W. S. J. KOSKI,J. KAUFMAN, C. F. PACHUCKI AND F. J. SHIPKO
3202
line hydrolysis.** Thc acidified solution gave no hydrogen; whether the B-H bonds remained in a protected situation or had served t o reduce half of the CF3 groups was not determined. A phosphorus analysis8 gave l7.7yG P; calcd., 17.0%. A final analysis for all components of the trimer was done by a reaction with HC1 and methanol-far easier to complete than the acid hydrolysis. The 58.0 mg. sample was heated with 1.112 mmole of HCl and 0.20ml. of CH30H in a sodalime glass tube for 15 hr. a t 86 . The resulting Hz was measured as 0.643 mmole (calcd., 0.638). The boric acid titration gave 0.318 nimole (calcd., 0.319). All of the HC1 had been converted t o CH3C1, so that the excess gas volume of the C H ~ C ~ - ( C F ~ ) Zfraction PH could be ascribed to (CF3)2PH: 0.326 mmole (calcd., 0.319). I n a parallel experiment, 83.5 mg. of the trimer had been heated with aqueous methanol-HC1 (8 days a t 8 5 " ) , and the (CF3)1PH was isolated and fully identified: 0.459 mmole (calcd., 0.459). I n this case the H? amounted t o 0.916 mmole (calcd., 0.918). Physical Properties of the Tetramer.-The less volatile phosphinoborine material, from the ( C F ~ ) Z P H - Breaction ~H~ with (CH3)20, had a mol. wt. of 742 (calcd. for bis-trifluoro(13) F. W. Bennett, 11. J Einel6iis aiid 12. S . Haszeldine, J . Chent. SOC.,3899 (1954).
[CONTRIBUTION FROM
THE
VOl. so
methyl-phosphinoborine tetramer, 727). The crystals, which melted sharply a t l l 6 " , were observed under a microscope and seemed to be orthorhombic. The vapor tensions of the solid, shown in Table IX, determined the equation loglo P m m = 12.683 - 4489.2/T. TABLE IX [( CI'J~PBHZ]: t("C.) 4 5 . 5 5 4 . 4 7 5 . 7 8 2 . 0 6 9 . 9 9 8 . 4 104.U pmm(0bsd.) 0 . 0 4 0 . 1 0 0 . 6 6 1.10 2 . 1 1 4 . 0 0 6,44 pmm(calcd.) 0 . 0 4 0 . 1 0 0 . 6 6 1 . 1 1 2 . 0 9 3.00 6.46 YAFOR 'rESSIONS O F SOLID
Analysis of the Tetramer .-A sample of tlic tetramer, roughly estimated as 23 mg., was sublimed into a soda-lime glass seal-off tube, into which 0.609 mmole of HC1 and 0.3 ml. of methanol were condensed. The sealed tube was heated for 7 days a t 93" and then yielded 0.268 mmole of Hz, 0.131 mmole of (CFa)?PH (fully identified by its 6.5 mm. vapor tension a t -78') and methyl borate titrating as 0.136 mmole. These results would correspond t o 24.3 mg. of [(CFa)?PBH211; calcd. values, 0.267, 0.134 and 0.134, respectively. Los ANGELES 7, CALIFORNIA
DEPARTMENT OF CHEMISTRY, THEJOHNS HOPKINSUNIVERSITY* A N D THE KNOLLS ATOXICPOWER LABORATORY, GENERAL ELECTRIC COMPANY t]
A Mass Spectrometric Appearance Potential Study of Isotopically Labeled Diboranes' BY W. S. KOSKI,*JOYCE J. KAUFRIAN,* C. F. PACHUCKIT AND F. J. SmPI(ot RECEIVEDJANUARY 16, 1958 The appearance potentials of the molecule ions formed by electron impact from BzH6, B'OaHs, BzDe and B'OzDe have been measured mass spectrometrically. A set of apparently self-consistent ionization potentials for these molecule ions has been estimated from the appearance potentials of the BIO enriched compounds. The resulting calculated ionization potentials for the fragments from B1°2Hs are compared with the ionization potentials the authors estimate for fragments from BI02Dc and are also compared with the results obtained from e&. The mass spectra of BzHc, B'OZH~,BzDs and BI02D~were also run a t 70 e.v. ionizing voltage in order to obtain a set of fragmentation patterns of the isotopically labeled diborancs under identical conditions; from these the monoisotopic spectrum of each type of diborane was calculated.
