J. Phys. Chem. 1985,89, 3922-3933
3922
Thermodynamlc Empirical Rules for the Solvation of Monoatomic Ions Reiko Notoya* and Akiya Matsuda Research Institute for Catalysis, Hokkaido University, Sapporo, 060 Japan (Received: June 20, 1984; In Final Form: April 23, 1985)
Two empirical rules are presented for the relative free energy of solvation of monoatomic cations: {(AGo,),/z,) - {(AGoJ),/zJ) equals /3s[{(AGo,)g-./z,} - ((AGO )g'w/zj)] (rule I) and pg(I,/zl) - A,, (rule 11), where (AG0Jgcs is the standard chemical free energy of solvation of ion i /or solvent s, z, is its valence, j is a reference ion, I, is the total ionization energy for ion i in the gas phase g, w denotes water, 8, and p s are constants for a given s, and A,, is a constant for a given j and s. It is found that these rules lead to the following conclusions. (i) (i) 8, = ps/pw = AJs/AJw. (ii) The cations are classified by rule I1 into three types: (a) rare gas, (b) those with more than three d electrons, and (c) those with 5dI0 + 4fI4 electrons. (iii) A,, for the (a) group can be identified with (AGo,),,/zJ based upon an extrathermodynamic assumption, and (AGoH+)gcs is estimated for 15 solvents, giving 11.71 eV for water; rules I and I1 can be put into the form (AG0Jg+Jz, = /3s{(AGo,)g,/z,) = e,p, for an individual ion where t, is a function of I J z , with different forms for different groups. (iv) Similar rules hold also for the solvation of halogen anions and the dissociatiov of diatomic metal halogenides and hydrides in the gas phase. (v) The donor and acceptor numbers of the solvent DN and AN of Gutmann and Mayer are given by absolute scales u, and Os, respectively, as a, = DN + 8.83 (eV) and Os = A N 211.2 based upon the two rules, and @, is given by u,/uW or Os/Ow. These results clearly show the donor-acceptor nature of the solvation of the monoatomic ions.
+
I. Introduction The nature of the solvation bond of an ion is a problem still in a black box, although many experimental and theoretical approaches have been advanced for the interpretation of the ionsolvent interactions.'-' From a thermodynamic point of view, we have a majpr difficulty in splitting the real free energy of solvation of an individual ion into the chemical and electrostatic terms, as pointed out by Guggenheim: which puts us in trouble for explaining the nature of the solvation bond based upon thermodynamic observations. However, the difference in the standard real or chemical free energy of solvation between two different ions in the same solvent, with each divided by the valence, is a quantity calculable by a thermodynamic cycle. The present work is concerned with the empirical rules for the relative free energies of solvation of monoatomic cations and anions in aqueous and nonaqueous media, which may allow us, on the one hand, to evaluate the chemical free energy of solvation for these ions based upon an extrathermodynamic assumption, but without any physical model, and on the other hand to understand the nature of the solvation bond for these ions. The standard real or chemical free energy of solvation of ion i for solvent s may be defined by the free energy change for a transfer to the gas phase g from solution, ( A E ) * - or (AG0Jm, which may be given by the difference in the electrochemical or chemical potential of the ion between the two phases
- -
(wi)g-
= Poi,g - ~
~ i , s
(1)
where the superscript degree denotes the standard state. The surface potential xs of the solvent may be given by (-J8-
= (AG"i)%- - z~Fx,
(3)
where the sign of xs is taken positive when the surface dipole of (1) "Ions and Molecules in Solution", 6th ISSSSI Mecting; Tanaka, N . , et al., Eds.; Elsevier: Amsterdam, 1983. (2) Ahrland, S. Pure Appl. Chem. 1982, 54, 1451. (3) Schwabe, K.; Queck, C. Abh. Soechs. Akad. Wiss. Leipzig, Moth.Notunviss. Kl. 1979, 53, 1 . (4) Jensen, W. B. Chem. Reo. 1978, 78, 1 . (5) Halliwell, H. F.; Nyburg, S. C. Trom. Faraday Soc. 1963.59, 1 1 26. (6) Boclais, J. OM.; Reddy, A. K. N . 'Modem Electrochemistry"; Plenum Press: New York, 1970; Vol. 1. (7) Jhon, M. S. "Extended Abstracts", 48th Fall Meeting of the Japanese Chemical Society, 1983; The Chemical Society of Japan: Tokyo, 1983; p 340. (8) Guggenheim, E. A. J. Phys. Chem. 1929, 33, 842.
0022-3654/85/2089-3922$01.50/0
the solvent turns its negative end toward the gas phase, and zi is the valence of ion i and F the Faraday. We shall start by giving the definition of the relative standard free energy of solvation of ion i in solvent s, i ~ J { ( ~ ~ o )atg ~ / ~ } , a given temperature as referred to a definite reference ion j in the same solvent ~ A J { ( A G ~ ) ~ - / Z=I {(ZFJ~-~/Z~I - {(ETj)g-s/zjJ = ((AG'i)gv/ZiJ - ((AG"j)g-s/zjI (4) with each divided by the valence of the ion. The standard real free energy of formition of ion i and the electron in the gas phase from its pure substance A E can be expressed in terms of ( A F ) g c s and the absolute standard electromotive force Oo, of the ionlpure substance electrode in solvent s by a thermodynamical - cycle AGOi = ziF@Oi,, (5)
(mi)gcs +
where Wi,,is given by the difference in the electrochemical potential of the electron in the gas phase and in the electrode m as (6) F@Oi,s= Poe,g - poe.m
- -
Using eq 5 and 6 for ions i and j, we o6tain ~ A J ~ ( A G O ) ~ +=, / ~ J - { ( Z F j ) / z j ) - F E O ~ ~(7) ,,
((mi)/Zil
where Eoij,,= - ODj,,. In this way iAJ{(AGo)g-/~Jcan be expressed in terms of the well-defined measurable thermodynamic - quantities AGOi, AGOj, and Eoi,,s. The numerical values for A- and A F can be obtained from the free energy of atomization of the pure substance and the ionization potential for the cations or the electron affinity for the and Eoijsfrom the electrochemical data and (9) "Selected Values of Chemical and Thermodynamic Properties". Natl. Bur. Srand. (US.)Circ. 1952, No. 500. (10) 'JANAF Thermochemical Tables"; Stull, D. R., et al., Eds.; The Thermal Research Laboratory, Dow Chemical Co.: Midland, MI, 1966-1970. (1 1) "Svoistva Elementov"; Samsonov, G. V., Ed.; Metallurgia: Moscow, 1976; Part I. (12) Tennodinamicheskie Svoistva Veschestv"; Ryabin, V. A., et al., Eds.; Khimiya: Leningrad, 1977. (13) Weast, R. C.; Astle, M. J. "CRC Handbook of Chemistry and Physics"; CRC Press: Boca Raton, FL, 1978-1979. (14) Vedeneyev, V. I.; et al. "Bond Energies, Ionization Potentials and Elktron Affinities";Edward Arnold: London, 1966. Parsons, R. "Handbook of Elwtrochemical Constants"; Butterworths: London, 1959. (15) Dqbos,D. "Electrochemical Data Book";Elsevier: Amsterdam, 1975. (16) Latimer, W. M. "Oxidation Potentials", 2nd ed.; Prentice-Hall: New York, 1952. (17) "Encyclopedia of Electrochemistry of the Elements";Bard, A. J., Ed.; Marcel Dekker: New York, 1973; Vol. 1 .
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985 3923
Empirical Rules for the Solvation of Monoatomic Ions TABLE I: List of the Ions and the Solvents Available for the Experimental Value of EoU,at 25 "c solvent nitromethane (NM) propylene carbonate (PC)
ion H', Lit, Na', Ag+, Cut, Mg+, CILi+, Na', K', Rb', Cs',
ref 19, 20 21, 22
Cn2+
H':ii', Na', K', Rb+, Cs', Ag', Pb2+, Ca2', Cd2+,Zn2+, Cu2', CIH', Ag+, Cuzt, Be2' pyridine (Py) H', Lit, Na', K+,Rb', acetonitrile (AN) Cs', Ag', Cut, Pb2', Ca2', Cd2', Zn2', Cuz', Cl-, Br-, Idimethyl sulfoxide (Me2SO) H+, Lit, Ag', TI', Cut, Cd2', Pb2', Cuzt methanol (MeOH) H', Lit, Na+, Ag', Cut, Pb2', CdZ', Zn2', Cu2', Cl-, Br-, I69 cations, F, CI-, Br-, Iwater (W) H', Lit, Na', Ag', Cut, ethanol (EtOH) Pb2'. Cd2'. ZnZt. Cu2+. CI-, Br-, I-' formamide (FA) H+, K', Rb', Tl', Cdzt, Zn2+, Cu2+,C1dimethylformamide (DMF) K', Rb', TI', Cut, Ca2' N-methylformamide (NMF) Lit, Na', K', Cs+ quinoline (Q) H', Rb', Cut hydrazine (Hz) H', Lit, Na', K', Ag', Cu+, Pb2', Ca2', Cd2', formic acid (FAc)
15-17 23, 24 15-17 0
-10
25 15-17 15, 16 15-17 26, 27 28-3 1 27 32 15, 32, 33
Zn2+ ammonia' (A)
H', Li', Na', K', Rb', Cs', Ag', Cut, Pb", Ca2+,Cd2', Zn2', Cuz', Cl-, Br-, I-
15, 32, 34-36
"At -35 "C.
