ALES~ANDRO D' APRANO
2920
Association of Alkali Perchlorates in Anhydrous Methanol at 25 o by Alessandro D'Aprano l.netitufe of Phymkal Chemistry, University of Pdermo, Pdermo, Italy
(Received M a y 22, 1978)
Equivalent conductance of alkali metal perchlorates in anhydrous methanol at 25" are reported. The Ka values have been determined by a new conductance equation including terms of order c"2, and contrary to a previous 1959 analysis, association has been found for all the perchlorates (including lithium and sodium). From z1 comparison of the association behavior of alkali perchlorates in different pure solvents in the range of dielectric constant between 80 and 30, the influence of cation solvation and the protic properties of solvent on the association process are considered.
Introduction A previous analysis of conductance data for lithium,I sodium,* potassium,2 and cesium3 perchlorate in anhydrous methartol by the Fuoss-Onsager conductance equation4z5 indicated that lithium and sodium perchlorates arc unamociated electrolytes. Recently, the association of alkali perchlorates has been found in waterG by a new conductance equation, including terms of order c''. Owing t o the electrostatic nature of ion pair formation, these results are in disagreement; due to the lowcr di.e!iectricconstant, in fact, the association of alkali perchlorate in methanol (D = 32.66) should be at least one order of magnitude greater than in water (D = 78.35). I n order to investigate if the lack of association found for LiC104 and the I\'aC1o4 in pure methanol was due to the mathcmaticsl approximations of the FuossOnsager previous t r e a t m ~ n t ,a~ new , ~ analysis of 1959 conductance clata1t2has been made by the new equaThe liniiting conductance values obtained from this new ana1:isis agree within 0.01 A units with those derived by th(: 1gtW .treatment, while the more realistic Values Of KA(.[J~C~O~:I = 14, KA(NaC104) = 19, KA(Kc10,) = 34, cud KA(CsC104) = 54 were obtained for the associatiort constants. the series of alkali perchlorates, the conductance of' rubidium perchlorate has been measured and t)he conductances of lithium, sodium, potassium, and cesium perchlorates were also redetermined in a concentration range below cmnx< D 3 X lo-', the critical concentration above which it is impossible t o assign uniyue partncrs bo ions to form pairs.' The resulting association sequence KA(LiC104) < KA(XaClO,,) .: liA(:KC10,) < KA(RbC104) < K ~ ( c s Cl0.J found f~ thc alkali perchlorates in methanol at 25' is in full iigrecment with that previously found6 in pure water, where the alkali metal cations are assumed to be er-t;ensivt:lysolvated. Experimental Section R4ethanol rvas rofluxed over AgN03 for 24 hr t o remove tracer of aldehydes or ketones, and then disThe . I b u r d of Physicul L'hemistru, Vol. 76, No. 20,1972
tilled in a closed system into a flask containing some magnesium turnings and traces of I,. After a further 24-hr refluxing it was fractionally distilled. All outlets to the air were protected by drying tubes. The middle cut wae used. Specific conductance was less than 2 X lo-* ohm-' cm-' and the amount of water, tested by Karl Fisher rcagcnt, was less than 0.01%. The anhydrous methanol was used immediately after distillation. A viscosity* of 0.5445 cP and dielectric constttntg of 32.66 were used in the calculations. Reagent grade perchlorates were recrystallized three times from conductivity water ( X O = 1-2 X ohm-' cm-I) and dried by heating under vacuum for 4-6 weeks at 150". The dried salts were litapt in a desiccator containing P205. Full details concerning electrical equipment and general technique have been outlined rlsewhere.l0 The cell used wm an erlenmeyer-type cell with an unplatiniaed electrodes and with a constant of 1.6698 cm-' determined by the Lind-Zwolenick-14xm method" using aqueous solutions of potassium chloridci. Conductance runs were made by the concentration method. I n order to test if the dried salts used were water free, two runs were made in dry methanol for each perchlorate after keeping the salts under vacuum (150") for 4 and 6 weeks, respectivrlj . The experimental values of the cquivalcnt conductance of alkali perchlorates in anhydrous methanol a t 25" are given in Table 1,12 where A is the equivalent (1) F. Accascina and G. Craia, Sci. Tec., 3, 11 (1959). (2) F. Accascina and G. Craia, ibid., 3, 203 (1959).
