THERMODYNAMIC EVALUATION OF INERT PAIREFFECT
March, 1958
acid and salt and may be written AE = E , E,I - 2a‘ where E , and Eel are the resonance and electrostatic energies already defined, and where 2 a’ is incorporated in the constant. The applicability of the above two equations has been discu~eed1~.1~ at some length. Inherent in them is the assumption that the entropies of proton addition to the polymethines should remain constant with n . This is not too optimistic an assumption for the case of linear alltrans species, but anyway it cannot be avoided because no entropy data are available. I n Table I are listed the pK. values of some simple polymethines; also included in the table are E,, and AE and the predicted p K . values for the illustrative case D = 3 . Linearity of a plot of K. versus AE obtains within experimental error for any varue of D within the range 1-4.5. The value D = 3 has been chosen as a mean value and has been used to plot Fig. 1; Fig. 1 has in turn been used to obtain the predicted values of pKa quoted in Table I. The p K , values predicted for any value of D in the range 1-4.5 do not differ significantly from those for D = 3.
+
TABLE I Moleoulco
n=O
Resonance energy, EI
2a‘ -I-0.8284 0.9920 2 a ’ f 1.0676
‘AE
(ev.) b
n = 2 n = 3 n = 4
+ 2a’ + 1.1104 2a‘ + 1.1516
2.710 1.856 1.590 1.461 1.397
n = 19
2a’
+ 1.2344
1.171
n = l
2a‘
P K ~ (exp.)e
PK. (theor.)
/
-15.0
-4.1
/ / /
-0.7 1 .o
/
1.75
/
4.65
..
2a’ -I-1.2732 1.105 5.5 / Gives the value of n in the general formula CHa CHs >N-(CH=CH).-CH=&< (With B = 20.0 CHI CB kcal./mole and D = 3. See reference 2 of text. a
.
The observed trend of pK, values consists then of the resultant of two parts. The resonance energy of the salt with (15) L. P. Hammett, “Physical Organic Chemistry,” McGraw-Hill
Book Co., Inc., New York, N. Y., 1940.
353
respect to the conjugate acid increases as n increases, thus leading t o a greater stabilization of the salt a t larger nvalues. Thus if the only operative part were the resonance energy one would expect pK, to decrease with increasing n. This, however, is the reverse of that observed and is in part responsible for the many obscurities in the literature. The electrostatic repulsion energy in the conjugate acid decreases as n increases, thus leading to a greater stabilization of the salt at the smaller n-values. Both effects together lead to an increasing stabilization of the conjugate acid with increasing chain length, and produce the observed p K , variation. The following equilibria also have been measured,18 and form a very illustrative example, since here there are no gross electrostatic effects operative CBHdH=C-
(CH=CH) ,,-NHCeHs
-+-
AH8 CBH~N=C-(CH=CH)~-NHCGH~
I
+ H+
CH: where n = 0, 1 and 2 . Here the polymethinium salt is now the conjugate acid, whereas formerly it was the base. If we refer to the acid dissociation constants of the polymethinium salts as pK.2, we may call those above pK.1. The resonance energy of the salt with respect to the conjugate base is’still given by E,, and thus increases as n . Accordingly the pKal values should also increase with chain length. However, the pK.1 values exhibit no well-defined trend, although their general tendency is to increase as expected. This development might suggest more experimentation, or perhaps further attests to the limitations of Huckel theory. It is appropriate a t this point to add a cautionary note. If one considers the various assumptions which have been made throughout ( L e . , entropy neglect, the use of Huckel theory for polyenes and the existence of a D)it becomes difficult to say with certainty that a resonance energy decrease with chain length is ruled out. This latter however is not the major concern of the present work. On the contrary interest is primarily directed to the fact that the experimental data can be reconciled to an increasing resonance energy if the compensating electrostatic part is made large enough. The writer wishes to thank Professor W. T. Simpson for many informative discussions and criticisms. He is also grateful to Dr. R. V. Nauman for much help on the matter of dielectric constant behavior. (16) G. Sohwarzenbach, Z. Elektrochem., 47,40 (1941): G.Schwarzenbsch and K. Lutz. Helu. Chirn. Acta. 23, 1179,1147. 1163 (1940).