literatures,ie36 for a variety of ionic species and solvents. The quantity iAj{(AGo)8.J~] for water will be denoted by 'Ajparticularly with subscript w for comparison of these ((AGo),/z], two quantities. Two empirical rules for the relation between iAj((AGo),,/Z) and iAj((AGo)8-w/~](rule I) on the one hand and between lAJ((AGo),,/z) and Zi/zi (rule 11) on the other will be presented in sections I1 and I11 for the monoatomic cations, where Ii is the ionization energy for ion i in the gas phase which is given by the sum of the successive ionization energies from the neutral atom to the valence state concerned. In section IV the relationship (18) Plambeck, J. A. In "Encyclopedia of Electrochemistry of the Elements"; Bard, A. J., Ed.; Marcell Dekker: New York, 1975; Vol. 10. (19) Bauer, D.; Foucault, A. J. Electroanal. Chem. Interfacial Electrochem. 1976,67, 19. (20) Badoz-Lambling, J.; Bardin, J. C. Electrochim. Acta 1974,19,725. (21) L'Her, M.; et al. J. Electroanal. Chem. Interfacial Elecfrochem. 1974, 55, 133. (22) L'Her, M.; Courtot-Coupez, J. Bull. Chim. SOC.Fr. 1972, 3645. (23) Mukherjee, L. M.;et al. J. Phys. Chem., 1969, 73, 580. (24) Schmidt, J. M. Ann. Chim. (Paris) 1929, I O , 426. (25) Courtot-Coupez, J.; et al. J. Electroanal. Chem. Interfacial Electrochem. 1971, 29, 21. (26) Pavlopoulos, T.; Strehlow, H. Z . Phys. Chem. (Munich) 1954,2,89. (27) Butler, J. N. In "Advances in Electrochemistry and Electrochemical Engineering"; Delahay, P., Ed.; Wiley: New York, 1969, Vol. 7, p 77. (28) Matsumura, N.; et al. Bull. Chem. Soc. Jpn. 1973, 47, 813. (29) Demange-Guerin, G. Taldnta 1970, 17, 1099. (30) Bardin, J. J. Electroanal. Chem. Interfacial Electrochem. 1970, 20, 157. (31) Boyer, K.W.; Iwamoto, R. I. J. Electroanal. Chem. 1964, 7 , 458. (32) Strehlow, H. In "The Chemistry of Non-Aqueous Solvents"; Lagowski, J. J., Ed.; Academic Pres's: New York, 1966; Vol. 1, p 129. (33) Pleskov. W. A. Zh. Fir. Khim. 1940. 14. 1477. (34j Pleskov; W. A.; Monossohn, 4. Acta'Physicochim. URSS 1935, 1, 87, 714; 1935, 2, 615, 621. (35) Pleskov, W. A. Acta Physicochim. URSS 1940, 13, 659. (36) Pleskov, W. A. Zh. Fiz. Khim. 1933, 4, 696; 1935,6, 1286; !937, 9, 12; 1940, 14, 1626; 1946, 20, 163.
o^
2
'
#/
B:r c1-i :
1-15 Relation between ((AGoi)gl/zi) - ((AGo,)gl/zj) and ( ( A G o i ) g - / ~ i-) ((AGo,),,/zj) for the monoatomic cations at 25 "C, with s = acetonitrile and j = H+.
Figure 1.
TABLE 11: List of b, r 2 , and 6 for the Solvation of the Monoatomic Cations for 15 Solvents
P,
6, eV
rz
DN," eV
NM PC FAc PY AN
0.916 0.953 0.956 0.961 0.974
0.05 0.02 0.21 -0.02 -0.03
0.9994 0.9996 0.9980 0.9999 0.9994
0.117 0.655
Me2S0 MeOH W EtOH FA
0.994 0.994 1.ooo 1.ooo 1.011
0.04 0.00 0.00 0.00 0.02
0.9993 0.9999 1.0000 0.9994 0.9998
1.292 0.824 0.781 0.868 1.041
DMF NMF
1.016 1.044 1.066 1.107 1.117
-0.02 0.02 -0.04 -0.12 -0.04
0.9997 0.9980 0.9994 0.9995 0.9995
1.153
solvent
Q
Hz A
1.435 0.61 1
1.908 2.558
"Gutmann's donor number of the solvent. between the two rules will be discussed and (AGol),,/z, for an individual ion will be given by rule I1 as a function of IJz1based
upon an extrathermodynamic assumption that an ideal ion of the rare gas type whose ionization energy equals zero has no chemical interaction with any solvent, and rule I will be given in terms of (AGoI),,/z, and (AGoI)gI-w/~, for an individual ion. In section V the numerical values of (AGO,),,, estimated from the two rules will be discussed in connection with those in the literature. In section VI the Gutmann's donor number of the solvent3' will be given by an absolute scale based upon the two rules. The two rules will be extended to the dissociation enthalpy of gaseous diatomic metal halogenides and hydrides in section VI1 and to the solvation of the halogen anions in section VIII, and finally the acceptor number of the solvent of M a y e P will be given by an absolute scale based upon the two rules. 11. Rule I for the Solvation of Monoatomic Cations The values of lAJ((AGo),,/z] for the monoatomic cations in nonaqueous solvents at 25 OC calculated by eq 7 are compared in the present section with the values of IAI{(AG"),/z) for water at t h e same temperature. Table I shows t h e list of t h e ions and t h e solvents which are available a t present for the estimation of lAJ((AGo)g%/~] from t h e experimental value of EolJ,s. T h e relation between lAJ((AGo)gcs/~]for acetonitrile and lAJ((AGo),,,/z) for water is shown in Figure 1 as an example, (37) Gutmann, V. "The Donor-Acceptor Approach to Molecular Interactions"; Plenum Press: New York, 1978. (38) Mayer, U.; et al. Monatsh. Chem. 1975, 106, 1235.
3924 The Journal of Physical Chemistry, Vol. 89, No. 18, 1985
Notoya and Matsuda
-2
5-
ri
0-
u
5
t
h
0
a Q
5?
-5-
.,a LA'
((AGO),
, /z), [
eI ~
-10-
V I
0
I Relation between [(AGoi)g-r/zi) - {(AGoj)-/zj) and {(AGoi)g,w/zi)- [(AGoj)g-/zj) for the monoatomic cations, with s = fused salt LiCl + KCI (mol 5% 59:41)at 450 O C and j = Ag+ and w = water at 25 O C and j = H+. Figure 2.
the hydrogen ion being taken as the reference ion. It is found that there exists an excellent linearity between iAj{(AGo),/~) and iAj((AGo)g-/~] with zero intercept. The situation for the relationship between iAJ{(AGo),/~) and iAj((AGo),w/z) for any cation in any other solvent in Table I is quite similar to that for acetonitrile, and the regression line for the relation is given by iAj((AGo)k;s/z] = &B,['Aj{(AGo),,/z)] 6, where & is a constant charactenstic of the solvent s and 6 the 6, and deviation of the regression line from the origin. The the square of the correlation coefficient 9 for the regression line for 15 solvents are summarized in Table I1 together with the Gutmann's donor number DN3' of the solvent expressed in electronvolts. The value of 6 for each solvent is quite small, and its mean value for 15 solvents can be regarded as practically zero. It may therefore be concluded that the regression line is given by the equation
+
os,
((AGOi)g-s/ZiI
- ((AG"j)g-s/zjI = Bs[{(AGOi)g--w/ziI
- {(AGoj)g-w/zjI1 (8)
which will be called hereafter rule I for the solvation of the monoatomic cations. The empirical rule I was found to hold also for fused salts as exemplified in Figure 2 by the relation between 'Aj{(AGo) /z} for LiCl-KCl (mol % 59:41) at 450 OC and 'd((AG"),,/~for water at 25 O C , Ag+ and H+ ions being taken as the reference for the respective solvents, as reported e l s e ~ h e r e . ~ ~ * ~ ~ Rule I was firstly expressed in terms of iAj((ACo)g,s/~] and ( A ~ ) g - w / z i 4 1 * 4by 2 using the values of ( A E ) g - w reported by R a n d l e ~ . ~However, ~ some different experimental values for ( A F ) g - w have been r e p ~ r t e dafter ~ , ~ Randles, ~ so that it may be better to express rule I in terms of the well-established thermodynamic quantities iAj((AGo)gcs/~)and 'Aj((AG0),,,/~) as given by eq 8.46,47 (39) Notoya. R.; Matsuda, A. J. Res. Inst. Caral., Hokkaido Uniu. 1980, 28, 1. (40) Notoya, R.; Matsuda, A. Nippon Kagaku Kaishi 1982, 990. (41) Matsuda, A. J. Res. Inst. Cafal., Hokkaido Uniu. 1979, 27, 10. (42) Notoya, R.; Matsuda, A. "Extended Abstracts", 32nd ISE Meeting, Dubrovnik, Yugoslavia, 1981; Lovredk, B., Ed.; The Organizing Committee of 32nd I.S.E. Meeting: Dubrovnik, Yugoslavia, 1981; p 541. (43) Randles, J. E. B. Trans. Faraday SOC.1956, 52, 1573. (44) Gomer,R.; Tryson, G.J. Chem. Phys. 1977, 66, 4413. (45) Farrel, J. R.; McTigue, P. J. Electroanal. Chem. Interfacial Elecirochem. 1982, 139, 37. (46) Notoya, R.;Matsuda, A. J. Res. Inst. Carol., Hokkaido Uniu. 1981, 29, 151.
