J. Phys. Chem. 1983, 87, 797-800
where z is the charge of the cation (i.e., zi = 1 and z. = 2) and the parameters s and Ak to Ek,valid for 35 OC)' are given in Table 111. The mean molal activity coefficient of the binary solution is given byl39l4 In y+ko = -zkspi2(1 + AkP/2)-1+ (2&)1 (3Ck/2)P (4&/3)13 (5Ek/4)14 (3)
with the same parameters as before. In the ternary solutions, the osmotic coefficient is13J4 9 = c ( z k + l)[email protected]
/C(zk+ 1)mk (4) and the activity coefficients of the salts are13,14 In y*i = In y+F + 0.5yj[(zi/zj) In yajO - In y+:]
In yij = In y+f + 0.5yi[(zj/zi) In y+: - In y+?] (6) The mean activities of KC1 and MgClz are then ai = mimclyh? and aj = mjm&+j3. As is seen in Table I, the equilibrium activities of potassium chloride in the inner and outer beakers are approximately equal. Any discrepancies are due to inaccuracies in the estimation of mKCl,equil from fitting the data shown in Figure 1 to eq 1. This seems to be the case in experiment 4. In series I1 both potassium chloride and water are transferred in substantial amounts, but in opposite directions. The driving force for this transfer, which leads to diffusion of potassium chloride up its concentration gradient in experiments 1-5 (see Figure 2) is obtained from the Gibbs free energy change accompanying the transfer of water (or of the solution) from the inner to the outer beaker. If only the initial and the final states are considered, there is a net transfer of 25 g of water from the inner beaker to the outer one, diluting the mixed solution there, and changing the Gibbs free energy of the system by AG = AGM AGE kJ. The change of Gibbs free energy of mixing AGM is AGM = RT[ni In (xifi/xiin)+ nj In (xjfi/xjin)+ 55.51(wd In xWfi- wwin In xWin)](7)
where RT = 2.562 kJ mol-l at 35 OC, nK is the number of moles of component k (i or j) in the system and xk is its mole fraction, w, is the mass of water in the system (in kg), and fi and in designate the final and initial stages, respectively. The change of the excess Gibbs free energy A G is~
where GE = yiG?
+ yjGjEo+ Gij
is the specific (per kg water) excess Gibbs free energy, and GkEo
= RTmk(1 - (bk0
+ In y+ko)
Gij = RTyiyp(0.091 - 0.027311/2)
The expression in parentheses in eq 11 is valid for 25 OC,13 but the numerical values are assumed to hold also for 35 OC, the contribution of this tenary term being small and any errors introduced thereby negligible. The values of AGM, AGE, and AG have been calculated and are shown in Table 11. It is seen that the total Gibbs free energy of the system changes (for the 171 g of solution after dilution) by -167 to -201 J for experiments 1-6, respectively. This is adequate for pushing the up to 1.93 to 8.21 mmol of potassium chloride (in experiments 14) through the liquid membrane, and, in the final stages, even up concentration gradients. In this respect the present experiments differ from previous ones:+ in which a crown ether or a similar selectively solvating substance has been used as the essential component of the liquid membrane. When the solvent is l-octanol,4 chl~roform,~ or tetrachloroethane6the acceptance of C1- anions into the membrane is low but they must accompany the selectively solvated K+ cations in ion pairs that migrate across the membrane. These ion pairs compete with H+C1- or Li+Cl- ion pairs, which migrate in the same direction, but at different speeds. The driving force for the uphill diffusion of Kt ions comes from the downhill diffusion of H+ or Lit ions (and the neutralization of the Ht by OH- ions4)until the latter have equilibrated between the two aqueous solutions. In the present study, in series 11, the impermeability of the membrane to Mg2+cations, and its ready acceptance of C1- ions (by solvating them with the substituted phenol) provide for the migration of a single electrolyte, which can be separated away from the system in a pure state at a concentration higher than its initial concentration in the electrolyte mixture. Registry No. K, 7440-09-7;KCl, 7447-40-7; MgCl,, 7786-30-3; HzO, 7732-18-5; dibenzo-18-crown-6, 14187-32-7; m-cresol, 10839-4.
