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Communications to the Editor
mass number 235 showed that the intensities of the peaks a t m/e 235.384 and 235.357 ([11B1310B71H22]+ and [11B1510B61H20]+, respectively) diminished much more rapidly than that at m/e 235.315 ([11B1910B11H16]+). This and similar observations at other mass numbers (Table I) showed that two components were present, and that for ions described by the general formulation [B2,Hn]+those with n I 16 persisted longer than those with n > 16. This implies strongly that the second component is icosaborane(16), a known5i6compound. The complete mass spectrum of B20H16 has not been reported, but has been described qualitatively as having ions of maximum intensity around mass number 232,6,9which is also a feature of the spectrum we report here. These results therefore confirm the original suggestion of Quaylel that features of the mass spectrum of crude decaborane( 14), B10H14, can be explained by the presence of species containing 20 boron atoms, but show that these are due to a mixture of &OH16 and B2oH26 rather than a single species BzoH24. The visual similarity of the spectra also suggests that the reaction product initially described by Hall and Koski2 as B2oH26 is in fact also a mixture of B20H26 and B20H16, and that the subsequent conclusion3 that it is a mixture of CgBloHz8and C9BgH29is erroneous. This implies serious limitations in the applicability of the computational method used by the authors of ref 3 for the analysis of low resolution mass spectra of the higher boranes. Icosaborane(26) is the heaviest neutral borane yet identified. Although its composition, B20H26, formally corresponds to that of an arachno-borane, BnHn+6,its stability over an indefinite period of time (decades) as a persistent impurity in technical-grade B10H14, together with its alternative method of preparation2 by deuteron irradiation of BloH14suggest rather that it is a conjunctonido-borane, (B10H13)2. The only other conjuncto-nidoborane that has been identified is (B5HJ2which exists in three isomeric formse7An interesting aspect of the conjuncto formulation of B20H26 is that eleven geometric isomers are possible (since the 5,5' and 5,7' isomers are geometrically distinguishable).
Heat of Transport of Aqueous Acids
Sir: For hydrogen-electrode thermocells containing an aqueous acid, the calculation of electrophoretic contributions1f2to the limiting slope of the thermoelectric power (TEP) vs. K the Debye-Huckel reciprocal length requires that we know the-infinite-dilution limiting value for the heat of transport Q" of the acid in the thermocell and how it varies with temperature. In an earlier paper,2 we have shown agreement to within 7% between experimental and theoretical slope values of T E P vs. K for aqueous HBr in hydrogen-electrode thermocells at 15,25, and 35 "C. It was also shown that the concentration dependence of the T E P is related to the concentration dependence of &HA, of S H t (transported entropy of the hydrogen ion), and of tA- (transport number of$he anion). Since each concentration-dependent term for QHA and for SH+ contains a contribution from the "direct" e f f e ~ t and ~-~ from the "electrophoretic" effect,l and since there is an electrophoretic contribution from the concentration dependence of t ~ - there , is a total of five terps for- the concentration dependence of the TEP, viz., QdHA, QeHA, S d H t , P H t , and=teA-. In Q ~ H Aand-SeHtthere occurs a factor that contains the difference of QO's of the hydrogen ion and the anion. This factor is needed at one temperature only, since all individual ionic Q"s are presumed to have the same temperature variation. In order to calculate the transportnumber-elgctrophoretic term a t various temperatures, values of QOHA must be known as a function of*temperature. We present a method to_calculate these &"HA'S at several temperatures and the Qors for the corresponding anions at 25 :Cc. Values for &"HA and Q"A- were calculated from a slightly modified form of eq 11r2which expresses the thermoelectric
power TEP of a hydrogen-electrode thermocell containing an aqueous acid HA. In eq 1,S o H z is the standardentropy of hydrogen gas (130.587J K-l mol-l at 25 'C6), S, is the transported entropy of the electron in the nonisothermal platinum lead wires (0.430 J K-' mol-' a t 25 "C7), a n d T is the Kelvin temperature. The transported entropy Si is a measurable single-ion property, not based on arbitrary conventions. For the hydrogen ion it is given by
Acknowledgment. We thank Dr. M. Shilton for advice on computer programs and the Science Research Council for financial support.