THERMODYNAMIC EVALUATION OF THE INERT FAIR EFFECT1 BY RUSSELL S. DRAGO W . A. Noyes Laboratory of Chemistry, Universitg of Illinois, Urbana, Illinois Received December 16, 1967
A study of the thermodynamic data for chlorides of the elements of the boron and carbon families has indicated that the instability of thallium(II1) chloride and of lead(1V) chloride can be attributed t o the fact that in a given family the strength of the covalent bonds formed by these elements decreases as the atomic number of the element increases. It is further shown that Sidgwick’s explanation of these stabilities, based on an inert pair of electrons, is not correct. A qualitative, quantum mechanical explanation for this phenomenon is proposed, and possible extensions of this concept are indicated.
Introduction I n contrast to the lighter elements, which usually use all their valence electrons in compound formation, the heavier elements of the boron and carbon families form more stable compounds when two of the valence electrons are not involved in bonding (e.g., TlC1, PbClz and BiCIJ. To explain this phenomenon, Sidgwick2 postulated the existence (1) Presented a t the Sept.. 19.56, Meeting of the Am. C h ~ m .SOC., Atlantic City, N. J., Division of Chemical Education. (2) N. V . Ridgwick, Ann. Reports, 20, 120 (1933).
of an “inert pair’) of electrons in the heavy elements, thallium, lead and bismuth. Although this explanation is readily invoked to correlate behaviors of these elementslaan adequate theoretical explanation has not been advanced. An evaluation of the thermodynamic data pertaining to the stabilities of some of these compounds will be made, and a qualitative quantum mechanical explanation based upon the valence bond approach (3) E. 8. Could, “Inorganic Reactions and Structure.” Henry Holt and Co., New York, N. Y.,1985, pp. 120,2413.
354
RUSSELL S. DRAGO
Vol. 62
will be proposed to explain the stability relationships. Discussion The currently accepted explanation for the existence of an inert pair was originally proposed by Grimm and S ~ m m e r f e l d . ~The inertness in the heavy elements was attributed to stabilization resulting from a completion of the ‘%” shell of electroiis, but more recently it is attributed to stabilization as a consequence of the “Lanthanide Contraction.” If the reluctance of %” electrons to participate in bond formation is truly a result of stabilization of these electrons, ionization potentials for these elements should indicate that a larger amount of energy is necessary to remove these electrons from the heavier atoms than from the lighter ones. However, from the values of ionization potentials given in Table I,6 it can be seen that “s” electrons are stabilized to a larger extent for fourth row elements (Ga and Ge) than for sixth row elements (T1 and Pb). Since the inert pair effect is not encountered2 in the compounds of gallium or germanium, the explanation advanced by Grimm and Sonimerfeld that stabilization of “s” electrons occurs is not adequate.
