2970
C. nt. CRISS, R. P. HELD,AND E. LUKSHA
ion to the center of the dipole. If one assumes that the center of the dipole for an unperturbed DMF molecule lies midway between the nitrogen and oxygen atoms and if any steric hindrance by the methyl groups is neglected, one would expect 6, to be slightly smaller than 6, because of the slightly less electronic shielding around the nitrogen atom. The fact that 6, > 6, leads one to conclude that the methyl groups do indeed exhibit some steric hindrance to most of the anions. The fluoride ion is the only ion which does not fit the curve in Figure 1. It may be that this ion is sufficiently small that it can approach the nitrogen without interference from the methyls, in which case 6, should be smaller than 6,. It is interesting to observe that when 6, = 0.68 for the fluoride ion, it falls in place in Figure 1
with the other ions. Whether this is an experimental artifact or real can only be speculated a t this time. On first consideration, one might expect that 6, for aqueous and DMF solutions would be widely different. However, an examination of molecular models shows that the distance to the center of the dipole through the oxygen atom for the two molecules is probably not very different, particularly since these molecules are highly distorted during ionic solvation.
Acknowledgment. The authors are indebted to both the U. S. Atomic Energy Commission and the National Science Foundation for their financial support through Contract AT-(30-1)-3019 and Grant GP-4995 respectively.
Thermodynamic Properties of Nonaqueous Solutions. V.
Ionic
Entropies: Their Estimation and Relationship to the Structure of Electrolytic Solutions112 by Cecil M. Criss,* Department of Chemistry, University of M i a m i , Coral Gables, Florida
$3194
Robert P. Held, and Eugene Luksha Department of Chemistry, University of Vermont, Burlington, Vermont 05401 (Received March 4 , 1968)
Thermodynamic data obtained in this laboratory and from the literature have led to a compilation of partial molal entropies of 1: 1 electrolytes in seve: nonaqueous solvents. For each solvent the absolute entropies of the ions can be expressed by the equation Sz"(X) = a b&'(HzO), where a and b are constants characteristic of the solvent and 8 z 0 ( H 2 0 )is the absolute entropy of the corresponding ions in water. The partial molal entropy of any particular electrolyte in the various solvents increases in the order NHI < N,N-dimethylformamide = EtOH < MeOH < N-methylformamide < formamide < H20 < DzO, indicating that entropies are most positive for those solvents having the higheskdegree of internal order. It is suggested that the absolute entropy of any given ion in a solvent is given by 82' = IcSBtl C,where Satris that part of the entropy of a solvent which arises because of its internal order and C is a constant characteristic of the ion. This equa$on is tested by relating S,, to the deviation from the ideal boiling point of the solvent, ATbp, and plotting Xzo us. ATbp. Linear relationships are observed. Both equations are useful for estimating ionic entropies for species for which there are no data.
+
+
Introduction Increased use of nonaaueous solvents as reaction media in inorganic chemistry, both in the laboratory and in industry, makes it of paramount interest to have information on the thermodynamic properties of dectrolytes in these solvents. In addition, thermodynamic data for these systems will give considerable insight into the structure of electrolytic solutions in general. In
view of the immense area covered, data of this type are very sparse, To merely repeat for each of these
~~
T h e Journal of Phyaical Chemistry
(1) Presented before the Division of Physical Chemistry a t the 153rd National Meeting of the American Chemical Society, Miami Beach, Fla,.. Aaril - 1967. (2) This paper was taken in part from the theses submitted by R. P. Held and E. Luksha to the Graduate School of the University of Vermont in partial fulfillment of the requirement for the Degree of Doctor of Philosophy. . . (3) TOwhom correspondence should be directed.
THERMODYNAMIC PROPERTIES OF NONAQUEOUS SOLUTIONS
2971
~~
Table I : Standard Partial Molal Entropies (cal/deg mol) of Electrolytes at 25" (mole fraction standard state) Eleatrolyte
HC1 LiCl LiBr LiI NaF NaCl NaBr N a1 KCl KBr KI RbCl CSCl CsBr CSI
--
SP "aa
-46.5 -38.5 -38.5 -33.2
... -31.4 -31.4 -26.1 -25.1 -25.1 -19.8 -17.5 -17.5 -17.5 -12.2
7
DMF~
EtOW
M ~ O H ~
NMF
Fa
HzOi
...