(3) F. Conti and G. Pistoia, J . Phys. Chem., 72, 2245 (1908). (4) It. M. Fuoss and L. Onsager, ibid., 62, 1839 (1958). (5) R. M . Fuoss, J . Amer. Chem. SOC.,81, 2059 (1959). (6) A. D'Aprano, J . Phys. Chem., 75, 3290 (1971). (7) R. M. Fuoss, J . Amer. Chem. Soc., 57, 2604 (1935). (8) G. Jones and 13. J. Fonwalt, ibid., 60, 1683 (1938). (9) L. J. Gostin and .'1 S. Albright, ibid.,68, 1001 (1946). (10) F. Accascina, A. D'Aprano, and It. M .F'uous, ibid., 81, 1058 (1959). (11) J. E. Lind, Jr., J. J . Zwolenick, and I1 M. E'uoas, ibid., 81, 1557 (1959).
292 1
ASSOCIATION OF ALKALIPERCHLORATES
conductance (ohm- cm+ equiv-l) an c the concentration (equiv/l.). All the conductance data including the previous 1959 datal-j were analyzed by a new conductance equation6 in order to find the conductance parameters .lo, KA,and 6. All the calculations were made on an T'XIVAC 1108 computer. Full details concerning the new equation and the scarch program have been rc.ported in a previous papereG The results of thc computer analysis are summarized in Table I1 whrre the various runs made in the present ~ o r karc identified by the number givcn in Table I, while the 1959 data by the letters. ~
~
Table 11: Derived C o n s t a n t s
A = Ao - S d G
Run
:LiC104
1
2 aa
NaC104
3 4
bb
KC104 IlbC10, CSClOc
5
6 cb 7 8 9 10
dc See ref 1.
KA
A0
110.58 2Z 0.002 13.68 2 0.01 1 1 0 . ~ ~ 8 i O . 0 0 13.662Z0.01 0 110.37 i 0.003 13.71 3~ 0.03 1 1 6 . 3 2 f 0.002 1 8 . 9 6 i 0.02 1 1 6 . 3 2 2 ~0.002 1 8 . 9 6 i 0.02 116.29 ct 0.004 1 8 . 7 0 i 0 . 0 4 123.15 f 0.001 3 4 . 2 2 f 0.01 1 2 3 . 1 6 f 0.001 3 4 . 3 0 i 0 . 0 1 1 2 3 . 1 6 f 0.002 34.25 i 0 . 0 2 1 2 7 . 0 1 1 0.008 4 4 . 1 9 i 0 . 0 9 1 2 7 . 1 2 i 0.007 4 4 . 9 6 i 0 . 1 0 131.57~k0.02 83.80i0.15 1 3 1 , 5 5 3 0.01 ~ 53.6Ozt0.16 131,5#ct 0.01 5 3 . 8 3 i 0 . 1 0
* See ref
2.
c
d
6
7.9 7.9 7.9 6.4 6.4 6.4 4.1 4.1 4.1 3.4 3.4 3.1 3.1 3.1
0.004 0.002 0,009 0.006 0.004 0.01 0.004 0,005 0,005 0.03 0.04 0.04 0.05 0.03
See ref 3.
Discussion From inspect)ion of the results given in Table 11, notc that all the perchlorates (including lithium and sodium) examined in the present work are associated in anhydrous methanol a t 25". The disagreement of this results from the 1959 analysis's2 can be easily explained considering the diff erences between the eciuations used. The linearized form of the Fuoss conductance equation5 WP
A = A0 - Sl/Cy
+ E c log ~ CY
+ JCY - KACTf'A
A0
- Rl/c
+ EC log c + J C
c log ~ CY
+ J c +~ (3)
The 1967 Fuoss-Hsia equation used in thc present work is a recently revised version including some variation on the lower limit of integration of the function describing the relaxation terms, the usc of a more complete Debye-Huckel expression for thc activity coefficient of free ions, and several other changw prctviously6 reported. As shown by t'he results obtained in the present research, the use of the now equation leads to much more reliable values of KAfor electrolytes in solvents with intermediate dielectric constants and demonstrates the influence of terms of the order c3'12 on the association of these systems when dcrivcd by numerical analysis of conductometric data. Alkali perchlorates have been invcstigated so far by several authors in various solvent of high or intermediate dielectric constant, such as, acetonitrile,15t16and ~ulfolanc.'~I n order t o have a complete set of specific information derived from each system, all these data have been reanalyzed by eq 3 used in the present research. The results of the computcr analysilj for all the systems examined are summarized in Tables 111, IV, and V where all the symbols have the usual mcaning. As may be noted in Tables 11, 11.1, IV, and V, for each solvent considered the association of alkali perchlorates increases as the cation crystallographic radii
(1)
or the simplified" A =
+E
J2c3/'y3I2- KACyf2A
Eleotrolyte