as the atomic number increases in a family of elements. The instability is thus expected from the thermodynamic data and an explanation based on rate considerations is not necessary (see AHozss for equation 1in Table 111). Any one or any combination of the following factors could result in an increase in the magnitude of the free energy value for equation 1 (i.e., make it more negative) and could account for the decrease in stability of the higher oxidation states of the heavier elements: (1) an increase in the crystal stabilities of the compounds in which the heavier elements are in the lower oxidation state; (2) a decrease in the crystal stabilities of the compounds in which the heavier elements are in the higher oxidation state; (3) a decrease in the bond strength of the compounds of the heavier elements in the higher oxidation state (ie., MCl,); (4) an increase in the bond strength of the compounds of the heavier elements in the lower oxidation state (ie., MCln - 2). Thermodynamic data are available (see Table 11) to permit an evaluation of all four of these effects’ and thus to ascertain the major cause of the observed stability relationships. An explanation of the observed stabilities based TABLE I on factors 1 and 2 would attribute the stability IONIZATION POTENTIALS FOR REMOVAL OF THE rrs” ELEC- differences t o crystal lattice effects. The standard TRONS heats of sublimation for the chloride compounds Energy t o Energy to Energy$, (Table 11) indicate that these effects are of some remove s remove ‘Y remove “sl’ electrons elect,rons electrons importance in determining the standard free Element (e.v.1 Element (e.v.) Element (e.v.) energies of equation 1; however, these effects are B 63.1 C 112.3 N 175.3 not large enough to account for the entire energy A1 47.3 Si 78.6 P 116.4 differences, and in many instances crystal lattice Ga 51.0 Ge 79.6 As 112.4 energies have almost no part in accounting for the In 46.9 Sn 69.9 Sb 99.5 observed stabilities. For example, the heats of T1 50.0 Pb Bi 100.7 74.0 formation (Table 111) indicate that solid GaCh is Causes for the occurrence of an inert pair can be more Etable than solid T1C13 with respect to deascertained by evaluating : (1) the instability of composition into the monochloride by 68.5 kcal./ many of the solid compounds of the higher oxida- mole (see AHQ equation 1); however, the heats tion states of the heavier elements; and (2) the of sublimation indicate similar crystal lattice instability in solution of compounds in which the stabilities for these compounds. Also, it is very unlikely that the observed trends in stability for element is in the higher oxidation state. Stabilities of the Solid Compounds.6-The de- all the solid compounds of the elements of the composition reaction of the higher-valent halides boron, carbon or nitrogen families could be accounted for simply on the basis of crystal stabilican be summarized by the general equation ties. The trends in bond energies (factors 3 and 4) MX,(solid) MX,-2(solid) + Xz(gas) (1) may be of much greater general applicability in where n is the maximum oxidation state of a par- explaining many of the phenomena attributed to the ticular element, and X is a halogen. inert pair. One of the first questions to be answered is The standard heats of reaction (2) can be used whether the tendency of the heavy elements to as a relative measure of the bond strengths of the decompose is due t o thermodynamic instability chloride compounds of the elements in the highest or is due to a kinetic instability caused by the oxidation state (factor 3) compounds of the heavier elements decomposing (7) The sum of these terms is related to the standard free energy at an appreciable rate while the compounds of the lighter elements decompose infinitely slowly. As ( A P ) for equation 1 by the expression AFO = AHQ - TAfP will be seen later, the thermodynamic data parallel the observed trends in stability, and the magnitude where 2’ refers to the absolute temperature and So refers to the standof the free energy of the decomposition reaction ard entropy. In the comparison of the relative stabilities of the chlo compounds of any one family of elements, it will be aasumed (equation 1) increases (Le., becomes more negative) ride that the entropy effects can be neglected. The limited entropy data
a.
1
.
i=
(4) H. G . Grirnrn and A. Sommerfeld, 2. Physik., 36, 36 (1926). (5) T . Moeller, ”Inorganic Chemistry,” John Wiley and Sons, Inc., New York, N. Y., 1952, p. 15G. ( 6 ) The evaluation k i l l be limited to the chlorides of the elements of the bW0n and carbon families, for in other instances. sufficient thermodynamic data have not been reported.
which are available are in accord with this assumption. Thus, an attempt mill be made to correlate the trends in stabilities ( L e . , free energies) with the standard heats associated with the four factors listed above. Since, as it will be seen shortly (see Table 111, eq. 1 such a correlation can be made, the assumption t,hat the entropy can be neglected seems t o be valid.
I
March, 1958
‘rHERMODYNAMIC
EVALUATION OF I N E R T PAIR EFFECT
TABLE I1 STANDARD HEATSOF FORMATION A N D SUBLIMATION (BCAL./ MOLE)
AHQzos formation
-
25.6 4.9
+
9
-
18
- 16 - 94.5 -166.2 -125.4 -128.4 83.9 83.6 - 85.9 - 25.5 -145.7 130 -130.3 - 78.85
-
Ref.
b H o m sublimation AHQnss evaporation
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 14
.. 45
Ref.
.. 9
*.
..