References and Notes (1) A. Quayie, J . Appl. Chem., 9, 395 (1959). (2) L. H. Hail and W. S.Koski, J . Am. Chem. Soc., 84, 4205 (1962). (3) E. McLaughlin, L. H. Hail, and R. W. Rozett, J . Phys. Chem., 77, 2984 (1973). (4) Mass spectroscopic measurements were carried out on an AEI MS 30 instrument at a nominal ionizing potential of 70 eV. High resolution work was carried out at a nominal resolution of 20000 (10% valley definition) using perfluorokerosene and dibromopentane as calibrants and internal standards. (5) L. B. Frledman, R. D. Dobrott, and W. N. Lipscomb, J. Am. Chem. Soc., 85, 3505 (1963). (6) N. E. Miller and E. L. Muetterties, J . Am. Chem. Soc.. 85. 3506 (1963); Inorg. Chem., 3, 1690 (1964). (7) R. N. Grimes, F. E. Wang, R. Lewin, and W. N. Lipscomb, Proc. Nail. Acad. Sci., U.S.A., 47, 996 (1961); D.Gaines, T. V. Iorns, and E. N. Clevinger, Inorg. Chem., 10, 1096 (1971). (8) The low mass region had a very intense decaborane fragmentation pattern, together with peaks of low intensity due to ions arising from species Mentified (tentatively) as BloH1,O and (positively) as 2-CIB,,Hl,. (9) H. R. Bachmann, H. Noth, R. Ruick, and K. L. Kompa, Chem. Phys. Left., 29, 627 (1974).
Department of Inorganic and Structural Chemistry The University of Leeds Leeds LS2 9JT, England
in which neither QH+nor the partial molal entropy S H t is mea~urable.~ _In order to obtain the equation used to calculate the Qo's we subtract the mass-action term R In m from both sides of eq 1and use standard-stat? values for the molality-dependent variables (TEP, tA-, &HA, and S H t ) . This results in
F(TEP)" = ( 1 / Z s o H , - S,) +
(3) Table I lists the values for Qomdetermined from eq 3. For each acid the value of (TEP)' was determined from the intercept of a plot _of TEP - ( R / F ) In m vs. ~ l / ~ /+( l 1 . 5 ~ ' / ~ Values ). for QOA- listed in column 5 were obtained by subtracting &OH+ = 13.127 kJ mol-12 from the values in column 4. The results shown in Table I for @m/kJ mol-l compare well with literature values. Our calculated value for HC1 is in excellent agreement with 13.5g8 from Haase and Hochl' and 13.E~7~ from Agar.l Haase and Hoch also
Norman N. Greenwood* John D. Kennedy Derek Taylorson
Received October 13, 1977
0022-3654/78/2082-0625$0 1.OO/O
0
1978 American Chemical Society
626
The Journal of Physical Chemistry, Vol. 82,No. 5, 1978
Communications to the Editor
TABLE I : Calculation of Heat of Transport at 26 "C Acid HCI HBr HC10, H,SO,h
(TEP)"/pV K-' 521.62d i 0.52e 523.02f i 0.33e 507.60g t 0.54e 551.88 i 1.0
to*-a
&HA/kJ
0.1791 0.1826 0.16135 0.187
13.58 i 13.54 i 12.57 c 35.29 c
mol-'b
0.16 0.15 0.18 0.41
G"L/kJ mol-'C 0.451 0.411 -0.556 9.04
a From ref 9 . Determined from eq 3. The standard value g 0 H + = 22.69 i 0.08 J K-' mol: was obtained by extrapolating the function &+ t R In m vs. rn''z/(l + ml'a) to infinite dilution for aqueous HCl.s The Q H C ~data used in this calculation were fzom ref 8b. The error in S O H + results from %standard error of t 0.05 J K-I mol-' in F(TEP)" and an error of *63 J mol-' in Q'HcI.' Determined from column 4 with Q o H + = 13.127 kJ This value is 4 J mol-' larger than that found in ref 2. Calculated from reevaluated data of ref 8a. Determined from reevaluation of data from ref 8a, by fitting the data to a linear equation in ~ ' / ~t/ 1( .15 ~ ' ' ~ )e . Standard error of the intercept, calculated b y the method of Deming.'O f From ref 2. g This work. Corrected to 1 a t m partial pressure of H, as in ref 8. An additional factor of ' / ,must be used in the heat-of-transport term of eq 3. The abscissa used was the same as in footnote d , except molarity was replaced by ionic strength.
TABLE 11: Calculation of Heat of Transport as a Function of Temperature (AG"/AT)/kJ
Acid HCl HBr NH,SO,H H,SO,h
T/K 293.15 298.15 303.15 288.15 298.15 308.15 302.15e 288.15 298.15 308.15
(TEP)"/pV
K-I
510.91b * 0.38c 521.62 c 0.52 532.71 c 0.62 502.3gd * 0.36 523.02 * 0.33 541.71 i 0.35 504.202 i: 0.52 526.6f t 1.5 551.8 f 1.0 572.1 c 2.0
taA-a
0.1744 0.1791 0.1838 0.1736 0.1826 0.1915 0.12948 0.176 0.187 0.199
$HA/kJ
12.35 i 13.58 f 14.85 i 11.21 i 13.54 * 15.54 c 14.71 i 29.76 f 35.29 i 38.99 c
mol-'
0.15 0.16 0.17 0.15 0.15 0.15 0.23 0.55 0.41 0.65
IC1 mol-' 0.25 c 0.02 0.22 c 0.02
0.46 i 0.04
a From ref 9. See footnote d of Table I. See footnote e of Table I. From ref 2. e Experimental (TEP)"s determined using thermostat temperatures of 24 "(734"C. At 29 "C sulfamic acid has a maximum K , of 0.103939.13 f This work. See footnote g of Table I. g Values of anionic mobility a t 25 "C from ref 14. Temperature coefficient for BrExperimental (TEP)'s were determined using a temperature difference of 1 0 K in each case. See also footnote h of Table I.