-34.3 -30.3 -25.7 -19.6
-24.4 -20.1
-11.6' -19.9" -10.1'
-5.53h -0.9
...
...
...
...
-16.7
-18.8 -12.5
-12.9 -7.6 -3.4 -5.1 0.3 6.4 0.6 2.8
-2.8 0.6 6.7 13.5 -3.9 11.6 17.7 24.5 21.7 27.8 34.6 26.9 29.0 35.1 41.9
-31.8 -25.8
... ... ...
...
...
..*
-11.6
...
...
-5.0
...
... -1.8 2.3
... ... ...
...
.
.
I
I
.
.
...
.
I
.
-0.9* 2.6'
... ...
... 3.ge
... I . .
... 10.1"
...
...
-8.8 0.2
... I
.
.
9.0 14.1 16.2 12.6 14.8
...
29
DlOj .
I
.
2.7 9.2 16.4 -3.0 13.7 20.1 27.3 23.9 30.3 37.5
... 31 .4k
... ...
C. M. Criss and E. Luksha, J . Phys. Chem., 72, 2966 (1968). ' Reference 6. a Reference 4. Reference 5 . a E. Luksha and C. M. Criss, J. Phys. Chem., 70, 1496 (1966). Recent, unpublished work in this laboratory indicates that the value for LiCl may be E. Luksha, Ph.D. Thesis, University of Vermont, Burlington, Vt., 1965. ' Calculated from heat, solubility, in considerable error. and cell data taken from the literature, except for HCl. Details of the calculations are given in footnote f. R. K. Agarwal and B. Nayak, J . Phys. Chern., 71, 2062 (1967). W. M. Latimer, "The Oxidation States of the Elements and Their Potentials in Aqueous Solutions," 2nd ed, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1952. J. Greyson, J. Phys. Chem., 71, 2210 (1967), except for CsC1. I n contrast to the other sources, Greyson lists entropies based on the molarity standard state, rather than the hypothetical 1 m standard J. Greyson, ibid., 66, 2218 (1962). state.
'
systems the almost limitless number of measurements that have already been performed on aqueous solutions does not appear practical. Consequently, it appears worthwhile to systematize the small amount of data which does exist and to attempt to formulate a relationship (empirical or theoretical) which will enable one to predict thermodynamic values for electrolytes in these solutions. The function which probably has been most successfully correlated in terms of the charge, radius, and shape of the ionic species is the finitely dilute partial molal entropy of the solute, 32". It would appear, therefore, that this function might be a logical starting point for developing a method for estimating thermodynamic data in other solvents. The only previously reported correlations involving this function in nonaqueous solvents are those of Latimer and Jolly4 and Jakusxewski and Taniewska-O~inska.5~~
Available Data A thorough search of the literature, along with measurements in this laboratory, has yielded a sufficient quantity of data to make a comparison of the partial molal entropies of 1 : 1 electrolytes in several different solvents meaningful. The solvents are: liquid ammonia, N,N-dimethylformamide (DMF), ethanol, methanol, N-methylformamide (NMF), formamide (F), water, and deuterium oxide. The molecular structures of the solvent molecules are widely different and the dielectric constants a t 25' vary from 17 to 182.4, making possible the examination of a series of solvents
exhibiting a broad variety of properties. A summary of the entropy data is presented in Table I. For reasons that become obvious later, the entropies are based on the mole fraction standard state. The change of standard state from the hypothetical 1 m to the mole fraction standard state is facilitated through the equation
where v is the number of ions per molecule, MI is the molecular weight of the solvent, and the subscripts N and m refer to mole fraction and molality, respectively.