26.5 32.3
8 10
28 (19) (39) (19) (29) 44.3
9, 12 8 10 13 10 10
..
.. ..
..
.. ..
7.9 (AHeO) 8 8 8 . 3 (AHeO) b 9.0( AHeO) 171.7 15 88.04 15 78.44 15 72 15 46.34 15 - 72.2 8 10 (8.8) - 71.5 8 10 (11.1) - 75.2 8 16.1 8 - 64.7 26.1 8 8 - 95.3 8 11 (15) - 93.9 14.1 8 10 Klemm” indicates that the heats of sublimation of T1Cla and. GaC13 are about the same order of magnitude. The ( ) indicate estimated values for the heats of sublimation a t 25’ from values at other temperatures. These values are probably correct to A4 kcal. and since this evaluation is concerned with orders of magnitude larger than this, this accuracy will suffice. Estimated by assuming Trouton’s constant is 22 and employing the reported boiling point of 137O.10
lf(gas)
+
Clz(gas) = MCl,(gas)
355 (2)
The standard heats calculated16 for reaction 2 are listed in Table I11 along with values for other changes that are to be discussed shortly. With the exception of the compounds of the second row elements, the values indicate a decrease in the strengths of the bonds holding the atoms together as the atomic number of the central atom increases within a family. Since the electronegativities of the last three elements in any one family are approximately constant,l7 the ionic character is roughly constant, and the decrease in bond energy can be attributed to decrease in the strength of the covalent bonds holding the molecule together. Thus, an important factor causing the instability of thallium trichloride can be attributed to a decrease in the strength of the covalent bonds between the thallium and chlorine. The difference in bond strength of the chlorides in the maximum oxidation state relative to the bond strength of the chlorides with an oxidation state of two less (ie., factors 3 and 4) can be obtained by considering the standard heat of the reaction (see Table 111) MCl,-2(gas)
+ Clz(gas) = MCl,(gas)
(6)
Since the reverse of equation 6 represents the most common decomposition reaction of, the highervalent halides, and since lattice energies are not involved in this reaction, the values of AHo obtained are a true measure of the relative bond strengths in the two oxidation states of the metal. The values of AHo a t 25” for this reaction can be calculated from the difference in the standard heats18pertaining to the reactions M(so1id)
M(so1id)
+
Clz(gas) = MCl,(gas)
+ nG Clg(gas) = MCL2(gas)
(7) (8)
TABLE 111 Comparison of AH0298corresponding to equations 2 and 6 (see Table 111) indicate that the instability STANDARD HEATS(- AH02ss) OF IMPORTANCE IN EVALUATING of thallium(II1) and lead(1V) chlorides is due to a THE STABILITIES OF THE SOLIDCHLORIDES
- AHozm (kcal.)
B AI Ga In TI C Si Ge Sn Pb
161.3 134.3 110.4 67.9
46.7 -5.0
191.7 213.2 172.4 147.6 109.4 197.2 233.7 200.3 192.7 115.2
decrease in covalent bond strength in these compounds; thus, of the four factors listed above, the
120.1 133.3 115.4 71.4 48.9
65.7 27.3
71.6 79.9 57.0 76.2 60.5
127 87.9
(8) U. S. Bureau of Standards, “Selected Values of Chemical Thermodynamic Properties,” Circular 500, 1949. (9) F. Irmann, H s l v . C h i n . Acta, 33,1449 (1950). (10) Kuhaschewski and Evans, “Metallurgical Thermochemistry,” 2nd ed., John Wiley a n d Sons, Inc., New York, N. Y., 1956. (11) L. L. Quill, “Chemistry and Metallurgy of Miscellaneous Materials: Thermodynamics,” McGraw-Hill Book Co., Inc., New York, N. Y., 1950. (12) W. Fischer and 0. Rahlfs, Z . anora. Chem., 206, 1 (1932).