;L+
A"'
I
I
5
IO
I
15 I t / q , [eVI
I
I
20
25
Figure 3. Relation between [(AGoi),/zi) - [(AGoj)-/zj] at 25 OC and Ilzi for the monoatomic cations, with j = H+;(0),(a) group; (A),(b) group; ( 0 ) .(4 group.
It is seen in Table I1 that the values of j3, for 14 nonaqueous solvents fall in the range from 0.916 for nitromethane to 1.1 17 for ammonia, suggesting that the free energies of solvation of a given cation for these solvents are close in value to the free energy of hydration of the cation. It is also seen that & has a tendency to increase with an increase of the Gutmann's donor number DN of the solvent. The relationship between j3, and DN and also rule I for the monoatomic anions will be discussed later. The difference in the standard real free energy of transfer from water to a nonaqueous solvent between two different ions i and j, lAJ((AGo)s-w/zI = { ( A ~ ) s - w / ~ -, ]{(Ac",),-w/zJ], with each divided by the valence, may be given by eq 9 based upon rule I 1AJ{wo)s-w/4 = (1 - 8,)['AJ'((AG0)g-w/zll
-
-
(9)
where (AE)stw = pol,,- P O ~ , ~ . Although we have not yet attained general consent to the numerical values of (AGO,), in the literature because of experimental difficulties as pointed out by Schwabe and Q ~ e c kit, ~is interesting to compare the values of lAJ{(AGo)s-/~) calculated by eq 9 with those estimated from the experimental values of ( A E ) s + w for some ionsolvent systems in Table I. For example, the values of lAJ{(AGo)S-/~)for i = Li+, Na+, K', Rb+, and Cs+ and j = H+ obtained from the experimental values of ( A R ) , , of Case and Parsons48 are scattered for transfer to methanol in the range 20 to -130 meV and to ethanol in the range 70 to -30 meV, while by eq 9 we obtain for methanol -36, -42, -47, -48, and -50 meV, respectively, and for ethanol 0 irrespective of the cation, and for transfer to acetonitrile the experimental values of lAJ((AGo)s-/z} are found to be -70, -140, -220, -240, and -230 meV, respectively, which are comparatively close to the respective calculated values -160, -180, -200, -210, and -220 meV. For transfer of the alkali-metal ions from water to nitromethane the values of lAJ{(AGo)stw/z} for Li+-Na+, Na+-K+, K+-Rb+, and Rb+-Cs+ differences are estimated at 17,76,28, and 3 1 meV, respectively, from the partition equilibrium of alkali perrhenates between the aqueous phase (10.6 wt % CH3N02)and organic phase (98.5 wt 7% CH3N02)determined by Friedman and Haugex~,~' while the calculated values are 87, 64, 20, and 27 meV, respectively. If one makes allowance for some uncertainty for the experimental values of (AR),,,, it may be said that eq 9 (47) Notoya, R.; Matsuda, A. 'Extended Abstracts", 33rd ISE Meeting, Lyon, France, 1983; Costa, M., Ed.; The Organizing Committee of 33rd I.S.E. Meeting: Lyon, France, 1987; p 257. (48) Case, B.; Parsons, R. Trans. Faraday SOC.1967, 63, 1224. (49) Friedman, H. L.; Haugen, G. R. J. Am. Chem. Soc. 1954,76,2060.
Empirical Rules for the Solvation of Monoatomic Ions
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985 3925
TABLE III: List of p, and A b for the Solvation of the Monoatomic Cations of the (a), (b), and (c) Groups, with j = H+ (a) group (b) group (c) group solvent P: Ajs," eV 9 Pab Ajs,6 eV 9 PaC Aja: eV NM 0.868 10.67 0.9956 0.810 11.41 0.9867 0.749 11.73 . 12.23 11.95 0.9865 0.776 0.844 11.15 0.9953 0.902 PC 12.02 11.74 0.9870 0.778 0.845 10.99 0.9949 0.909 FAc 12.38 0.9864 0.785 12.07 0.852 0.9947 11.27 0.909 PY 12.59 0.797 12.12 0.9873 0.856 0.9951 11.43 AN 0.922 0.9862 0.814 12.78 0.878 12.39 11.61 0.9954 0.943 MezSO 12.78 0.9864 0.812 12.47 0.881 11.64 0.9951 0.942 MeOH 0.816 12.88 0.9864 12.54 0.886 0.9952 W 0.947 11.71 0.9864 0.816 12.85 0.886 12.54 0.9951 11.71 0.948 EtOH 12.93 0.9865 0.823 0.896 12.65 0.9951 11.81 0.958 FA 0.826 13.02 12.65 0.9857 11.92 0.9952 0.894 0.963 DMF 13.43 0.853 0.9865 13.10 0.925 11.92 0.9952 0.989 NMF 13.74 0.870 13.40 0.9864 12.51 0.9944 0.944 0.997 Q 0.904 14.36 13.95 0.9832 0.977 13.09 0.9953 Hz 1 .os1 0.912 0.9847 14.41 13.97 0.9948 0.985 1.062 13.13 A ~~
reflects the trend of iAJ((AGo)s-w/~} in its sign and magnitude fairly well. As is known, FriedmanSohas found that the solubilities of the rare gases in water and nonaqueous solvents can be correlated linearly with the solubilities of these gases in nitromethane in the log-log plots, which implies that the standard free energies of dissolution of the rare gases can be correlated by the similar equation as rule I. It is interesting that the different types of solute-solvent interactions such as dissolution of the ions and the rare gases can be expressed by the similar empirical correlation. In the present treatment, however, our discussion will be focused on the ionic system only.
9 0.9887 0.9884 0.9875 0.9886 0.9888 0.9885 0.9884 0.9888 0.9885 0.9883 0.9882 0.9886 0.9886 0.9886 0.9886
-1; -
3
5
I
a
-5
111. Rule I1 for the Solvation of Monoatomic Cations
It has been long recognized that the enthalpies of hydration of the monoatomic cations can be correlated qualitatively with their ionization energies in the gas phase.51 In the present section empirical rules will be shown for the relation between iAJ((AGo),/z) and ZJq. Let us first compare iAj((AGo)g+w/~) for water with Zi/zi for 69 ionic species in Figure 3, the hydrogen ion being taken as the reference. It can be seen that the cations are divided into three groups and there exists a good linear relation for the cations of each group which is given by the regression line ((AGOi)g-w/ZiI - {(AGoj)g-w/zjI = pw(zi/zi) - Ajw (10) where pw for each straight line is a constant characteristic of water and -Ajw equals iAj((AGo),/~) for an ideal ion whose ionization energy equals zero. According to rule I, we can expect for any solvent in Table I the same situation as for water. Figure 4 shows the relation between iAj{(AGo)g9/~)for acetonitrile and Zi/zi by using the values of iAj{(AGo)8.J~} obtained from those of Eoij,sfor the cations listed in Table I and for the other cations by using the values obtained from iAJ((AGo)-/~) by eq 8. In fact, we obtain the similar linearity as in Figure 3. In this way for any solvent available the same type of linear relation as eq 10 is obtained for the cations of each group, which is given by the regression line l(AGoi)g-s/zil - ((AGOj)g-s/zjI = Ps(zi/zi)
I A UA d R A VA V l A WA I
I
IS
' H
(bl
W
IB UB
m B RB
VB
VlB FlB 0 2
He
- Ajs (11)
where ps is a constant characteristic of solvent s and -Ajs equals iAJ((AGo)8J~) for an ideal ion of Zi = 0. Equation 11 will be called hereafter rule I1 for the solvation of monoatomic cations. It should be emphasized that the monoatomic cations can be classified into three groups by rule II.52 These groups will be specified with symbols (a), (b), and (c) in the order of the magnitude of ps. The values of ps, Ajs, and the square of the (50) Friedman, H. L. J . Am. Chem. SOC.1954,76, 3294.