determined 13.347for HBr and 12.217 for HC104,both of which compare well with ours. Agar reported the value 3E1.18~for H2S04,which is in very close agreement with our value. In comparing our values for $OA-/kJ mol-l with those of Agar,' differences in convention must be taken into account. This was done by adding 0.451 to his values, yielding 0.539 for bromide, 0.451 for chloride, -0.465 for perchlorate, and 8.48 for sulfate. In order to calculate QoHA'sat temperaturesother than 25 "C, the temperature variation of SoHz and S , must be taken into account. We calculated S o H z using12
SoHz/(J K-l mol-') = 130.587 + 66.926 log (T/298.15) (4) and calculated S,(Pt) using an equation of Temkin and Khoroshin7
(Se/F)/pV K-' = 4.54 + 0.044(T- 300)
(5)
which is valid for T I220 K. A lack of literature values for SoH+at temperatures other than 25 "C forced us to assume that S O H + remain constant over the small temperature rapge 15-35 "C. Table I1 summarizes the calculation of & O m for several acids at different temperatures. From Table I1 it appears that our HCl result of 0.25 for (AQ"/Ar)/kJ K-l mol-' is consistent with the only result found in the literature, viz.,j.17 for 0.01 M HCl.15 For other chlorides at 0.01 M, (AQ/AT)/kJ K" mol-l is in the range 0.15-0.21. Our values for HBr and H2S04fall within thepacceptable range for 1-1 electrolytes, especially when experimental errors are considered and when the result for H2S04is multiplied by 2 / 3 , because of the three ions in
solution. The excellent comparison of our results with literature values makes us very confident of our method of using (TEP)"'s to determine &"HA.
Acknowledgment. We gratefully acknowledge that this work has been supported by an M. J. Murdock Charitable Trust grant of Research Corporation. References and Notes (1) J. N. Agar, Adv. Electrochem. Electrochem. Eng., 3, 31 (1963). (2) A. D. Payton, S. G. Angelos, E. L. Shuck, and A. H. Zimmerman, J . Chem. Soc., Faraday Trans. 1, 71, 2111 (1975). (3) J. N. Agar in "Annual Reviews of Physical Chemistry", Vol. 15, H. Eyring, Ed., Annual Reviews, Inc., Palo Alto, Calif., 1964, p 478. (4) E. Helfand and J. G. Kirkwood, J . Chem. Phys., 32, 857 (1960). (5) E. Helfand,R. J. Bearman, and V. S.Vaidhyanathan, J. Math. Phys., 4, 160 (1963). (6) W. M. Latimer, "The Oxidation States of the Elements and Their Potentials in Aqueous Solution", 2nd ed, Prentice-Hall, Englewood Cliffs, N.J., 1952. (7) M. I. Temkin and A. V. Khoroshin, Zh. Fiz. Kbim., 26, 500 (1952). (8) (a)A. D. Payton, €3. H. Boyd, C. M. Houck, E. H. Temple, and A. H. Zimmerrnan, J. Electrochem. Soc., 120, 373 (1973); (b) W. G. Breck, G. Cadenhead,and M. Hammerli, Trans. Farahy Soc., 61,37 (1965). (9) R. Parsons, "Handbook of Electrochemical Constants", Butterworths, London, 1959, pp 85, 87. (10) W. E. Deming, "StatisticalAdjustment of Data", Dover Publicatlons, New York, N.Y., 1943. (11) R. Haase and K. Hoch, 2.Pbys. Cbem. (Frankfuxt am Main), 46, 63 (1965). (12) H. M. Spencer and J. L. Justice, J. Am. Cbem. Soc.,56, 231 1 (1934). (13) E. J. King and G. W. King, J. Am. Cbem. Soc., 74, 1212 (1952). (14) E. G. Taylor, R. P. Desch, and A. J. Catotti, J . Am. Chem. SOC., 73, 74 (1951). (15) 6.D. Butler and J. C. R. Turner, J . Phys. Cbem., 69, 3598 (1965).
Arthur D. Payton"
Chemistry Department Wiliamette University Salem, Oregon 97301
Michael S. Showell Received July 13, 1977
