equilibrated with vapor at p o can be used to measure the area of the adsorbed film. When there is no condensation between particles the area so measured is that of the dry surface (plus a small correction for the thickness of the film). Harkins and Jura5 used this relation to make an absolute measurement of area for an anatase powder. This absolute method cannot be used when there is capillary condensation between sample particles. As shown in Fig. l A , H , for this sample is 0.63 cal./ g. when 0.6 g. of benzene has been adsorbed. Converting to ergs and dividing by the enthalpy6 of benzene gives an area of 39 m.2/g., less than half that of the dry powder. If there were no condensation between particles the H , curve of Fig. 1A should level out as indicated by the dotted line. The value at saturation should be the enthalpy-area product (an area of 85 m.2/g. was assumed). I n the region where the dotted line first leaves the experimental values it represents an estimate only, based on the HarkinsJura results for a sample that had little or no interparticle condensation. The difference between H , for a dry sample and one for preadsorbed vapor is the integral net heat of adsorption for the amount of vapor adsorbed. This relation is used to replot the data of Fig. 1A as heats of adsorption, Fig. 1B. The upper curve shows experimental values and the middle curve (5) W. D. Harkins and G. Jura, J. Am. Chem. SOC.,66, 919, 1362 (1944). (6) F. E. BarteU and R. M. Suggitt, THISJOURNAL, 68, 36 (1954).