(13) W. Klemm, Z . physik. Chem., B12, 17 (1931). 24, 1677 (19541,E n d . (14) F.Ya. Kulba, J . Can. Chem., U.S.S.R., Translation. (15) W. M. Latimer, “Oxidation Potentials,” 2nd ed., PrenticeHall, Inc., New York, N. Y., 1952. (16) The values for the standard heats, a t 2 5 O , of the gas phase reaction 2 can be calculated b y the addition of the standard heats ( a t 25’) which refer to the general equations 3.4 and 5.
M(8) I- n/2 CMg) + M C l M MCL(S) -+ MCL(g) M (g) M (5)
-
(3) (4) (5)
The AH0 values corresponding to equation 3 (the heats of formation of the solid chlorides) and equation 4 (the heats of sublimation of the solid chlorides) are contained in Table TI. The AH0 values for equation 5 can be obtained by multiplying the values for the heats of sublimation of the metals contained in Table 11b y -1. I n thoseinstances where the compounds concerned are liquids, the heats of evaporation are employed i n step 4 of these calculations. (17) H. 0. Pritchard and H. A. Skinner, Cham. Reo.., 66, 745 (1955). (18) The A H Q mvalues for equations 7 and 8 can be calculated from the data on the heats of formation and sublimation oonhined in Trtble 11.
356
RUSSELL S.DRAGO
most important cause for the inert pair effect is factor 3.19 Since an important factor leading to instability of thallium(II1) and lead(1V) chlorides has been identified, a reason for this instability can be proposed. Consideration of the hybrid bond types involved in the formation of these molecules and of the energy requirements of each type reveals the reason these molecules should be unstable with respect to decomposition into molecules that utilize two less valency electrons in bond formation. These considerations permit an extension of the information concerning the chlorides to other compounds of these elements. Correlation between Bond Type and Stability. -The covalent contribution to the bonding for the elements of the boron family in the trivalent state can be described as due to ‘%p2”hybrid bonds, while the bonding in the monovalent state probably involves only the “p” electron. The covalent bonding in the tetravalent compounds of the carbon family can be described as “sp3,” while the bonding in the dihalides involves only the “p2” electrons. The standard heat corresponding to equation 2 can be considered as the resultant energy of the following steps For the boron family elements
Vol. 62
significance in causing the instability observed in the compounds of the heavier elements. The following valuesz2 were calculated for equations 10a and l l a
-
Element Ma’
kcal., w. loa M(g) s2p M(g) SP*
A1 Ga In T1
83.67 109.5 100.8 108
A.HD198
AH%a kcal., eq. 1 l a B p+ ~~
c ~ ~ + M c ~ ~ ~ , ~ ( ~ )
-296.9 -281.9 -248.4 -217.4
The data indicate that the instability of thnllium(II1) and lead(1V) compounds can be attributed to a decrease in the covalent bond forming ability of thallium and lead ( l l a and b). For example: The difference in covalent bond forming ability (equation l l a ) of the elements thallium and gallium is 64.6 kcal. while the AHoZss for decomposition of solid gallium I11 chloride into the monochloride is 68.5 kcal. more negative than for the corresponding thallium compounds. In general, if the elements in the boron and carbon families can undergo chemical reactions and form strong enough covalent bonds ( l l a and b) to supply the energy for promotion (loa and b) and have enough energy in excess to make the magnitude of the free energy large, a stable compound utilizing all the valency electrons in bond formation will result. M (8”) (gas) M (SP? (gas) (loa) When weak covalent bonds are formed, as is the case 3 R4(sp2)(gas) + Clz +MCla(spZ)(gas) (lla) for thallium(II1) and lead(1V) chlorides, a lower energy state can be attained by the system by For the carbon family elements utilizing only the “p” electrons in conipouiid formation. In this case, two less electrons will be M(s2p2)(gaa)--j M(spa)(gas) (lob) involved in bond formation, and we observe the M(sp8)(gaS) 2Cldgas) + MCldspa)(gas) Ulb) From these reactions, it can be seen that AHo stability relationship attributed to the inert pair. The ‘decrease in covalent bond forming ability of for equations 10a and 10b is the promotion energy these elements as the atomic number increases can involved in the hybridization of orbitals, and is an indication of the stabilization of the “s” electron be attributed to the following effects: (1) The relative to its promotion to the “p” orbital. AHo radial part of the bond orbitals is changing in such for equations l l a and l l b is the “bond forming a manner as t o indicate a spread of the valence ability” of the activated element. If AHo as- electrons over a larger arealz3resulting in less oversociated with reaction 10 is large, or if AHo as- lap and weaker covalent bonding. (2) The number sociated with reaction 11 is small, compounds in of inner shell electrons increases and the coulonibic the high oxidation state will become less stable repulsion between these electrons and the inner and the elements will react by utilizing oiily the electrons of the other bonded atoms increases. 