The method of obtaining bond dissociation energies by ionization and dissociation of molecules by electron impact has been used with considerable success in a number of types of compounds. If one represents the process taking place as R1 - Rz
+ e - +R1+ + Rz + 2e-
then by the equation A(Ri+)
=
I(Rd
+ D(Ri - Rz)
(where A (RI+) is the mass spectronietrically nieasured appearance potential of R1+, I(R1) is the ionization potential of R1 and D(R1 - Rz)is the dissociation energy of R1 - R?, either the ionization potential of R1 or the bond dissociation energy R1 - R? may be calculated directly from the measured A(Rl+), pronzded that one knows the value for the other unknown in the equation. h necessary condition for the above equation to hold true is I(R1) < I ( R z ) . ~If I(Rl) > I(Rz), then A(R1+) > I(Rl) D(R1 - Rz). I n order to interpret correctly the appearance potentials of fragment ions, it is necessary to know what neutral fragments are simultaneously formed and the states of electronic excitation of the neutral fragments
+
(1) T h i s research was supported by t h e United States Air Force through t h e Air Force Office of Scientific Research of the 4ir Research and Development Command under contract No A F lS(6001 1520 Reproduction in whole or in part 16 permitted for any purpoae 01 theIlnited State5 Government 1 2 1 1) P \ t e \ e n i o n Pi < I I I i l l , 5uL 10 I-> I I ' I I I I
and the niolecule ion. However, it has bceii shown that in a number of cases the simplest set of assumptions suffices for the interpretation of thc data. There have been two recent papers3 in which the investigators have reported the appearance potentials of some boron compounds, but with the exception of assigning 10.9 e.v. as the I(BH3) by employing the relation 9(BI13+)
=
I(BH3)
+ D(BH3 - EHa)
and using D(BH3 - BH3) the dissociation eiicrgy of a B2H6 into two BH3 fragments (28.4 =t 2 kcal./mole) , no calculations have been publishcd in this field. We have measured mass spectrometrically thc appearance potentials of the molecule ions formed by electron impact from BZH6, Blo2H6,BZD6 and B'OzDs. Unfortunately, no ionization potentials had ever been reported for any of the ions except B and an estimate for BH3. MJe have attempted to calculate a self-consistent set of ionization potentials for these molecule ions formed from diborane using what thermochemical data were available, and have compared these results for fragments from BzH6with those from CzHe and B2D6. The progress on the electron impact induced dis(3) (a1 R. W. Law and J. L. Margrave, J . C k e m . P h y s . , 26, 1086 (19515); (h) J . I,. hlargrave, J . Phys. C h e w . , 61, 38 (1057). ( 1 1 IB-B/ .-This would arise froin the terium would just be statistically distributed. H H ' dissociation of two B-H bonds (we still feel (In this case we have used the lower value of 3.00 that the terminal B-H bonds may dissociate first, e.v. for D(B-B)). Bz+.-The D(B-B) in the BP molecule has been since in the hydrocarbons the C-H bonds which dissociate first are the ones with the lowest bond found to be either 3.4S'O or 3.00 e.v.I1 The latter energy). The dissociation of two B-H bonds value appears to be more acceptable for the B? mould then be followed by a rapid intramolecular molecule itself.? Up to the CzHzf or the BsHL+ions we have made H+ rearrangement to ii)B-B/ . The bonding of the same assumptions for the final state of the hyH \H drogen extracted from the diborane molecule as this molecule ion would be simliar to that of BzC14. other investigators have postulated for the hydroThis arrangement would involve the