(51)Bosolo,F.;Pearson, R. G. "Mechanism of Inorganic Reactions", 2nd 4.; Wiley: New York, 1967. (52)Notoya, R.; Matsuda, A. J . Res. Inst. Caral., Hokkaido Uniu. 1982, 30, 1.
T 1'
Figure 4. Relation between ((AGo,),/zi) - ((AGo,),,/zjJ and Ii/zi for the monoatomic cations at 25 OC, with s = acetonitrile and j = Ht: (0), (a) group; (A), (b) group; (oh (c) group.
Figure 5. Classification of the monoatomic cations into (a), (b), and (c) groups in the periodic table
correlation coefficient r2 for eq 1 1 are summarized in Table I11 for the (a), (b), and (c) groups. The value of ps for the (a) group IS close to unity which lies in the range 0.868 for nitromethane to 1.062 for ammonia, and ps decreases in the sequence of the (a), (b), and (c) groups for any solvent. It is seen from comparison of Tables I1 and 111 that the order of the magnitude of 8, follows that of p s , and IrZ- 11 for rule I1 is larger than that for the rule I by about 1 order of magnitude. The cations of the three groups can be characterized by (i) the electronic configuration of the ion and (ii) the free energy of
3926
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985
TABLE
IV: Electronic Configuration of the Monoatomic Cations of the (a), (b), (a) group Li+ Na+ K+ Rb+
cs+
Cr2+ Cr3+ Mn2+ Fe2+ Fe3+
Ar Ar Ar Ar Ar
Be2+ Mg2+ ea2+ Sr2+ Ba2+
He Ne Ar Kr Xe
co2+
Ar Ar Ar Ar Ar
Ra2+ AP+ SC'+ Y3+ Ti2+
Rn Ne Ar Kr Ar
Zr4+
Kr Xe 4f14 Ar 3d3 Kr + 4d2 Xe
V2+ Nb3+ La3+
eo3+ Ni2+
cu+
cu2+
u4+
MO~+
Ru2+ Rh3+ Pd2' Ag+ Cd2+
+ +
u3+
LU'+ Th4+
Zn2+ Ga2+ Ga3+ As3+
+ 3d2
+ 4f + 4f3 + 4fs + 4P Xe + 4fI4 Rn Rn + Sf3
Ce3+ Ce4+ Nd3+ Sm3+ Gd3+
and (c) Groups for Which EolirIs Available
(b) group
He Ne Ar Kr Xe
HP+
Notoya and Matsuda
Xe Xe Xe Xe Xe
In+ 1 ~ 3 +
Sn2+ Sb3+ Te4+ os2+ 1r3+ pt2+ H+
+ Sf2 + Sf4
Np3+
Rn Rn
Pu'+
Rn + 5p
Am3'
Rn
(c) group
+ 3d4 + 3d3 + 3d5 + 3d6 + 3d'
Au+ Au3+ Hg2+ ~ 1 3 +
Xe Xe Xe Xe Xe
Pb2+ Bi'+ Po3+
Xe Xe Xe
TI+
+ 3d7
+ 3d6 + 3ds + 3dI0 + 3d9 Ar + 3d1° Ar + 3d1° + 4s Ar + 3d1° Ar + 3dI0 + 4s2 Kr + 4d3 Kr + 4d6 Kr + 4d6 Kr + 4d8 Kr + 4dI0
+ 5d1° + 4fI4 + 5d8 + 4fi4 + 5d1° + 4fi4 + SdIO+ 4fi4 + 6s2
+ 5d1° + 4fI4
+ 5dI0 + 4fI4 + 6s2 + 5di0 + 4f14 + 6s2 + SdI0 + 4fI4 + 6s2 + 6p
+ 4dI0 Kr + 4dI0 + Ss2 Kr Kr Kr Kr Kr
+ 4d1° + 4di0 + 5s2 + 4di0 + 5s2 + 4dI0 + 5s2
Xe
+ 5ds + 4fI4
+ 5f6
dissociation of the gaseous atom into the ion and the electron in water, as will be discussed in what follows. (i) The classification of the cations into three groups in the periodic table of the elements is represented in Figure 5. The electronic configuration of the cations of each group for which the experimental values of Eoij,,are known is shown in Table IV." It is found that the (a) group cations belong to IA-VA (1-5 in the notation recommended in 1983 by the American Chemical Society Nomenclature Committee and approved in principle by relevant IUPAC committee^)'^ groups in the periodic table, including A13+in the IIIB (1 3) group, and these ions are characterized by the electronic configuration of the rare gas type with the exception of Ti2+,V2+,and Nb3+. The lanthanides and the actinides also belong to the (a) group. The (b) group cations belong to VIA-VIB (6-16) groups which are characterized by more than three d electrons in the outer shell. The (c) group cations belong to IB-VIB (1 1-16) groups in the 6th row of the periodic table which are characterized by 5dI0 + 4f14 electrons with the exception of Au3+ only, as seen in Table IV. (ii) The real standard free energy of dissociation of a gaseous atom A into its ion and the electron in water AF,,[A] is given where Eoi,,[A] is the standard elecby Z ~ F ( E " ~ , ~-[ A ] tromotive force for the system of ion i in water associated with its neutral atom A in the gas phase and EO,, is that of the hydrated electron which was estimated at -2.77 V." The quantity Aco,,[A]/zi defined in this way makes it possible for us to compare the facilities of ionization of an atom in the gas phase and in the bulk of water. Figure 6 shows the comparison of A F , , [ A ] / z i with Ii/zi, in which the (a) group cations are characterized by the negative value of A F , , [ A ] /ti with the ~~
(53) Matsuda, A.; Notoya, R.; Hiratsuka, H. J . Res. Inst. Catal., Hokkaido Uniu. 1980, 28, 19. (54) Hart, E.; Anbar, M. "The Hydrated Electron"; Wiley-Interscience: New York, 1970. Rotenberg, Z. A. Elektrokhimiya 1972, 8, 1198.
5L
G
4
-I
T&
O r
---I-
&, [eW
Figure 6. Relation between Afi,w[A]/~iat 25 OC and Ii/zi: (0),(a) group; (A),(b) group; (Oh (c) group. TABLE V: Criteria for Classification of the Monoatomic Cations into the (a), (b), and (c) Groups"
criterion periodic table electronic configuration -
(a) group (b) group IA-VA VIA-VIB X" X + d3-I0
AGoi.w[Al/zi HSAB concept
negative hard
(4group IB-VIB (6th row) X + 5d1° + 4f14
positive positive intermediate soft
"X is the electronic configuration of the rare gas type.
exception of a slight positive value for A13+,U4+, and Ce4+,while it is positive for the cations of the (b) and (c) groups with the exception of the slight negative value for Os2+,and the (c) group cations are located at the upper border of the region of the (b) group cations. In this way the monoatomic cations can be classified into three groups by the Aw,,[A]/zi vs. Ii/zi plots. It is therefore suggested from the energetic point of view that the atomic species A of the (a) group cations have a tendency toward spontaneous dissociation into the ion and the electron in
Empirical Rules for the Solvation of Monoatomic Ions
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985 3927
-14
- 12 -70
09
10
4
II
Figure 7. Relation between ps and @, for the solvation of the monoatonic cations of the (a), (b), and (c) groups. 0
water as known typically for the alkali metals, and most of the atomic species of the (b) group have a possibility to be splitted into the ion and the electron in water by photoexcitation with visible ray, but the atomic species of the (c) group have in general difficulty for photodissociation in aqueous medium. The criteria for the classification of the cations discussed above are summarized in Table V. It should be stressed that the classification of the monoatomic cations by rule I1 in the periodic table practically coincides with the classification of the ions based upon the hard and soft acids and bases (HSAB) concept presented by Ahrland et and P e a r ~ o n , ~indicating ~,~' that the (a) group cations can be regarded as the hard acid, the (c) group cations as the soft acid, and the (b) group cations as the intermediate. A measure of the softness for the monoatomic cations has been given by AhrlandS8as the difference between Zi/zi and the heat of hydration for the ion. It is noted that the softness scale of Ahrland is closely related to the quantity A E , w [ A ] / q . The empirical rule I1 shows that the ionization energy of a monoatomic cation plays a significant role in the ion-solvent interactions whether it belongs to the (a), (b), or (c) group.