Infrared Matrix Isolation Spectrum of the Si& Molecule Zakya H. Kafafl, Robert H. Hauge, Lelf Fredln, and John L. Margrave* Department of Chemistry and Rlce Quantum Instltute, Rlce University, Houston, Texas 77251 (Received April 19, 1982; I n Flnal Form: September 17, 1982)
Infrared spectra of Si212Cand Si213Cisolated in solid argon at 15 K have been reported in the 400-4000-cm-' region. Two absorptions at 1188.9 and 658.2 cm-' that exhibit carbon-13shifts of 35.2 and 14.9 cm-', respectively, have been detected. Based on the measured IR data, we conclude that the molecule has CZusymmetry with a lower limit of 110' for the SiCSi bond angle. Introduction The Sic2electronic spectrum has been seen in radiation from stars by several groups'-' and was first produced in (1) Merill,
P.W.Publ. Astron. SOC.Pac. 1926, 38, 175.
the laboratory by Kleman.5 Weltner6 studied both the absorption and emission spectra of the silicon dicarbide (2) Sanford, R. F. Publ. Astron. SOC.Pac. 1926, 38, 177. (3) Shane, C.D. Lick Obs. Bull. 1928, 13, 123.
0022-3654/83/ 2087-0797$0 1.50/0 0 1983 American
The Journal of Physical Chemistry, Vol. 87, No. 5, 1983
molecule. His matrix isolation spectra agreed with the previous gaseous observations of McKellar4and Kleman,5 but with the addition of three distinct weak bands. He also observed a series of bands at 4893 A in the neon matrix spectrum which corresponds to the 4906-A weak band previously observed in the gas p h a ~ e . ~He , ~tentatively assigned this series of bands to the symmetrical Si& molecule with IR absorptions at 1205 and 1187 cm-l in neon and argon matrices, respectively. The high-resolution study of this absorption spectrum by Verma and Nagaraj' using the flash discharge technique indicated that the 4906-a band belongs to the molecule Sic2and not to Si&. Gilra8studied the spectrum of C3 in a King furnace in the 2500-6500-A and 600-3300-cm-' regions. After the addition of silicon, he observed the blue continuum earlier reported5and determined its wavelength dependence. Sic, vibration-rotation bands were seen at 1740 cm-'. Strong unidentified features at 1100-1200 cm-l were also detected. Recently, Bondybe? used a pulsed YAG laser to vaporize silicon carbide and studied the excitation, emission, and absorption spectra of Sic2in the gas phase and in a Ne matrix. His results are in good agreement with the most recent study' except for a slightly higher bending frequency ( N 172 cm-l) predicted from the observed overtone. Failure to detect the fluorescence spectrum of Si2Cwas attributed to a low emission quantum yield for this molecule. Also no spectrum was observed for S i c which may be due to disproportionation of Sic into Sic, and Si or C2 and Si since both Si, and Cz were present as major fluorescent molecular species. Mass spectrometric studies on the vaporization thermodynamics of hexagonal silicon carbidelOJ1indicated that Si, Sic2,and Si2C were the major atomic and molecular species present in the equilibrium vapors above solid silicon carbide. Based upon the above-mentioned studies and further evidence presented in this paper, we were able to identify an IR absorption at 1188.9 cm-' consistently occurring in our Si/H20, Si/HF, and Si/H2 studies12-14as being due to disilicon carbide, Si2C. This molecule was present as an impurity in the system as a result of silicon reacting with the high-density graphite crucible. Because of its possible astrophysical importance and its presence in the vapors over the Sic, Si-Sic, and C-Sic systems at high temperatures,loJ1the infrared study of matrix isolated Si2% and SiZl3Cwas undertaken. N
Experimental Section Vapors of Siz12Cwere obtained by heating elemental silicon in a high-density graphite cell in the temperature range 1450-1700 O C . The temperature of the cell was measured with an optical pyrometer. Vapors of Si23C were produced by heating a mixture of elemental Si and graphite enriched in 13C (90%) in the same cell under the (4) McKellar, A. J . R. Astron. SOC.Can. 1947, 41, 147. (5) Kleman, B. Astrophys. J . 1956, 123, 162. (6) Weltner, Jr., W.; McLeod, Jr., D. J. Chem. Phys. 1964, 41, 235. (7) Verma, R. D.; Nagaraj, S. Can. J.Phys. 1974,52, 1938. (8) Gilra, D. P. Spectres des Molecules Simples au Laboratoire et en Astrophysique. Communications pr6senGes au Colloque International d'Astrophysique. Universite de Liege, Liege, Je. 21-23, 1977 (1980). (9) Bondybey, V. E. J. Phys. Chem. 1982,86, 3396. (10) Behrens R. G.; Rinehart, G. H. Natl. Bur. Stand. (U. S.), Spec. Publ. 1979, NO.561-1, 125. (11) Verhaegen, G.; Stafford, F. E.; Drowart, Jr., J. J . Chem. Phys. 1964, 40, 1622.(12) Ismail, 2. K.; Hauge, R. H.; Fredin, L.; Kauffman, J. W.; Margrave, J. L. J. Chem. Phys. 1982; 77, 1617. (13) Ismail, 2. K.; Fredin, L.; Hauge, R. H.; Margrave, J. L. J. Chem. Phys. 1982, 77, 1626. (14) Fredin, L.; Hauge, R. H.; Kafafi, Z. H.; Margrave, J. L. To be published.