Discussion In the entropy correlations for liquid CH30H,5 and CzH60H,athe total entropies of the solvated electrolytes have been divided into their ionic components by assigning, through a trial-and-error method, a value for 32" for the hydrogen ion. The division is made in such a manner that Szofor both cations and anions in a given solvent, when plotted against S2" of the corresponding ions in water, fit on the same curve. I n all three cases the relationship is linear. Similar treatments have been carried out for all the solvents listed in Table I using the mole fraction standard state, and a linear relationship i s observed in every case. (4) W. M. Latimer and W. L. Jolly, J . Amsr. Chem. SOC.,7 5 , 4147 (1953). (5) B. Jakusaewski and 8. Taniewska-Osinska, Lod. Towarz. Nauk WydziaZIII, Acta Chem., 7 , 32 (1961). (6) B. Jaliusaewski and S. Taniewska-Osinska, ibid., 8, 11 (1962). Volume 78, Number 8 August 1968
2972
C. M.CRISS,R. P. HELD,AND E. LUKSHA experimental uncertainties in the data, we consider the agreement to be satisfactory. One of the most striking features of the data in Table I is that for nearly every electrolyte, there is a gradual increase in TZoin the order
.-10 .-20
NI-18 < DMF = EtOH
Ot
Figure 1. Partial molal entropies (cal/deg mol) of the ions in F, NMF, and DMF us. the corresponding entropies in water a t 25".
The assignment of 32" for H+(aq) is -13 eu.7 Figure 1 shows the results for NMF, DMF, and F. Apparently the observed linearity is a general phenomenon for every solvent pair. The ionic entropies in any given solvent, X, can be presented by equations of the type
S2O(X) = a
+ bS2O(H20)
(2)
where a and b are constants which are characteristic of the solvent and S2"(HzO) is the absolute entropy of the corresponding ions in water. Table I1 lists the values of a and b along with the uncertainty in slope and the standard deviation between the calculated and the experimental values for the various solvents. Table 111 lists the ionic entropies (mole fraction standard state) in each of the solvents. Similar to the
Table 11: Constants for Eq 2 a t 25" Solvent
DzO HzO F NMF MeOH EtOH DMF "8
a
b
Aa
0.8 0.0 -1.6 -5.7 -10.9
1 . 0 4 h 0.01
h0.4
1.00
0.0 h1.8 rt1.8 h0.8 h0.8
0 . 6 4 rt 0.05 0.72 4 0.06 0 . 8 2 rt 0.02
-15.9
0.79 h 0.03 0.79 rt 0.05
-22.4
0 . 8 2 i0 . 0 6
-16.0
41.4 h2.3
a A is the standard deviation between the calculated and the experimental values.
previous investigators,4-6 we consider these ionic entropies to be absolute entropies. Additional support for this view is presented in the article immediately preceding this one,8 in which the absolute entropies of the ions in DMF were obtained by an entirely different technique. When the entropies of the ions determined by the two techniques are compared in the same standard state, the difference is 1.5 eu. In view of the The Journal of Physical Chemistry
< MeOH < NhIF < F < HzO < DzO
The only exception is NaBr, for which Szo is more negative in EtOH than in DMF. As one would expect, the constant a in eq 2 follows the same trend. An examination of the common physical properties, such as dielectric constant, dipole moment, viscosity, boiling point, heat of vaporization, and entropy of vaporization, shows that as the solvents are listed in Table I there is no physical property or simple combination of physical properties which is either monotonically increasing or decreasing. Consequently, any a priori method employing a simple relationship, such as the derivative of the Born equation, for correlating entropies in the various solvents does not appear promising. Attempts at explaining the order in terms of solvent basicities appear equally unfruitful, since agreement among investigators concerning the relative base strengths of such diverse solvents, obtained through other arguments, is almost totally lacking. On the other hand, if one considers the physical properties of the solvents collectively, along with current theories about the degree of H bonding in many of these liquids, a pattern emerges. Ionic entropies are most positive for electrolytes in those solvents which appear to have the highest degree of internal structure. This observation has been made in the case of water and DzO by Greyson,S who attributed the larger entropies of the alkali metal halides in DZO over those in water as being caused by the higher degree of order in DzO. Frank and Evans10 and Frank and Wen'l have explained many of the properties of water on its high degree of order and, because of H bonding, its ability to polymerize three dimensionally to form "flickering clusters" or "icebergs." A similar argument can be applied to formamide, which also has a high degree of H bonding. In the solid state, this solvent, because of H-bonding positions, polymerizes in large sheets, the sheets being held together by van der Waals forces similar to that of graphite. l2 Presumably, fragments (7) This assignment makes ?h0for H'(aq) equal to - 5 eu for the hypothetical 1 m standard state. This is close to the values suggested by others for the absolute entropy of the aqueous hydrogen ion. See C. M. Criss and J. W. Cobble, 1.Amer. Chem. SOC.,86, 5385 (1964). (8) C, M.Criss and E. Luksha, J . P h y s . Chem., 72,2966 (1968). (9) J. Greyson, ibid., 66, 2218 (1962). (10) H. S. Frank and M. W. Evans, J. Chem. Phys., 13, 607 (1945). (11) H. S. Frank and W.-Y. Wen, Discussions Faraday Soc., 24, 133 (1957). (12) G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond," W. H. Freeman and Co., San Francisco, Calif., 1960.