IV. Relationship between Rules I and I1 and Estimation of (AGO,), for an Individual Ion In this section the relationship between rules I and I1 will be discussed comparing the parameter 8, with ps and Ajs for the (a), (b), and (c) groups, and (AGoi)ecs for an individual ion will be estimated by rule I1 based upon an extrathermodynamic assumption. For convenience the symbols p, and A,, in eq 11 for the respective groups will be specified by superscript a, b, or c as p t , ,p: or p: and Aj:, Aj;, or Aj;, and p, and Ajs without specification by superscript will be used for representing any of the parameters for the three groups. Figure 7 shows the graphic representation for p t , ,p: and p: plotted against 8, using the values in Tables I1 and 111. An excellent linearity for each group is obtained which is given by p t = 0.9470, + 0.004 for the (a) group, p: = 0.8370, + 0.003 for the (b) group, and p; = 0.8168, + 0.06 for the (c) group, and the gradients of these straight lines are practically identified with pwa,p$, and pwc,respectively, and the second term in each equation can be neglected as compared with the first term, so that the correlation is given by p: = &pwa,psb = Pfiwb,and p: = p,pwc for the corresponding group. Figure 8 shows the graphic representation for Aj:, A,:j and Aj: plotted against 8, using the values in Tables I1 and 111. A ~~~~~~
I
0.90
I .oo
I
4
1.10
Figure 8. Relation between Ajs and 6, for the solvation of the monoatomic cations of the (a), (b), and (c) groups with j = H ' .
good proportionality is also obtained for each group which is given for the correby A j t = @,Ajwa,Aj: = &Ajwb,and Aj; = @,AjWc sponding group. On the other hand, the two types of proportionality described above can be obtained analytically from rules I and 11. We obtain an identical equation from eq 10 and 11 for the cations of the (a) group based upon rule I
(PS" - 8spwa)(zi/zi) - (AjS" - PsAjwa) 0
(12)
and the similar equations as eq 12 are obtained for the cations of the (b) and (c) groups. It follows from these identical equations
p,
8s = P:/Pwa
= Psb/Pwb = P,"/PWC
(13)
= Aj:/Ajwa
= Ajsb/Ajwb = Aj;/AjwC
(14)
as obtained graphically from Figures 7 and 8. Equation 14 shows that rule I holds for the ideal ions in the respective groups whose ionization energies equal zero. In view of the s, w interchange symmetry, rule I1 can be put into the form for the ions of any group, eq 13 being taken into consideration [((AGoi)g-s/zil - ((AGoj)g-s/zj) + Ajsl / ~ s= [((AGoi)g-w/zi) - ((AGOj)g-w/zjJ + Ajwl/~w= zi/zi (15) It follows from eq 15 that rule I can be derived from rule I1 since Aj,/ps equals Ajw/pwaccording to eq 13 and 14. In case the ions i and j belong to the same group, Ajs/ps can be identified with Zj/zj because of the i, j interchange symmetry of eq 15 in this case. Equation 15 can be expressed as [((AGoi)g-s/ziJ - ((AG"i)g-s/ziLj=~I / ~ s= [((AGOi)g-w/Zil - ((AGOi)g-w/~il~i=~l / ~ w= zi/zi (16) where ((AGoi)g-s/~i)li=Oand {(AGoi),-w/zi),i=o stand for (AGoi)gI-s/~iand (AGoi)g-w/zi for an ideal ion of Zi = 0, respectively, which are given by ((AGoi)g-s/ziI~i=o = {(AGoj)g-s/zj) - Ajs
(17)
{(AG"i)g-w/ziI~i=o = ((AGoj)g-w/zjI - Ajw
(18)
~
( 5 5 ) Anrland, S.;Chatt, J.; Davies, N. R. Q.Rev., Chem. SOC.1958, 12, 265. ( 5 6 ) Pearson, R. G . J . Am. Chem. SOC.1963, 85, 3533 (57) Pearson, R. G . Chem. Br. 1967, 3, 103. (58) Ahrland, S. Chem. Phys. Lett. 1968, 2, 303.
In order to estimate the value of (AGoi)e-s for an individual ion from eq 15 or 16, we consider eq 16-18 for the ions of the three groups separately using superscripts a, b, and c for p,, (AGoi)gcs, and Zi, and introduce an extrathermodynamic as-
3928
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985
Notoya and Matsuda
sumption that the ideal ion of the rare gas type, (a) group, has no chemical interaction with any solvent, i.e. ((AGoi)gcsa/ZiI,i-O = I(AGoi)g-wa/ziI,l=o = 0
Te4+
(19)
zr4+
Then we obtain from eq 17 and 18 (AGoj)g+J~j
= Aj:,
(AGoj)g.-w/~j = Ajwa
Hf4+ Th4+
(20)
At3+ As3+
which makes it possible for us to estimate (AGOj)- for the reference ion j from rule I1 whether it belongs to the (a) group or not. We obtain from eq 15 using eq 13, 14, and 20 I(AGoi)gcsa/zi)/Ps" = ((AGoi)g-wa/ZiI/pwa = zia/zi
I$+ Sb3+ Be2+
2 Y
3
(2la)
H+ cu2+ Ni 2 A
&
h
0 W4
I(AGoi)gcsb/ziI/~s" = I(AGoi)g-wb/zi)/pwb = (Z:/zi) ((Ajwa- Ajwb)/pwb)= (Z?/zi) - 0.94, eV (21b)
2+:;
a
+
v
sn2+ Pb2+
Ea2+
((AGoi)g-,'/ziI/p," = l(AGoi)g-wc/zi)/pwc = (Z:/zi) ((Ajwa- AjwC)/pwC) = (Z:/zi) - 1.43, eV (21c)
cu+ L L+ Na+
+
-
for the respective groups. The numerical values in eq 21b and 21c are calculated by using the values of pw and Ajw for the (a), (b), and (c) groups in Table 111. It is found from eq 21a-21c that ((AGoi)B-J/zi)/psis a function of only Zi/q for an ion of any group and rules I and I1 can be put into the form (AGOi1g-s = iBs(AGoi)g-w
(22)
(AGoi)gr/Zi = tip:
(23)
K+ R b+
C S+
O0.S 0.9
1.0
1.1
PP
Figure 9. Relation between (AG0Jg9/zi and p: at 25
OC.
for an individual ion in any group, where ti
ti
= (pwb/pwa)[(zib/Zi)
= zia/zi
(24a)
+ I(Ajwa - ~ j w ~ ) / p w ~ =I I 0.936((Zib/zi) - 0.94), eV (24b)
ti
= (pwc//pwa)[(~t/zi) + ((Ajwa - AjwC)/pwC1l= 0.862((Z:/zi) - 1.43), eV (24c)
for the ions of the respective groups. The parameter 'iequals Zi/q itself for the (a) group cations, but it shows a slight deviation from Zi/zi for the (b) and (c) group cations which may be attributable to the specific interactions due to the d and/or f electrons of these ions. It may be unreasonable, however, to assume the extrathermodynamic assumption for the ideal ion of the (b) or (c) group since the specific interactions due to the d and/or f electrons may reflect on the values of Ajsb and Ajwbor Aj,' and AjwC. In this way it may be concluded from rules I and I1 based upon the extrathermodynamic assumption that (AGoJgCs for a monoatomic cation is proportional to (AGoi)g-w, and (AGoi)g'-s/~i is given simply by the product of the two independent parameters characteristic of the ion and the solvent, ti and p:, respectively. The numerical values of (AGoi)gcs will be discussed in the following section.
V. Numerical Values for It has been shown by eq 20 in the preceding section that (AGoj)g--s/zjfor the reference ion j is given by Aj:. In case j = H+, Aj: represents (AGoH+)g'-s, and its value is given in Table I11 for 15 solvents. The value of (AGoH+)g-wfor water is found to be 11.71 eV; the lowest one for (AGoH+)gcs is 10.67 eV for nitromethane and the highest one is 13.13 eV for ammonia. The values of (AGoi)gcs/zi for other cations can be calculated by eq 4 using the values for iAj((AGo),/~) and (AGOH+)? The values of (AGoi),/zi for a number of cations estimated in this way are plotted in Figure 9 against the values of p t for 15 solvents in Table 111. It is found that there exists an excellent proportionality between (ACoi)g-s/zi and p; which is given by eq 23 derived in the preceding section. Figure 10 shows the relation between (AGoi)gcw/~i for water and ti calculated by eq 24a-24c for the cations of the three groups,
5
I
I
1
I
I
5
IO
15
20
25
ei, (eV1
Figure 10. Relation between (AGoi)g+w/zifor water and ei at 25 (Oh (a) group; (A), (b) group; ( O h (c) group.