Kafafi et al.
I/ ( c m -
Flgure 1. The asymmetric stretching region of Si,"C (A, B, C) and Si,'2C/Si,13C (A', B', C') in solid argon.
same conditions. Gaseous disilicon carbide in excess argon was then deposited on a polished copper surface for a period of 1 h. The mirror was then rotated 180' and IR reflection spectra of matrix isolated Si212Cand Si213Cwere recorded on a Beckman-IR 9 spectrophotometer. Frequencies of IR absorption peaks were measured with an accuracy of f0.5 cm-'. The rates of deposition of Si and Si2Ccombined and of argon were determined with a quartz crystal microbalance. Pure silicon (99+%) was purchased from MCB. Graphite enriched in carbon-13 (90%) was supplied by Monsanto Research Corp. Matheson argon (99.99%) was further purified by passing it through hot titanium (900 "C) prior to deposition. An Air Products Displex closed cycle helium refrigerator has been used in all matrix experiments. Spectra of trapped pure silicon showed the presence of bands due to monosilane (SiH,) and silylene (SiH2)which are the result of the reaction of silicon atoms with molecular hydrogen on the matrix surface.', The hydrogen impurity probably resulted from cracking of the organic pump oil. Passing liquid nitrogen rather than water through the copper heat shield surrounding the furnace considerably reduced the amount of SiH, and SM2present in the matrix. Detailed descriptions of the matrix isolation apparatus have been given earlier by Ismail15 and Kauffman.l6
Results During our recent studies on reactions of silicon atoms with H20,12HF,13and H2,14there was a strong unidentified band that appeared at 1188.9 cm-' in argon matrices. The intensity of this band did not depend on the concentration of HzO or HF or H, (also present as an impurity in the H20 and HF studies) in the matrices. When silicon atoms were vaporized at different temperatures from the high-density graphite crucible and codeposited with excess argon on the copper surface for a period of 1 h, spectra such as those presented in Figure 1(A, B, and C) were obtained. When a mixture of elemental silicon and graphite powder enriched in carbon-13 (90%) was heated in the same graphite crucible, and their vapors were cocondensed with excess inert gas, spectra such as those shown in Figure 1 (A', B', and C') were produced. Besides the bands due to S M 2 and SiH,, we observed a peak at 1188.9 cm-' that exhibits a carbon-13 shift of 35.2 cm-l. The intensity of this peak (15) Ismail, Z. K. Ph.D. Thesis, Rice University, 1972. (16) Kauffman, J. W. Ph.D. Thesis, Rice University, 1981.
The Journal of Physical Chemistry, Vol. 87, No. 5, 1983 799
I R Spectrum of Si&
I 1188.9 cm-'
Figure 2. High-resolution infrared spectra of Si,%
and SI,'3C in s o l i
increased as a function of the furnace temperature. On the basis of Weltner'ss and Gilra's6 observations as well as the above results, the bands at 1188.9 and 1153.7 cm-' were assigned to the asymmetric stretching mode of the molecules Siz12Cand Si2l3C,respectively. Figure 2 shows high-resolution spectra for the two absorption bands observed for Si?T! and Si213Cin solid argon. A weak band at 658.2 cm-' was detected at a higher furnace temperature (-1660 "C)with a higher concentration of Si& as evidenced by the higher intensity of the 1188.9-cm-' absorption peak. This new absorption at 658.2 cm-' seems to grow with the same relative intensity as its counterpart at 1188.9 cm-'. It also shows a carbon-13 shift of 14.9 cm-l and so it seems reasonable to associate it with the same molecule, SizC. Other unidentified features appeared at 1101,1094,525, and 505 cm-'. The band at 1100 cm-' exhibits a carbon-13 shift of -35 cm-' while the 1094-cm-' absorption shows a dependence on hydrogen concentration.
Discussion When silicon is vaporized with an isotopic mixture of carbon-13 and carbon-12, two new bands appear at 1153.7 and 643.3 cm-' besides the two original ones observed at 1188.9 and 658.2 cm-' that are due to the pure carbon-12 isotopic molecule. One can conclude from this mixed isotopic study that the molecule contains only one carbon atom. When the graphite crucible was heated in the absence of silicon, the 1188.9 and 658.2-cm-' bands disappeared. Both of these bands show a dependence on the temperature of the furnace and the higher the temperature, the more intense they are. Mass spectrometric studied0have shown that possible candidates which have an appreciable vapor pressure in this temperature range are Si, Sic2,and Si2C. Since it cannot be silicon atoms or Sic2,one concludes that it must be Si&. The next question that arises deals with the geometry of Si&. Disilicon carbide may have a linear or nonlinear and symmetric or asymmetric configuration. The molecules C317316and SiC26,7,9 are known to be linear in their ground electronic states in the gas phase as well as in inert gas matrices. They both have low bending frequencies, 63 cm-l for C3 and 1477or 1729cm-' for Sicz. By analogy (17) Gausset, L.; Herzberg, G.; Lagerqvist, A.; Rosen, B. Astrophys.