formation of gen extracted from the ethane molecule.6,12 one B-B bond, the breaking of two B- -€I--B There seem to be some regularities in this series bridge bonds and the reformation of two B-H of our calculated ionization potentials for the moleterminal bonds. The net result would be the same cule ions formed from diborane when compared to as if two bridge bonds were broken and a B-B bond the molecule ions from ethane.13 formed. The values for which there can be little ambiguity are certainly I(B&) and probably I(BsH5). I(BIH4) = A(B2Kr+) + D(I1z) - 2D(B--EI--B) f Comparing these values to those of ethane, the D(R-B) = 10 93 e.v. I(BzH8) and I(CzH8) are quite close with I(B2Hs) I(B2H4)could equal S.70, 12.17 or 10.g3 C.V. Our being a little higher. The I(B?H6)is on the order choice for the most likely value is I(B2H4) = 10.93 of one electron volt lower than I(CzH5). e.v. because we have the feeling that the correct The other ionization potentials for the molecule structure for the molecule ion may well be the last ions from diborane listed in Table 111 are the values one. calculated by us which we feel may correspond to There are a number of possible choices for the the most nearly correct mechanism for the forprocesses taking place and for various structures mation of each molecule ion. For the ionization of the lower fragment ions which in turn lead to a potentials of diborane molecule ions containing number of choices for the calculated ionization even numbers of hydrogens we get values close to potentials. 'In Table I1 we have listed the proc- and just a little higher than the values for correesses we assume to be taking place in each case sponding hydrocarbon molecule ions containing the same even numbers of hydrogen atoms. For the TABLE I1 ionization potentials of molecule ions from diborane PROCESSES, C O X F I G U R A T I O S S AXD CALCULATED IONIZATIOS containing odd numbers of hydrogen atoms we get POTESTIALS FOR VARIOUSDIRORANE FRAGMESTS values about 1 e.\-. lower than the corresponding values for the carbon compounds. Configuration ,;:,: The same types of calculations were perrorincd II ,IT\ 11' ,)E\\ IL, I i .!j for the ionization pofentials of the nioleculc ions 11 '11 '11 froni Listed in Table IV are the appcaraiice potentials of the fragments formed by electron im7.86 pact from deuterated diborane and BO ' enriched deuterated diborane. 1 1 1 . 9 ~ I n Table 111 a comparison is made of the appearance potentials of the corresponding ions from B lo2Hsand B lo2Dswith their ionization potentials 6 . 7 9 calculated by the same mechanism for each pair of molecule ions. T n most cases the appearance POtentials and calculated ionization potentials of of H:! in the above step, it is also possible to form a B-B bond after the two terminal hydrogens are removed from the diborane molecule. For the value of a single B-B bond in these compounds. we shall use the value D(B-B) = 3.47 e.11.~ This would give
H
R-=R
"
'6
'"'"
H-B-B' B--13
-El'
'
1Z.(h
n'. S. K o - k , , .7. C h r m P h y i . , 21, 7 4 2 (1952). (10) G. Herzberg, "Spectra of Diatornir Molecules," D. Van Nostrand Co , N e w York, N . Y . , l Y X . (11) A . G. Gaydon, "Dissociation Energies aud Spectra o f I)i.itumic Alolecules," Chapman-Hall, London, 1017. (12) J. A . Hipplc, Phya. Reo., 63, 530 (19281. (I:{) G C . Ellentou, J . Chcin. Phys., 16, 456 (lU47). (9) P C . Maybury and
July 5, 1958
COMPARISON
APPEsRANCE POTENTIALS O F ISOTOPICALLY 1,ABELED
O F SIMILAR
TABLE 111 FRAGhlENTS FORMED BY ELECTRON IMPACT FROM DIBORANE AND DEUTERATED DIBORANE WITH THOSE FORMED FROM E T H A N E
--.,
R.V.