was found to be too drastic, especially for 1: 1ionophores in solvents with intermediate dielectric constants. Thc anomalies accumulated in the litcrature for these systems using eq 1 and 2 have been examincd recently by Justice.13 I n particular for thc association constant, the KA values derived from eq 1 must at least include all the effects due t o tcrms higher than those linear in concentration which were not considcred in the arbitrary truncated integration. Recently the entire problem has bectn reexamined by F ~ o s s and ' ~ the arbitrary cutting of terms in concentration has bcen reduced by a now integration of the equations of continuity and motion, this time rvith retention of terms of order c3". The resulting equation can be put in the form
(2)
for an unassociatcd electrolyte, which have been used previously to analyze sodium, potassium, lithium, and cesium perchlorates conductance data, were obtained by retaining terms through those linear in concentration in the intcgration of the differential equation which describes the relaxation field. This approximation, made in order to simplify thc form of the equation,
(12) Table I will appear following these pa-cs in the microfilm edition of this volume of the journal. Single copies m a y be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 1155 Sixteenth St., N.W., Washington, D. C. 20036, by referring t o code number JI'C-72-2920. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche. (13) J. C. Justice, Electrochim. Acta, 16, 701 (1971). (14) K. L. Hsia and It. M . Fuoss, Proc. N a l . Acad. Sci. U . S., 57, 1550 (1967). (15) It. L. Kay, B . J. Hales, and G. .'1 Gunningham, J . Phys. Chon., 71, 3925 (1967). (16) F. Accascins and S.Schiavo, Ric. Sci., 7, 550 (1966). (17) B . F. Prini and J. E. Prue, Trans.Para&!/ Soc., 62, 1257 (1906). The Journal of Physical Chemistry, Vol. 70,N o . 20, 1972
2922
LiClO4' NdXQi KC204 RbC1Od CYCIO~ a
KA
AD
Sslt
1'13.29 & 0.04 li30.42:t-0.13 187.68 :k 0.06 139.59 :t 0.19 13'l.iEi~k0.05
See ref 11.5.
19.55 & 0.01. 20.77JI0.5 28.42 zk 0.14 31.95 0.4 35.20d~0.15
d
c
4.5 4.4 3.4 3.2 3.0
0.02 0.08 0.02 0.06
0.02
See ref 16.
Table V: lDeiived Constants for the Alkali Perchlorntea in Pure iSu1folane at 30" a ho
LECIIO., NaC104 416104 RbCl04 C~@/14q 'I
11.05' :& 0.000 10.334 : k 0.001 1Cf.760 :k 0.001 10.839 :.& 0.001 11.045 3 0,092
KA
7 . 7 4 J I 0.2 9.05 i- 0.04 9.86 4 : 0.03 10.16 & 0.04 11.25 zk 0.06
d
ri
4.7 4.2 3.9 3.8 3.5
0.05 0.08 0.07 0.09 0.13
See ref 17.
__-_I
--.__.
10
Figure 1. Log KA vs. ( 1 / D T ) X IO6 for the a.lkali perchlorates in different pure solvents: e, CsClOa; a, RbClQa; 0, MClOa; 9, NaCI04; 8 , LiClOa.
~ l _ _ _ l -l l -l^I llllll~-~-
Gal6
(ih->103
l l ~ _ ^ - . l . l l - - ~
increase. This behavior has so far been explained by taliling into aecounl the effect of solvation of the cation on the ion pairing.18-23 The behavior of association constants 01 the alkali perchlorates in the different solvent considered, in the present analysis is shown in Figure 1 whcre log K A is plotted against 1/DT. The most. interesting f m t evident in Figure 1 is that, while for CsCLOn ~t linear relationship between log K A and
The 3ournal of Physical Chemistry, "01. 76, No. $0,SO79
1/DT exists, the plots €or the others alkali perchlorates become more concave down either if Lhe atomic number of the eation decreases or if the hydrogen bonding capacity of the solvent increases. From these results, the association behavior of alkali perchlorates in different solvents appears t o be governed on the one hand by the degree of solvation of the cations and on the other hand by the protic properties of solvent,. The latter may be in relation with the pontdated d d i t y of perchlorate mion t o form hydrogen bond2 with protic solvents.za (18) A . D'Aprano and R. M. Fuoss, J . Phys. Chem., 67, 1704 (1963). (19) A. D'Aprano and R. M.Fuoss, ibid., 67, 1877 (1963). (20) A. K. Bodenseh and J. B. Ramsey, ibid., 69, 543 (1965). (21) W. R. Gilkerson and B. Ezell, J . Am.er. C'h,em. Sobc., 87, 3812 (1965). (22) W. R . Gilkerson and B. Eaell, ?;bid.,88, 3484 (1966). (23) F. Accascina, A. D'Aprano, arid R. Triolo, J~ Phys. Chem., 71, 3469 (1967).