2973
THERMODYNAMIC PROPERTIES OF NONAQUEOUS SOLUTIONS Table I11 : Standard Absolute Ionic Entropies (cal/deg mol) at 25' (mole fraction standard state)
CS'
-36.1 -28.1 -21 .o -14.7 -7.1 -7.1
FGI Br I-
-10.4 -10.4 -5.1
H+ Li + Na + K+ Rb
...
-26.5 -22.5 -15.6 -8.0
-23.3 -14.2 -9.1
... ...
... 0.7
Average obtained from LiI and NaI. K I and CsI.
-7.8 -3.2 3.0"
* Average obtained
ASaoivo
+ So
-2.4 2.9 8 . I*
1.9 5.4
... 8.2
...
...
from NaI and KI.
of these sheets exist in the liquid state, giving rise to two-dimensional icebergs and a correspondingly less ordered solvent than water. NMF has been reported to form chain polymers in the liquid state.l32l4 This would give rise to one-dimensional icebergs, resulting in a still less ordered solvent. From H-bonding arguments alone, one can only speculate on whether CH8OH and CZH60H are more or less ordered than NAIF, but of the two, one would expect that CzHjOH would be less ordered because the more bulky ethyl group would interfere with the H-bonding process. D M F is virtually non-H-bonded, consequently one might expect this solvent to have less order than the alcohols. On the other hand, it has a high dipole moment, which could possibly lead to an internal structure approaching that of the alcohols. Although liquid ammonia has long been accepted as an H-bonded solvent, its physical properties indicate that its H bonds are fairly weak. For example, its low viscosity, dielectric constant, boiling point, and heat of vaporization all indicate relatively weak interactions. It is our view that there is a higher degree of interaction between D M F molecules than between ammonia molecules and, consequently, probably a higher degree of order in DMF. Just recently, some of these same views concerning the internal structure of F, NMF, and DMF, as related to solvation enthalpies, have been expressed by Finch, Gardner, and Steadman.l5 It is instructive to attempt to describe these concepts quantitatively. By definition of the standard state, any change in the entropy of an electrolytic solution at infinite dilution is assigned to the solute. Therefore, the infinitely dilute partial molal entropy of an electrolyte is related to the degree by which a solvent is either ordered or disordered during the addition of an electrolyte. The standard partial molal entropy of a solute, Szo,is given by
32" =
-13.5 -15.6' -2.8 2.0
...
... -8.5 -2.5 1.6
-22.0 -17.7 -10.5 -2.7 3.0 5.2
(3)
where ASso~vois the standard entropy of solvation of
-9.9 -5.3 -4.2 4.6 8.2 10.4 -4.6 4.4 9.5 1 5 . Id
Obtained from LiBr.
-13.0 -9.6 1.4 11.5 16.7 18.8 -5.3 10.2 16.3 23.1
.*. -8.6 2.4 12.6
... 20.2 -5.4 11.3 17.7 25.0
Average obtained from
the gaseous ions and S o is the entropy of the gaseous ions. The entropy of solvation can be considered to be made up of three quantities: (1) an entropy decrease caused by the loss of the degrees of freedom of the gaseous ions, A&" ; (2) an entropy increase caused by the disordering of the solvent structure, ASD" ; and (3) an entropy decrease resulting from the ordering of the solvent molecules around the ions, ASo". Substitution of these terms into eq 3 gives
32" = ASD' + ASo"
+ ASF" + So
(4)
The last term is independent of the solvent and is constant for a given gaseous electrolyte. The third term on the right is equal to the entropy change on dissolution of a gas in a solvent to form an ideal solution. For a given pair of gaseous ions, this term will be constant for the various solvents when entropies are based on the mole fraction standard state. The nonideal part of the entropy change for formation of these solutions is absorbed into the first and second terms on the right side of eq 4. The entropy of orientation of solvent molecules around an ion may be considered to be a function of both how many and to what degree molecules are affected. For example, a solvent consisting of molecules with a high dipole moment should exhibit strong ion-solvent interactions in the first solvation sphere but relatively small interactions outside of this sphere, where the electric field surrounding the ion has been diminished. On the other hand, solvents having molecules with small dipole moments would exhibit weak interactions with the ion in the first solvation sphere, but the ion would exert its influence to a greater distance, since the field surrounding the ion is not re(13) G. R.Leader and J. F. Gormley, J. Amer. Chem. SOC.,7 3 , 5731 (1951). (14) L. A. LaPlanche, H. B. Thompson, and M. T. Rogers, J. Phys. Chem., 69, 1482 (1965). (15) A. Finch, P. J. Gardner, and C. J . Steadman, ibid., 71, 2996 (1967).