OC:
which can be expressed by a single straight line with the gradient equal to pwa,indicating the validity of eq 23. It is interesting that the values of ti calculated by eq 24b for the divalent cations of the first transition series follow the Irving-Williams order65for the stabilization of the complexes of these ions with a given ligand Mn(I1) < Fe(I1) < Co(I1) < Ni(I1) < Cu(I1) > Zn(I1) 9.95 10.40 10.79 11.19 12.24 11.93 suggesting the donoracceptor nature of the solvation bond of these cations. It may be possible to estimate the surface potential % at infinite dilution by eq 3 from the difference between (AGoH+)- estimated in the present treatment and (AGoH+)gCsdetermined by experiment. For water we obtain xw = +0.41 V from the comparison of (AGoH+)g-w = 11.30 eV determined by R a n d l e ~with ~~ (AGoH+)g-w = 11.71 eV in the present work. For nonaqueous solvents, using the values for 11.55 eV for methanol, 1 1.53 eV for ethanol, 11.18 eV for acetonitrile, and 11.45 eV for formamide determined by Case and Parsons48and the values for (AGoH+)gy in Table 111, we obtain X M ~ O H= +0.09 v, X E ~ O H=
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985 3929
Empirical Rules for the Solvation of Monoatomic Ions /
1.05 "IO1
ps
t/: I1
I .oo
D
0 95
i
,
I
I
I
+
NM
0 goo
10
20 30 DN (kcol mol-')
The values of D N are shown in Table I1 in electronvolts for 12 solvents. It is noted that 0, can be related qualitatively to D N for a series of solvents, indicating a tendency to increase with increasing DN. Let us now consider quantitatively the relation between 0, and DN. Figure 11 shows the P, vs. D N plots for the solvents in Table 11. There exists a good linearity for eight solvents, nitromethane, acetonitrile, methanol, ethanol, water, formamide, hydrazine, and dimethylformamide, but pyridine, dimethyl sulfoxide, propylene carbonate, and ammonia are ruled out from this regularity. The linear relation in Figure 11 can be expressed by the following regression line for the eight solvents P, = 0.103(DN 8.83) (25)
40
50
60
Figure 11. Relation between fl, and the Gutmann's donor number DN
for 12 solvents. +0.18 V, xAN = +0.25 V, and xFA = +0.36 V, indicating the negative end of the surface dipole toward the gas phase.59 We obtain also xDMF = -0.1 V for dimethylformamide from comparison -of (AGoNa+)gcs = 4.73 eV in the present work with (AGoNa+)gcs = 4.83 eV determined by Damaskin et a1.,60indicating the positive end of the surface dipole toward the gas phase. The values for xs have been reported in the literature: xw = +0.1 to 0.2 V,6' x M ~ H= -0.17 to -0.29 V, x E ~ O H = -0.19 to -0.29 V, xFA = +0.05 V,62 xAN = -0.1 V,63 and xDMF = -0.75 Ve60 It is found that the values for xs estimated in the present treatment are larger than the values reported in the literature by a few hundred millivolts, but the order of xs is given by W > FA > AN > EtOH > MeOH > DMF in the present treatment in agreement with that reported in the literature. On the other hand, Izmai10v~~ estimated the values for (AGO,), based upon the donoracceptor concept of the solvation bonding of an ion. H e used extrapolation of -[lAJ{(AGo)gcs/z) = ( A G o J ) g v + [l((AGoX), - (AG01),)/21 to l/n2 0, where subscnpts i and x denoted isoelectric alkali and halogen ions, respectively, and n is the quantum number of the lowest vacant orbital of the ions, assuming that the ionsolvent interaction energy is reciprocally proportional to n2 and the difference (AGO,), - (AGo,),, approaches zero with increasing n. The value of (AG0H+)- = 11.12 eV obtained by Izmailov in this way is smaller than that in the present treatment by about 0.6 eV, which results in the negative surface potential when referred to the Randles value (A?H+)g-w = 11.30 eV. It will be shown in the following section that the parameters 0, and p t can well be correlated to the Gutmann's donor number of the solvent.
-
VI. Relationship between P, and Gutmann's Donor Number DN V. Gutmann has introduced the donor number of a solvent in order to interpret the ion-solvent interactions by the electron donor-acceptor approach.37," The donor number of Gutmann, DN, has been defined as the molar enthalpy for reaction of a donor solvent with the reference acceptor SbC15in 1,2-dichloroethane. (59) Randles, J.; Schiffrin, D. J. Electroanal. Chem. 1965, 10, 480. (60) Ganjina, I. M.; Damaskin, B. B.; Kaganovich, R. I. Elektrokhimiya 1972, 8, 93. (61) Frumkin, A. N.; Iofa, Z. A.; Gerovich, M. A. J . Phys. Chem. (Moscow) 1956,30, 1455. Frumkin, A. N . 'Potenzialy Nulevogo Zaryada"; Nauka: Moscow, 1979. (62) Trasatti, S. In "Modern Aspects of Electrochemistry";Conway, B. E.,Bockris, J. O M . , Eds.; Plenum Press: New York, 1979; Vol. 13, 81. (63) Case, 8.; Hush, N.; Parsons, R.; Peover, M. J . Electroanal. d e m . 1965, 10, 360. (64) Izmailov, N . A. Dokl. Akad. Nauk SSSR 1960,134,1390; 1963,749, 884. (65) Irving, H.; William, R. J. P. Nature (London) 1948, 162, 145. (66) Gutmann, V.; Wychera, E. Inorg. Nucl. Chem. Lett. 1966, 2, 257.
with the square of the correlation coefficient 9 = 0.9843. Equation 25 shows that the value of 0, becomes equal to zero for the solvent of D N = -8.83 eV, and consequently (AGOi&- for this ideal solvent may also be equal to zero for any cation according to eq 22, or in other words, such an ideal solvent has no chemical interaction with any cation. It may therefore be possible to define the Gutmann's donor number in an absolute scale as referred to the ideal solvent on the basis of eq 25 and rule I. Let us denote the absolute scale of the donor number of a solvent defined in this way as a, us = D N 8.83, eV (26)
+
then it is found that the coefficient 0.103 in eq 25 can be identified with the reciprocal of the absolute donor number of water aw = 0.78 8.83 (ev), and we obtain from eq 25 and 26
+
P, = .,/ow
= Pt/PWa
(27)
taking into consideration eq 13. According to eq 27, p t can be converted to a, by multiplying a W / p w a= 10.15 to p t , and rule 11, eq 23, can be expressed by an equivalent equation in terms of ci and us (AGoJgcs/~i = ( p w a / a w ) ~ i=~ ,0 . 0 9 9 ~ i ~ ,
(28)
Equation 28 shows that the solvation free energy of an ion for solvent s is proportional to the bond energy of the molecular adduct SbC15solvent,whether the ion belongs to the (a), (b), or (c) group. It may therefore be concluded that the solvation bonding of a monoatomic cation can be interpreted essentially by the electron donor-acceptor concept as emphasized by Gutmann3' and Izm a i l ~ v the , ~ ~parameter p: gives an absolute measure of the electron-donating property or the absolute basicity of the solvent, and the parameter ci gives an absolute measure of the electronaccepting property or the absolute acidity of the cation. Using a, = 8.83 eV for dichloroethane, we can estimate the parameters P, and p t for dichloroethane by eq 27 at 0.919 and 0.870, respectively, and the absolute acidity ci for SbC15can be estimated at 10.15 eV by eq 28 within an accuracy of neglecting the entropy term of the molecular adduct SbC15-dichloroethane. It is not clear at present, however, why the values of DN for four solvents described above show some deviation from the linearity between P, and DN, as seen in Figure 11, whereas rule 11, eq 28, is equally well applicable to these and other solvents in general. On the other hand, a measure of the softness for the monoatomic cations in water has also been given theoretically by Klopmad' as the difference between the energy of the lowest unoccupied molecular orbital of a cation in the gas phase and the energy of desolvation of the ion calculated by Born equation, which follows the sequence of the softness in the Ahrland's scale.5* According to Klopman theory, the hard-hard interactions are essentially electrostatic (charge controlled) while the soft-soft interactions are essentially covalent (orbital controlled). It is noted, however, that (ACoi)gcs/zi for a cation can be expressed empirically by a single formula-the product of the absolute acidity of the cation and the absolute basicity of the'solvent-whether ~~~
~~~~~
~
(67) Klopman, G. J . Am. Chem. SOC.1968, 90, 223.
3930 The Journal of Physical Chemistry, Vol. 89, No. 18, 1985
Notoya and Matsuda
/ /OH
n
-
0
0
~
TL
~
~
5
ePb "
'
" IO
~
~
15
'
"
"
20
Ii. Lev1 Figure 13. Relation between D'(MC1) and Ii: (0),(a) group; (A), (b) group; (a), (c) group.
D' (MC 11, [eVI Figure 12. Relation between D'(MF) and D'(MC1).
the ion belongs to the hard or the soft group. Therefore, it seems that the Klopman theory does not hold for the ionsolvent interactions since the solvation bond of the cation reveals the nature of the typical dative bond independent of the hard or soft nature of the cation.