7
Ion
I
A from B%HB
BzH6' BzHs*
11.9 7.88
11.9 f 0 . 1 11.9 f . 1
B2134'
10.93
12.3 f .1
B&+
8.7s
14.2 i . 1
-- R . V .
Ion
BZH2'
11.36
13.8 f .1
13zHf
10.62
2 0 . 1 zk
.1
BzDe-' BzD6+ B2D4H+ BzDa' BzDaH' BzD2 BzDiH' BzDz' BzDH' BzD'
nz
12.00
2 1 . 1 31
.1
Bz'
+
3205
DIBORANES
I
12.0 8.01 7.9, 10.90 10.90 8.81 8.71 11.50 11.50 11.71 8.7, 12.61
-A from B%Ds
12.0 f O 12.1 f 12.0 f 12.3 f 1 2 . 3 zt 14.3 f 14.2 f 14.0 zk 14.0 f 18.3 i
-
I
Ion
E.v.
A from CtHe
. l .1 .1
CzHe+ CzHs+
11.6 8.7
11.6 f 0 . 1 12.9 f . 2
.1 .1
CzHa'
10.8
12.1 zk
.I
C?H3+
9.9
CzHz+
11.2
15.0 &
CzH'
11.3
27.0 i 1 . 0
Cz+
12
31.5 & 1 . o
.1 .1 .1 .1
21.8 i .2
.1
15.2 i . 3 .3
Now we should like to calculate ionization potenTABLE IV hPPEARANCE POTENTIALS OF THE FRAGMENTS FORMEDtials for the BH, ions. This is difficult because we X Y ELECTRON IMPACT FROM DEUTERATED DIBORANEAMI do not know exactly what fragments are formed B ENRICHED DEUTERATED DIBORANE in these dissociations and we know nothing about Appearance potential, e.v. tn/c
BzDs
B%De
32 31 30 29 25 27 26 25 24 23 22 21 20 17 16 15 14 13 12 11 10
1 2 . 1 =t0 . 1 12.0 f .1 12.2 i .1 1 2 . 4 =t .1 12.9 f . 1 13.7 f . 1 13.9 f . 1 13.9 i .1 14.2 f . 1 14.9 f . 2 20.0 i . 2 23.3 f . 2 12.6 f. . 2 13.5 f 13.5f 14.7f 15.2 f 18.6 f 18.7f
.1 .1 .1 .2 .1 .2
12.0
* 0.1
Ion from B'ozDa
BZD6'
12.1 i .1 12.0 z!z .1 12.3 & .1 12.3 i.1 1 4 . 3 f .1 14.2 f . 1 14.0 i . 1 14.0 f . 1 18.3 f . 1
BzDs' BzDdH' BzDd+ BzD3H+ BZD3' BzDzH' BzD2+ BzDH' BzD+
21.8 f .2
Bz+
1 2 . 7 4 ~. 2 13.6 i . 2 13.6 i: . 1 14.2 i . 2 1 4 . 8 f .1 19.0 f . 2 18.6 f .1
BD3+ BD?' BD+ B+
the amounts of extra energy-electronic, vibrational or otherwise-possessed by these fragments. The best interpretation that can be made of the A(BH3+) is to set an approximate upper limit of I(BH3) in the neighborhood of 11-12 e.v. It is not significant to carry the detailed analysis for BH,+ ions beyond this point because of the number of possible combinations involved. We are carrying out these further calculations merely as a matter of academic interest. The electronic configurations for the lowest states of B, BH, BH2 and BH3 have been assigned. While no unambiguous order can be inferred from the electronic configurations, we feel the following order for the ionization potentials should be reasonable. I(BH3)
> I(BH) > I ( B ) E I(BH2)
I(B) is known with great accuracy* and I(BH3) can be estimated using the known heat of dissociation of diborane. These values should a t least serve to bracket I(BH) and perhaps give an estimate of I(BHz). Our calculations lead t o I(BHI) 5 11-12 e.v.