24 Although the thermodynamic data which would “p” electrons in bond formation. Because it is permit an evaluation for the compounds of the elepossible to calculate the promotion energy from reported spectral data on electronic transition in ments of the nitrogen family have not been obthe atomic energy levels of the elements,zo~D1 and tained, it would be expected that similar effects will account for the observed stabilities of the combecause the bond forming ability can be determined pounds of these elements. by subtracting the promotion energy from the Stabilities in Solution.-The standard electrode AHo values corresponding to equation 2, it is potentials, EO, for the boron and carbon family possible to decide which of these effects is of greater elements indicate decreased stability in solution (19) The data pertaining to equation 9 indicate t h a t the instaof the high oxidation state of the heavy elements.
-
+
bility of gallium(1) chloride results in a large negative 4 H Q value
M(g)
+ n - 2/2Clz(g) -+ MCl(m - 2)(g)
(9)
for equation 6 and indicates the importance of factor 4 in explaining why the inert pair was reported not t o occur in this compound. Similarly, on the basis of the heats of formation one would expect tin(1V) chloride t o be nearly as stable a s germanium(1V) chloride (see Table 111, A H @for equation 2). The greater stability observed for germanium(1V) than for tin(1V) (equation 6) is probably due to the instability of germanium(I1) relative to tin(I1) chloride. (20) C. E. Moore, “Atomic Energy Levels, Circular 487,” National Bureau of Standards, Volumes I and 11. ( 2 1 ) Backer and Goudsmit, “Atomic Energy States,” McGraw-Hill Rook Co., Inc., New York, N. Y., 1932.
(22) The spectral data which are necessary for the calculation of the promotion energies for thulliuni and f o r the elements of the carbon family (other than carbon) have not been reported. The value of thallium was estimuted from a derived relationship between the second ionization potential of gallium and indium and the promotion energies of these atoms. I n the case of the elements of the carbon family i t will be assumed t h a t since the third ionization potentials are nearly the same, the promotion energies probably also are. These assumptions are very crude and more experimental work is required before a more reliable decision can be made. (23) L. Pauling, THIS JOURNAL, 68, 662 (1954). (24) C. A. Coulson, “Valence,” Oxford University Preps, New York, N. Y . , 1952, pp. 177-178.
Pllarch, 1958
NOTES
For the carbon and nitrogen family elements, the Eo parallels the stability of the oxides formed. The factors affecting the Eo’s of the boron family elements can be evaluated by a process analogous t o that employed by Latimer.16 The over-all reaction can be divided into the following energy steps and AH0298 for each step can be calculated from data contained in the literature.16
the instability of not only the chlorides, but also for most of the unstable compounds of lead and thallium. It is proposed that this factor is the main cause for the stability relationships attributed to the inert pair. Since the bonding in the compounds thallium(II1) methyl and thallium(II1) fluoride is stronger than that in thallium(II1) chloride, one would expect greater stability for these compounds. Coordination of thallium(II1) chloride with strong Lewis bases might also enhance the stability of this compound by formation of stronger hybrid bond types. Many of the stereochemical observations that have been attributed to the inert pair can be explained on the basis of the above proposal. If the covalent bond strength of the compound under consideration is large, there will probably be a large amount of “s” character in the bonds and the unshared electron pair will occupy a hybrid orbital having directional character. If the covalent bond strength is weak, then the lowest energy state will be obtained by keeping the electron pair in the nondirectional “s” orbit and a stereochemically inactive, inert pair will result. Thus, although the interatomic distances in the ion SeBrs- are explained26 by assuming inertness of the 4s electrons and use of 4p34d25s hybrid bonds, the molecule Se(C6H6)zBrzhas a structure in which the four bonds are directed toward four of the five apices of a trigonal bipyramid, one equatorial position being occupied by the stereochemically active pair of unshared electrons in a hybrid orbital.26 The difference can now be explained by assuming the existance of stronger covalent bonds in Se(CeH5)2Brz. Acknowledgment.-The author wishes t o express his thanks t o his fellow staff members and to Mr. Laurence Dempsey a t the University of Illinois for their helpful suggestions regarding the preparation of this manuscript.