VII. Rules I and I1 for the Dissociation of Gaseous Diatomic Molecules It will be shown in the present section that rules I and I1 for the solvation of the monoatomic cations can be extended to the dissociation of the gaseous diatomic metal halogenides and hydrides, if we define the dissociation energy D'(MX) of the molecule MX by the energy required to separate the constituent atoms into cation M+ and anion X-at infinite distance. The value of D'(MX) defined in this way can be calculated by eq 29 using the usual dissociation energy D(MX)68 D'(MX) = D(MX) + Zi - A, (29) where Ziis the ionization energy for monovalent cation i and A, the electron affinity for anion x. The values of A, used here are 4.1, 3.81, 3.51, 3.29, and 0.75 eV for F, Cl, Br, I, and H atoms, respectively. l 4 The values of D'(MX) for the metal fluorides, bromides, iodides, and hydrides will be compared on the one hand with the values of D'(MC1) for the chlorides (rule I) and on the other with the values of Zi (rule 11) for a number of ionic species, as was done for iAj{(AGoi)m/zi]and iAJ{(AGoi)p/zi) for the solvation of the monoatomic cations. Figure 12 shows the relation between D'(MF) and D'(MC1) as an example. It is found that D'(MF) is proportional to D'(MC1) for the cations available at present. The situation for the other halogenides and hydrides is quite similar to that for the fluorides, and we obtain eq 30 for the cations of the (a), (b), and (c) groups D'(MX) = &D'(MCl)
I/
(30)
with the square of the correlation coefficient 9 > 0.9540, where 8, is now a constant characteristic of anion x. Equation 30 shows that rule I for the solvation of the monoatomic cations holds good for the dissociation enthalpies of the diatomic metal halogenides and hydrides. Furthermore, we obtain a proportional relation between D'(MX) and Zi for the (a) group cations D'(MX) = Zip/ (31) with r2 > 0.9317, as illustrated in Figure 13 by D'(MC1) vs. Zi plots, where p$ is a constant characteristic of anion x. Equation 31 shows that rule I1 holds good for the single bonds of the halogenides and hydrides of the (a) group cations. It is noted, (68) Krasnov, K. S. "Molekulyarnye Postoyannye Neorganicheskikh Soedinenii"; Khimiya: Leningrad, 1979.
1.50 -
p," 1.00 -
0.50-
1
I
I
I .oo
0.50
1.50
4 Figure 14. Relation between pxpand 0, for the gaseous diatomic metal halogenides and hydrides. TABLE VI: List of 0, and px' for the Gaseous Diatomic Metal Haloeenides and Hvdrides
ion F
c1BrI' H-
8,
P2
1.10 1.oo 0.97 0.92 1.11
1.28 1.14 1.10 1.05 1.25
however, that eq 31 does not hold quantitatively for the cations of the (b) and (c) groups, but these ions are located under the straight line eq 31, as seen in Figure 13, indicating the softness nature of these ions. The values of p, and p: in eq 30 and 31 are listed in Table VI, and the graphical representation for the relation between p: and 8, is shown in Figure 14. It is found that pxa is proportional to 8, with the gradient equal to pCla; Le., we obtain
P, = P?/PCla
(32)
in analogy to eq 13 for the solvation of the cations. It may be concluded from eq 30-32 that the nature of the single bond of the metal halogenide and hydride can also be explained by the electron donor-acceptor concept, and the parameter pxa characteristic of anion x can be regarded as an absolute measure of the electron-donating property or the absolute basicity of the anion for the formation of the diatomic bond. It will be shown in the following section that the parameter p: for the halogen anion determined in the present section gives also the electrondonating property for the solvation of the anion.
'
~
'
~
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985 3931
Empirical Rules for the Solvation of Monoatomic Ions TABLE VII: List of (AGO,), the Halogen Anions solvent F 3.88
(in electronvolts) for the Solvation of
CI-
Br-
1-
2.65 2.48 2.33 2.15 2.88
2.39 2.28 2.09 2.07
2.06 1.95 1.82 1.87
c1// Br-
E, 0 ,
and AN for the Solvation of the e., eV
e.
AN
A
1.om 0.943 0.878 0.843 0.700
8.02 7.44 6.93 6.63 5.52
266 252.7 249.1 230.1 189.8
54.8 41.5 37.9 18.9 -21.4
FAc FA NM
1.087 0.943 0.875
8.47 7.35 6.82
294.8 25 1 231.7
83.6 39.8 20.5
W MeOH EtOH AN
2.50 2.50 2.32
3-
TABLE Mi: List of 8, Halogen Anions solvent B.
Water
Methanol Ethanol
4-
j I
Ammonia
ad
3-
i
-
h
01 (3
a 2-
I
4 I -
(AG~,,+,,,
Figure 15. Relation between (AGO,), and (AGO,), for Cl-,Br-, and I- ions in methanol and ethanol at 25 OC and in ammonia at -35 OC.
As is known, Marks and D r a g 0 ~ ~ 9have ' ~ derived a four-parameter equation for predicting the enthalpies (-MI)of reaction of ionic acids and bases in the gas phase based upon the Mulliken's ionic-covalent description of the charge-transfer complexes where D A and 0, are parameters assigned to each acid and DB and 0, to each base,and they have given numerical values of these parameters for a series of acids and bases. Although this equation may be applicable for predicting the enthalpies of reaction of a wide range of acids and bases in fairly good approximation as emphasized by Marks and Drago, the values of -AH(MX,) for reaction of a given anion with a series of cations calculated by their equation using the numerical values of the four parameters given by them (Table I in ref 70) have an excellent linear correlation with the values of -AH(MCl,) for reaction of chlorine ion with the same series of cations which is given by -AH(MX,)/n = [(-AH(MCl,)/n)] + C, with the square of the correlation coefficient 9 > 0.9985,where C, is a constant characteristic of anion X- and n = 1 or 2. It should be noted that this correlation is inconsistent with the empirical relation eq 30 for the diatomic metal halogenides and hydrides. Therefore, the Marks and Drago treatment of the cation-anion interactions in the gas phase based upon the Mulliken theory seems to leave some question.
VIII. Rules I and I1 for the Solvation of Halogen Anions The standard chemical free energy of solvation of halogen anion x for solvent s can be evaluated by eq 4 from the ~ the solvent. The values of xAj((AGo)g.Jz) and ( A G O H + )for values of (AGox)gIJ estimated in this way are listed in Table VI1 for a series of solvents. Although the number of the ion and the solvent in the table is limited, it is possible to examine the validity of rules I and I1 for the solvation of the halogen anions by com~
~
~~~
(69) Marks, A. P.; Drago, R. S. J. Am. Chem. Soc. 1975, 97, 3324. (70) Marks, A. P.; Drago, R. S.Inorg. Chem. 1976, 15, 1800.
Figure 16. Relation between (AGO,), in water, ethanol, and ammonia.
and p: for the halogen anions
on the one hand with (AG0,jp and on the other with the absolute basicity of the anion pXp obtained in the previous section from rule I1 for the dissociation of the metal halogenides. It is found that there exists a good linearity between (AGO,)and for C1-, Br-, and I-, as illustrated in Figure 15, which is given by the regression line paring (AGO&
(AGO,),
= Os(AGOx)g-w
(33)
with 9 > 0.9996 for methanol, ethanol, and ammonia and 9 = 0.9920 for acetonitrile, where 0, is a constant characteristic of the solvent. Equation 33 shows that rule I holds good for the solvation of the halogen anions. The parameter 0, obtained from eq 33 is shown in Table VI11 for eight solvents. Furthermore, there exists a good linearity between and the absolute basicity pXp of anion x for a given solvent, as illustrated in Figure 16, which can be expressed by the regression line (AGOx)gcs = 4 P x a - Po)
(34)
with 9 for water 0.9947,for methanol 0.9979,for ethanol 0.9960, and for acetonitrile 0.9829,where e, is a constant characteristic of solvent s and po has a definite constant value 0.80 independent of the solvent. Equation 34 shows that rule I1 holds also for the solvation of the halogen anions with a correction term po for the absolute basicity of the anion, but the physical meaning of po is not clear at present. The parameter c obtained from eq 34 is listed in Table VIII. It follows from eq 33 and 34 that can be correlated to e, by
0s = d e w (35) which is analogous to eq 13 for the solvation of the cations. Figure 17 shows the 0, vs. e, plots for eight solvents obtained from the
3932 The Journal of Physical Chemistry, Vol. 89, No. 18, 1985
Notoya and Matsuda
TABLE IX: Summary of the Empirical Rules for the Solvation of the Monoatomic Ions and the Related Correlations solvation (cation) dissociation (MX) solvation (anion) rule I rule I1
= Ps(Ac$)gtw ( A G i)g+Jzi = €ips
D’(MX) = pXD‘(MC1)
D’(MX)= q p x a
( A c o x ) g c s = Ps(AGox)g+w (AGO),+, = fs(pxa - 0.8)
0s = psa/pwa = Psb/Pw b = PSClPWC= osio, us = DN t 8.83, eV
ox = PxalPCea
ps=
E J E ~=
Os=
AN
(Aczi)g,
eJew
+ 211.2
q = Iilzi, eV (hard ions, (a) group) q = 0.936 {(IJz.) - 0.94}, eV (intermediate ions, (b) group) q = 0.862 ((Ii/zi) - 1.43}, eV (soft ions, (c) group) 1.51
FA I
1.0
FI
EtOH
1
OO
20
40
80
60
100
AN
Figure 18. Relation between j3, and the Mayer’s acceptor number AN cs,
Figure 17. Relation between j3, and anions.
of the solvent.