corresponding ions are very close. There is a tendency for the potentials of the deuterated compounds to be just slightly higher than those for the protiated compounds. This difference of -0.1 e.v. is something which might be expected in view of the difference of 0.12 to 0.18 e.v. found between I(CD4) and I(CHJ.I4ti5 However there is a discrepancy, the appearance potential of BzH+ is 1.8 e.v. higher than that of BzD+. At present we have no satisfactory explanation for this. There could be a subtle difference in the process taking place in the formation or ionization of BzD+ as compared to BzH+. This difference, if real, is still only apparent in the appearance potential of BzD+ from BIo2Deand not in the appearance potential of B2+ from B"ZD6 which agrees to within experimental error with the appearance potential of Bzf from B"2He.
While these values are upper limits since we have no assumptions regarding excess energy, the order of the magnitudes of the ionization potentials is as expected. We later checked this order by calculating the ionization potentials for the molecule ions produced by bombardment of BC1, where there is less chance for ambiguity in the fragments formed. It can be seen in Table V that OUT calculated values for the ionization potentials of the boronchlorine fragments have not only the same order as those for the boron-hydrogen fragments but to within experimental error have approximately the same values. le
(14) F. P. Lossing, A. W. Tickner and W.A. Bryce, J. Chem. P h y s . , 19, 1254 (1951). (15) F. P . Lossing, K. U. Ingold and I. H. S. Henderson, ibid., 22, 621 (1054).
(16) The values of the ionization potentials of the BC1, molecule ions were calculated from the quoted literature values. Very recent experimental studies indicate that these values may be altered somewhat.
I(BH2) j 8.12e.v. I ( B H ) 5 10.Oee.v.
T.4BLE TABLE \‘I COMPARISOS OF THE CALCULATED IONIZATION POTENTIALS FRAGMENTATIOX PATTERX OF B1O2D6 L ~ S I N G70 \.’oI,TEI,EC. OF SIMILAR FRAGMENTS COSTAISISG ONE B A T O M FORMED TROSS PROM D I B O R A N E A S I ) F R O M R O R O S TRICHLORIDE Relative abunilunce
Proin diborane
From horon trichloride
I(BH3) 5 11-12 e.v.
I(BCla) 5 1 2 . 0 e.v.
I(BH2) 5 8.12 e.v. I ( B H ) 5 10.06e.v. I(R) 8.296 e.v.
I(BCI2) 5 8 . 5 e.v. I(BC1) 6 9 . 8 e.v. I(B) 5 8 . 4 e.v.
The values for the appearance potentials for BD, molecule ions are quite close to those of the BH, ions in most cases. Again there is a discrepancy, this time just within the limits of our experimental error, of 0.4 e.v. between A(BH3f) and A(BD3+). While the error may be experimental, this discrepancy is worth noting because there may well be n fundamental difference in the nature of bridging of completely protiated and completely deuterated boron hydrides. Deuterated diborane is known to have a vapor pressure of 235 mm. a t -112’ compared to 225 mm. for diborane a t this temperature, which is in line with the fact that the A(BD3+) is lower than the A (BH3+). The ionization potentials of the fragments formed in the dissociation of diborane by electron impact were calculated from the appearance potentials of the Bl0 enriched compounds (containing 9GyOBIO) to avoid the complications in using diboranes with normal isotopic abundance of boron. We have studied the lowest appearance potentials of the fragments from the diboranes containing the normal isotopic abundance for comparison purposes. -4ssignment of the molecule ions corresponding to each observed appearance potential of the Bl0 compounds has enabled us to correlate many of the observed appearance potentials resulting from the fragmentation of the normal diboranes with the appropriate molecule ion.