-+ -+
Eq.describing the anergy step 26 (12) M(s) M(g) (13) M(g) M+a (9) 3.3(14) M + S (9) nt+* (as) (15) M(s) M+8 (as) 3e-
H O m (kcal.) In 66 58.2
A1 75.0
T1 44.5
Ga
1322.5
1219.3
1303.6
-1432.8
-1438.9
-1309.5
-1301.3
-
-
-
+
1232.4
-+
125.4
50.4
32.0
46.8
Comparison of the above data pertaining to indium and thallium indicate that indium(II1) is more stable because of the lower energy required to remove the three electrons, i.e., step 13. The greater stability of gallium(II1) as compared with thallium(II1) can be attributed to the higher solvation energy of gallium(II1) (step 14). Thus, both of these factors must be considered in order to explain the stability relationships of these ions in solution. Since the nature of the species represented by M+3(aq) is not known, it is not possible to give a quantum mechanical explanation for the stabilities in solution. It would also be of greater consequence to evaluate the stability of the trivalent ions relative to the monovalent ions but the necessary data are lacking for boron, aluminum and gallium. Extensions of These Concepts.-The decrease in covalent bond forming ability with increase in atomic number is probably the principal cause for (25) Step 12 represents the heat of sublimation of the metal: step 13 ia the sum of the energies of the first three ionization potentials; step 14 represents the heat of hydration of the gaseous ion, and, the aum of these three energies (step 15) represents t h e standard heat of the over-all reaction. I t isindicatpd t h a t steps 12 and 13 are endotherpic while step I4 is exothermic. Since the values of AH0290 parallel the values for the Eo’s, the entropy charge can be considered to be nearly constant.
357
(26) L. Pauling, “Nature of t h e Chemical Bond,”’ 2nd E d . Cornell University Press, Ithaca, N. Y., 1948,p. 184.
NOTES LIABILITY OF Cr(1V) TO SUBSTITUTION BY ALLENE. OGARDA N D HENRYTAUBE Contribution from the George Herbert Jones Laboratory, University of Chicago, Chicago 97, Ill. Receiued August 86, 1967
We have studied the dissociation of CrC1++ in acid solution as it is induced by 1 e- oxidizing agents. The particular oxidizing agent used was Mn+++, prepared in situ by oxidizing Mn++ with Ce(1V) or Co+++. The dissociation is induced also by Ce(1V) or Co+++ alone, but the kinetic analysis of these systems is more difficult because the inducing agent is much more rapidly consumed than is the case when Mn+++ is used.
The rate of dissociation was folIowed spectrophotometrically and specific rates were calculated from the initial changes in optical density (OD). The curvature in a plot of (CrCl++) vs. time (the curvature being attributable to slow consumption of Mn+3) is slight enough so that the initial specific rates could be fixed reasonably well. Experimental Of the materials used, only the preparation of CrC1++aq merits detailed description. Green CrClr.6Hs0 is dissolved in 0.05 M HCIOI, and after remaining for ca. 12 hr. to permit CrClz+ to dissociate, the solution is passed through a cation-exchange resin (Dowex 50-X4 was used). Ions such aa CrC12+ are eluted by washing with 0.15 M HCIO,, and CrCl++ aq is brought through by washing with 1 M HC104.