Lev1
for the solvation of the halogen
values in Table VIII. In fact, the relation between Paand tIIis given by 8, = 0.1278, and the coefficient 0.127 can be identified with the reciprocal of e, = 8.02 eV, indicating the validity of eq 35. In order to explain the physical meaning of e,, the parameter j3, will be compared with the acceptor number A N of the solvent i n t r o d u d by Mayer et al.’* The acceptor number A N has been defined by them by the chemical shift of the 31Presonance frequency of N M R spectra of Et3P0 in the reference solvent nhexane. Mayer has recently reported the numerical values of A N for a number of solvents,’l and the solvents in Table VI11 except ammonia are available for the comparison of A N with 0,. Figure 18 shows the relation between j3, and AN, which is given by the regression line j3, = 0.0037(AN 211.2) (36)
+
with r? = 0.9664. It follows from eq 36 that j3, becomes zero for an ideal solvent whose acceptor number equals -21 1.2; consequently, (AGO,),:, for this solvent can be regarded as zero according to eq 33, or in other words this ideal solvent has no chemical interaction with any halogen anion. It may therefore be possible to define the acceptor number of Mayer in the absolute scale as referred to the ideal solvent. Let us denote the absolute scale of the acceptor number defined in this way as 8, e, = AN + 211.2 (37) then the coefficient 0.0037 in eq 36 can be identified with the reciprocal of the absolute acceptor number of water Ow = 54.8 21 1.2 = 266 and eq 36 can be put into the form
+
8, = o s / e w
(38)
(71) Mayer, U., ref 1, p 219. (72) In this paper the periodic group notation is in accord with r e n t actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the pblock elements comprise group 13 through 18. (Notethat the former Roman number deignationi~ pigerved in the last digit of the new numbering: e.&, I11 3 and 13.)
-
8s Figure 19. Relation between the absolute acidity acceptor number 8, for the solvent.
c,
and the absolute
in analogy to eq 27 for the solvation of the cations. The parameter 8, calculated by eq 37 is shown in Table VI11 together with A N of Mayer. Using eq 35 and 38, we can convert 8, to t, by the equation 8,
= (tw/Ow)O, = 0.030,
and (AGO& can be expressed in terms of 0, and equation equivalent to eq 34 W 0 x ) g . 3 = (tW/@W)Wx.- Po) = 0.034(Pxa - 0.8)
(39) pxa by
an
(40)
It may be concluded that the solvation bond of a halogen anion is also a typical dative bond essentially similar to that of the molecular adduct Et3POsolvent, and E, as well as 0, gives an absolute measure of the electron-accepting property or the absolute acidity of the solvent. Figure 19 shows the graphical representation for the relation between 8, and 0, for seven solvents in Table VIII, which is given by 6, = 0.0290,, indicating the validity of eq 39. The value of AN for ammonia is estimated by eq 37 and 39 at -21.4 from t, = 5.52 eV in Table VIII.
IX. Concluding Remarks Although the solvation bond of the monoatomic ion has been discussed by most of the authors assuming the electrostatic nature of the ion-solvent interactions with emphasis on the ion-water system, it has been shown in the preceding sections that the free energy of solvation of an ion is simply proportional to the bond strength of the molecular adduct SbCISsolvent or Et3POsolvent, representing the donor-acceptor nature of the ion-solvent inter-
J. Phys. Chem. 1985,89, 3933-3935 actions. The electron-accepting and -donating properties or the acidity and the basicity of the ion and the solvent for the formation of the solvation bond have been defined in the absolute scales based upon the thermodynamic empirical rules. For convenience the empirical rules and the related correlations developed in the
3933
preceding sections are summarized in Table IX. It is hoped that these thermodynamic rules are helpful to the further development of the theoretical and experimental approaches to the elucidation of the problems related to the bonding of the monoatomic ions.
Eiectrochemlstry at Very High Potentials: The Use of Uitramlcroeiectrodes In the Anodic Oxidation of Short-Chain Alkanes John Cassidy, S. B. Khoo, Stanley Pons,* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
and Martin F'leischmann Department of Chemistry, The University, Southampton. England SO9 5NH (Received: August 24, 1984; I n Final Form: February 18, 1985)
The use of ultramicroelectrodes in aprotic solvents containing no intentionally added supporting electrolyte allows the observed anodic oxidation limit in acetonitrile to be considerably extended. The anodic oxidation of methane, butane, and other aliphatic alkanes is clearly observed under steady-state conditions at potentials up to approximately 4.3 V (Ag+ reference). The oxidation of the solvent occurs significantly at potentials greater than 4.5 V and appears to result in radical coupling reactions forming both soluble and insoluble polymers.
Introduction The electrochemical oxidation of alkanes (chain lengths greater than 5 carbons) was first accomplished by Fleischmann, Pletcher, and Clark14 in the late 1960's and early 1970's. In very dry aprotic solvents and various supporting electrolytes, it was possible to observe part of the voltammetric wave of the oxidation of n-pentane, isopentane, n-hexane, 2-methylpentane, 3-methylpentane, n-heptane, 2,2-dimethylpentane, and n-octane. It was shown that anodic oxidation of these substrates led to the formation of the corresponding carbenium ion which reacted rapidly with the electrolyte system. These studies were extended to strongly acidic systems to stabilize the carbenium species by the same w o r k e d 6 and later by Fritz and Wurminghausen' and Pitti et a1.8 The anodic oxidation limit in the solvents used has clearly been shown to be a function of the support electrolyte anion added, and follows the order C10, < BF4- < PF6-.14 The question of the contribution of the oxidation of the solvent to the current at the anodic limit has not been fully explored. Tourillon et a1.9 have observed the formation of polymeric acetonitrile/electrolyte films at the platinum/solution interface in, for example, the acetonitrile/perchlorate system at +2.6 V. Whether the solvent itself is catalytically activated or whether it reacted with oxidized electrolyte is not entirely clear. The films are obviously conductive and allow the continued passage of current after their formation. (1) Fleischmann, M.; Pletcher, D. Tetrahedron Lett. 1968,6255. (2) Clark, D.; Fleischmann, M.; Pletcher, D. J. Electroanal. Chem., 1973, 42, 133. ( 3 ) Clark, D.; Fleischmann, M.; Pletchcr, D. J. Chem. Soc., Perkin 1979, 1578. (4) Fleischmann, M.; Pletcher, D. Chem. Ing. Techn. 1972,44, 187. ( 5 ) Bertram, J.; Fleischmann, M.; Pletcher, D. Tetrahedron Lett. 1971, 349. (6) Bertram,J.; Coleman, J.; Fleischmann, M.; Pletcher, D. J . Chem. Soc., Perkin 1973,374. ( 7 ) Fritz, H.; Wurminghausen, T. J . Electroanal. Chem. 1974, 54, 181. (8) Pitti, C.; Bobilliart, F.; Thiebault, A,; Herlem, M.Anal. Left. 1975, 8, 241. (9)Tourillon, G.;Lacazc, P.; Dubois, J. J. Electroanal. Chem. 1979,100, 247.
0022-3654/85/2089-3933$01.50/0
We shall see that with no intentionally added supporting electrolyte the voltammetric limit of the system is greatly extended. Under these conditions it becomes possible to study the anodic reactions of compounds with extremely high oxidation potentials. It is clear that because of the high resistance of most pure solvents that added supporting electrolyte is necessary to carry the charge passed at a large electrode through the bulk solution. The extremely small currents present in the ultramicroelectrode systems described herein may be carried in the bulk by ions present from autoprotolysisof the solvent, or by the presence of impurities at low levels. The quantitative treatment of the problem has been discussed.lOJ1 The use of ultramicroelectrodes in solutions containing little or no deliberately added supporting electrolyte has been demonstrated p r e v i ~ u s l y . ' ~It~is~ pointed ~ ~ ~ ~ out that many other interfering processes are also eliminated in electrochemical experiments where supporting electrolytes are absent; these include ion-pair association reactions of the reactant and its electrogenerated intermediates and intermediates with the supporting electrolyte, specific adsorption of the electrolyte leading to double layer corrections and other considerations, and problems associated with the isolation and characterization of the products of the electrochemical reaction.
Experimental Section Full details of the preparation of platinum microdisk and gold microring electrodes have been described previously.22 The platinum disk electrodes used in this work had diameters from 0.6 to 25 pm. These were mounted in soda glass tubes. The (10) Bond, A.; Fleischmann, M.; Robinson, J. J . Electroanal. Chem. 1984,
172,11. (11) Bond, A.; Fleischmann, M.; Robinson, J. J. Electroanal. Chem., in press. (12) Bond, A.; Fleischmann,M.; Robinson, J. J. Electroanal. Chem. 1984, 168, 299. (13) (a) Oldham, K.B.J. Elecrroanal. Chem. 1981,122,l.(b) Heinze, J. J . Electroanal. Chem. 1981, 124, 73. (c) Shoup, D.; Surbo, A. J . Electroanal. Chem. 1982,140,231. (d) Aold, K.;Osteryoung, J. J. EIectroanal. Chem. 1981, 122, 19. (14) Howell, J. 0.; Wightman, R. M. Anal. Chem. 1984,56, 524.
0 1985 American Chemical Society