hlass
In / e
0.24 7.G7
33 32 31 30 29
100,oo 12.17 40.90 5.12 21.71 6.47
2s 27 2C 2.; 21 23
(i7,30 2.53 412 0.14
33
I*
21
20
1.23
17 16
0.13 1.4ii 1.31 21.80 1.17 9.4*i
15
14 13 12 11.5 11 10
0.73 13.98
4
18.51 3.30 1.69
.P 2
ported by Dibeler, Mohler and Williamson1* is quite good, in view of the fact these fragmentation patterns are very sensitive to a slight difference it1 total deuterium content. I n Table VI is presented the cracking pattern of Bl02D6throughout the en-
TABLE VI1 MOKOISOTOPIC MASSSPECTRA OF DIBORANES AND DEUTERATED DIBORANES Relative abundance
Species
normal diborane)
B’%H, (calcd. from Bla enriched diborane)
R?H6
ino.on
100.00
B”?H, (calcd. from
R.”I
M.ni
,52,08
B2f13
25.21
26.25
BnI-Tp
76.92
72.32
B2H
6.04
6.33
B2
2.75
2.47
Species
BZDS B~DJTI B~DA BpDsTT BzDa BzDzH BzDz BzDH B2D BzH B?
The second portion of this research was a comparison of the fragmentation patterns and monoisotopic spectrum calculations obtained from the mass spectra of B2H8, BlozH6, B2D6 and B1’2D6. There is good agreement between our observed values for normal diborane and diborane containing 9GY0 BIO and those obtained by h’orton’‘ and l l l a r g r a ~ e . ~ bThe agreement between our observed for deuterated diborane and the va*ues re(17) F. J. Norton. THISJ O U R N A L , 71, 3488 (1949).
B”,D, B ‘‘3 D, H (calcd. from normal deuterntrd dihoranr)
B’%D, B%D, H (calcd from Bl’I enriched deuterated diboranc~)
100.00
100.00
12.67
8.33 46. M
49.20 5.14
3.10
21.71
26.42 1.91
0.89
G7. G3
72.36
2.21
2.48 4.15
4.98
-0.03 1.59
0.04 1.24
tire mass range, since there are no previously reported values for this mass spectrum of this cornpound. Table VI1 contains the monoisotopic spectra of the protiated diboranes calculated from normal diborane (B1l2HZ)and from BIO enriched diborane (Blo2H,). These two spectra are quite similar and the ionization probabilities for I3 1 1 2 , 13”B10 and (18) V. H. Dibeler, F. L. blohler a n d 1,uiira \Tillininson, . I . Re A’oll. B U Y .Stnndovds, 44, 489 (1950).
July 5 , 1%5S
COMMENTS ON THE PROPERTIES OF BOLAFORhl
Bln2 molecules must be very nearly the same for each type of molecule. Table VI1 also contains the monoisotopic spectra of the deuterated diboranes calculated from (B112Dr and B112D,H) and from B"2D6 (BlnzD, and Bl02D,H). These samples contained 97-98% D and as a result there were some molecules of BzDsH originally present. There is no way to distinguish between ions from B2D6 and from B2D6H once the H atom has been removed and the contributions to B2D4, B2D3, BzDz,etc., are the sums of the fragments from the B2D6 and B2DsH molecules. The agreement between the monoisotopic spec-
ELECTROLYTES
3207
tra of deuterated. diborane calculated from B2Ds and B1*2D8is quite good, especially in view of the fact that there were slightly different total percentages of deuterium in the two compounds. A comparison of the values obtained for the monoisotopic spectra of the diboranes and the deuterated diboranes confirms the observation made previously on normal deuterated diboranes" that there is an isotope effect in the fragmentation of deuterated diborane Due t o the scarcity of parent ions BzXs+ in the diborane mass spectra, no attempt has been made to calculate the weighing factors for the rupture of B-H or B-D bonds. BALTIMORE, MD.