Volume 78, Number 8 August 1Q68
2974
C.M. CRISS,R. P. HELD,AND E. LUKSHA
duced as much by the smaller dipoles. Consequently, one may conceive of the net entropy of orientation of solvent molecules around an ion as being approximately constant for solvents consisting of molecules with not too widely different dipole moments. If, indeed, we assume this to be the case, eq 4 reduces to
S2" = ASD"
+C
(5) where C is a constant, which is strongly dependent upon the charge density of the ion. If one assumes further that for each solvent the original structure is disrupted to the same degree in the vicinity of the ion, then ASD" will be proportional to the amount of structure in the pure solvent, and eq 5 can be written as
32"
=
k&t,
+C
(6) where S s t r is the entropy of the solvent because of its internal structure and k is a constant. Accordingly, 32" should be a linear function of that part of the entropy of a solvent which arises from the order existing among the solvent molecules, and, consequently, plots of 32" (mole fraction standard state) for various ions ws. S s t r for different solvents should lead to a series of linear relationships, one for each ion. I n order to quantitatively test eq 6, a meaningful numerical value must be assigned to Xstr for each solvent. One possible way of doing this would be to use the entropy of self-association of the various solvents in some inert solvent. Unfortunately, these data are not presently available for most solvents, so that a more indirect approach must be employed. One would expect liquids having a large amount of internal structure to exhibit large molecular interaction energies. l6 By separating the interactions which lead to an ordered solvent, such as dipole-dipole interactions or H bonding, from those which do not, such as van der Waals forces or entanglement of long chains, one should obtain quantities proportional to Sstr. In principle, nearly all the common physical properties could be used for estimating values proportional to Sstr, but because of the availability of and difficulty in interpreting data, boiling points appear most useful. The quantity of interest should be the difference between the actual boiling point of the solvent and the ideal boiling point, that is, the boiling point that would be observed if the effects of H bonding and dipole-dipole interactions were removed. To estimate the ideal boiling point for a given solvent, whenever possible, we have plotted the boiling points of a series of non-€Ibonded compounds, having the same molecular symmetry as the solvent molecules, against their molecular weights and have extrapolated them to the molecular weight of the solvent. For formamide and the N-substituted formamides, where no satisfactory series could be found, the boiling points of the vinylamines have been used as the ideal boiling points, even though some H bonding undoubtedly exists. Table I V lists the The Journal of Phyaical Chemwtry
Table IV: Determination of the Deviation from the Ideal Boiling Point' Extrapolated seriesb or model compound
Bp, 'C
Solvent
DzO HzO F NMF
101 4 100 0 218' 183
MeOH EtOH DMF
65.0 78.5 153
8"
-33.3
A, B, C, D A, B, C, D Vinylamined N-Methylvinylamine A,E,F, G E, B, H, I, J N,N-Dimethylvinylamine K, L, RII, N
BP (idaal),
BP (dev),
O C
OC
-72 -74 56 55a
173 174 162 128
-52
55'
117 97 98
- 90
57
- 18
' Unless otherwise indicated, all data were taken from "Handbook of Chemistry and Physics," 48th ed, R. C. Weast and S. M. Selby, Ed., The Chemical Rubber Publishing Company, Cleveland, Ohio, 1967. Letters represent compounds used in extrapolation: A, dimethyl ether; B, diethyl ether; C, diisopropyl ether; D, di-sec-butyl ether; E, methyl ethyl ether; F, isopropyl methyl ether; G, t-butyl methyl ether; H, ethyl isopropyl ether; I, t-butyl ethyl ether; J, ethyl isoamyl ether; K, trimethylamine; L, triethylamine; M, tripropylamine; and N, triisobutylamine. G. Somsen, Ph.D. Thesis, University of Amsterdam, 1964. Probably exists as ethylenimine. e Estimated from the boiling points of vinylamine and N,N-dimethylvinylamine. W. J. Rabourn, U. S. Patent 3,149,164 (1964). This is also in agreement with the estimated value obtained from propene-1-N,N-dimethylamine and butene-1-N,N-dimethylamine. See R. Tiollais, H. Bouget, J. Huet, and 4. LePennec, Bull. SOC.Chim. Pr., 1205 (1964). Two earlier works lists the boiling point around 40".