[CONTRIRUTION FROM THE DEPARTMENT OF CHEMISTRY AND INSTITUTE FOR THE STUDY O F
METALS,UNIVERSITY OF
CHICAGO]
Some Further Comments on the Properties of Bolaform Electrolytes BY STUART A. RICE RECEIVED NOVEMBER 9, 1957 The equilibrium and transport properties of bolaform electrolytes are considered with emphasis on the necessity for selfconsistency of molecular parameters. It is shown that the application of the hydrodynamic theory of short chains leads to results in agreement with secondary dissociation constants and with the distribution of end t o end distances, The diffusion coefficient of a bolaform electrolyte is calculated and the role of ion atmosphere asymmetry discussed, the result being: 5) = Do[l q i q 1 ~ / 2 D k T f~ q i ~ ~ h / 4 D k T I .
+
I. Introduction From the structural point of view bolaform electrolytes partially bridge the gap between ordinary electrolytes and polymeric electrolytes. It is therefore to be anticipated that the properties of solutions of bolaform electrolytes will likewise be intermediate between the properties of solutions of small electrolytes and of polyions. For example, the very precise conductance measurements of FUOSS,et ~ l . , l have - ~ demonstrated the existence of ion pair formation between the bolaform ion (bolion) and its counterions even in solvents such as water. The magnitude of the dissociation conKz fBRB+C-
+BRB+
+ C-
stant for the reaction varies with the dielectric constant in the expected manner,' and charge separations computed from the Bjerrum relation6 for the ratio of the dissociation constants of a dibasic acid are consistent with the known structures of the bolions. It has been proposed that the phenomena of ion pair formation in bolaform electrolytese is closely related to a similar phenomenon observed in solutions of polyelectrolytes.7-9 A study of the equilibrium and transport properties of bolaform electrolytes therefore has relevance for the analogous but much more difficult problems arising in the consideration of these same properties of poly(1) R. M.Fuoss and D. Edelson, THISJOURNAL, 75, 269 (1951). (2) R. M.Fuoss and V. H. Chu, ibid., 75,949 (1951). (3) H. Eisenberg and R. M. Fuoss, ibid., 75, 2914 (1953). (4) 0.V. Brody and R. hl. Fuoss, J. Phys. Chem., 6 0 , 156 (1956). (5) N. Bjerrum, 2. physik. Chem., 106, 219 (1923). (6) S. A. Rice, THISJOURNAL, 78, 5247 (1956). (7) F. E. Harris and S. A. Rice, J. P h y s . Chem., 68, 725, 733 (1954). (8) S.A. Rice and F. E. Harris, J . Chem. P h y s . , 24,326,336 (1956). (9) F. E.Harris and S. A . Rice, ibid., 26, 955 (1956).
electrolytes. I n this communication we shall extend our previous discussion6 t o an examination of the magnitude of the ion pair dissociation constant, of the limiting conductance and of the concentration dependence of the frictional coefficient in dilute solution. Throughout our emphasis will be on the necessity for internal consistency between molecular parameters deduced from equilibrium and non-equilibrium properties in a manner rather different from the classical analysis of F u o ~ s . ' ~ ~ 11. The Secondary Dissociation Constant as a Function of Chain Length We consider first the ion pair dissociation constants and the intercharge separations required to fit the experimental data. The dissociation equilibrium discussed in section I may be characterized by the mass action expression
where KSois the intrinsic dissociation constant for the group in question (K1 = 2Ks0),a is the degree of dissociation and cc- is the concentration of the counterions to the bolion. The relationship between the degree of dissociation CY and the electrostatic energy of interaction, x,readily can be shown to be6 where X plays the role of an absolute activity. In general, the relation required for closure of the set of equations is In ao-
+ In X - In K,O
= 0
(3)
where a,- is the activity of the counterions. Equations 2 and 3 suffice for the calculation of the counterion activity or, if this is known, of