'
boiling points of the solvents under investigation, the corresponding extrapolated series or model compounds from which their ideal boiling points were estimated, and the deviations from the ideal boiling points, ATbp In accordance with the above discussion, we assume that ATbp is proportional to Sstr and modify eq 6 to
32" = k'ATbp
f C
(7) where k' is a constant. Figure 2 shows that plots of S2" vs. ATbp for the alkali metal and halide ions are indeed linear, as predicted by eq 7. The constant, a, in eq 2, which represents an average for all the ions, is also included. The values of k' and C for each ion are listed in Table V. One interesting feature is that k' is approximately the same for all ions. This fact suggests that the original solvent structure is completely disrupted in the vicinity of the ion for all the ions considered. The values of C are what one would expect for the partial molal entropy of the ions in a solvent with no internal structure. The fact that they are all (16) The converse of this statement is not necessarily true. For example, large molecules have higher interaction energies than smaller ones because of increased van der Waals forces, but this in itself will not lead to a greater order within the solvent.
2975
THERMODYNAMIC PROPERTIES OF NONAQUEOUS SOLUTIONS Table V: Constants for Eq 7 at 25'
+zo-
Ion
k ' , oal/deg2 mol
H+ Li + Na + K+ c s+ c1BrI-
0.22 f: 0.04 0.19 rt 0.02 0.20 rt 0.02 0.23 rt 0.02 0.22 rt 0.02 0.19 rt 0.02 0.23 h 0.02 0.25 rt 0.02
C,cal/deg mol
-47.1 -39.7 -32.6 -29.5 -20.0 -24.6 -24.5 -20.7
A=
rt3.6 rt2.2 rt2.6 rt2.2 h2.5 h2.5 rt1.8 rt2.6
' A is the standard deviation between the calculated and the experimental values.
k' in eq 7 will be affected in the same way for each ion, so that the entropy curves will remain parallel to each other. Equations 2 and 7 are useful for estimating entropies 60 80 100 I20 140 160 I60 Deviation from ideal Boiling Point of ions for which no experimental data exist. For the solvents discussed in this paper, the constants a and b Figure 2. Partial molal entropies (cal/deg mol) of ions in in eq 2 have been evaluated, and, consequently, the various solvents us. deviations from the ideal boiling points entropy of any simple singly charged ion can be calof the solvents. culated. For solvents which are not discussed in this paper, eq 7 can be employed to estimate Szofor an ion for which C has already been evaluated. Unfortunegative simply means that the ions would introduce nately, at the present time it is difficult to estimate some order in the solvent by orienting the solvent ATbp accurately so that the calculated entropies are molecules. correspondingly uncertain. However, the use of this It is evident that AThp is not an entirely satisfactory function does give a semiquantitative approach to the parameter for evaluating quantities proportional to Sstr. problem and a t the present time appears to be the most For example, it suggests that water is more ordered than practical approach. DzO, which is contrary to current views.$ However, considering the rather crude manner in which ATbp Acknowledgment. We are grateful to Professors must be estimated and the fact that entropy data in Henry Frank and Loren Hepler for helpful suggestions. nonaqueous solutions are generally not as accurate as in I n addition, we are indebted to both the U. S. Atomic aqueous solutions, the agreement with eq 7 is better Energy Comission and the National Science Foundation than can be expected. Furthermore, it should be for their financial support through Contract ATnoticed that even if ATbpvalues are in error, the value of (30-1)-3019 and Grant GP-4995, respectively.
Volume 79,Number 8 August 1968