J. 1965, 142, 45.
(18) Weltner, Jr., W.; McLeon, Jr., D. J. Chem. Phys. 1966,45,3096.
The Journal of Physical Chemistry, Vol. 87, No. 5, 1983
TABLE 11: Relation between the Bending Frequency (cm-I) and the Force Constants (mdyn/A ) of Si,C (Ai) 400 350 300 250 200 150 100
4.715 4.624 4.544 4.478 4.423 4.380 4.349
0.592 0.455 0.335 0.234 0.151 0.086 0.040
0.941 1.032 1.111 1.178 1.233 1.276 1.307
0.537 0.425 0.327 0.245 0.178 0.125 0.088
to those molecules which have the same number of valence electrons as Si&, one would expect that disilicon carbide would be a symmetric linear molecule of Dmhsymmetry. For such a centrosymmetric molecule, one expects two infrared active modes that are Raman inactive: the asymmetric stretching and the bending modes. Assuming the 658.2-cm-l absorption as the bending frequency which is highly unlikely because of its very high value, one calculates a carbon-13 shift of 21.2 cm-l compared to the measured shift of 14.9 cm-’. This difference of 6.4 cm-l between the observed and calculated shifts makes the assignment of this frequency to the bending mode of linear Si$ highly improbable. Further evidence against the molecule being linear is the very high anharmonicity (102.0 cm-’) for the asymmetric stretching mode that would be needed to obtain agreement between the calculated and measured carbon-13 frequency shifts for the asymmetric v3 mode, Av,. Preliminary normal coordinate analyses have been carried out by assuming the possible asymmetric linear configuration and the two observed frequencies, 1188.9 and 658.2 cm-’, as the Si-C and Si-Si stretching modes, respectively. The results of these calculations indicate that it is impossible to get reasonably good agreement between the calculated and the measured isotopic shift for the v2 (Si-Si) mode. The other possibility is to assign this 658.2-cm-‘ frequency to the bending mode, but this can be eliminated on the basis of the arguments given previously for the symmetric linear geometry. If Si& is bent, one would think that the symmetric structure would be thermodynamically more favorable than the asymmetric one since the Si-C bond is expected to be much stronger than the Si-Si bond. Assuming that Si& has a symmetric bent configuration, one can assign the 658.2- and 1188.9-cm-’ peaks to the symmetric and asymmetric modes, respectively. From the Teller-Redlich product rule and the measured asymmetric frequencies of Siz12Cand Si213C,one calculates a lower limit of 110’ for the bond angle of Si&. A preliminary normal coordinate analysis has been carried out for Si& by using Schachtshneider’s program18and the measured frequencies for the asymmetric and symmetric stretching modes of Si;T and Si;%. A bond angle of 110’ and a bond length of 1.75 8, were assumed. It was not possible t o calculate a unique force field due to the lack of a measured value for the bending frequency. One is able to get a perfect fit, i.e., identical values, between the measured and calculated frequencies for Si212Cand Si2’3Cfor a large range of values of the bending frequency. Table I lists measured and calculated frequencies for all Si,C isotopomers by assuming u2 = 250 cm-l. Table I1 gives a set of force constants for uz varying from 400 to 100 cm-’. An average force constant, ksic = 4.5 mdyn/A, has been determined for Si& from the normal coordinate analysis. Comparing this value with that of SiC2,6ksic = 7.4 mdyn/8,, which is the expected value for a Si=C double bond, leads one to belive that the Si-C bond in Si2Cis close to being a single bond. This in turn suggests that the molecule may be carbene-like which
Kafafi et al.
would explain why it is bent. It may also suggest that a bond exists between the silicone. Large stretch-stretch as well as stretch-bend interaction force constants were necessary for reproduction of the measured frequencies. This should not be too surprising if one thinks of this molecule as a three-membered ring where possible Si-Si bonding may exist since the calculated distance of 2.86 A lies close to the range of typical Si-Si bond lengths. Varying the bending frequency from 400 to 100 cm-’ caused little change in the values of ksic and ksicsc force constants. It is difficult to predict the value of the bending frequency since it will strongly depend on how much the two silicons interact with each other. One would expect it to be higher than that observed for Sic,. The fact that the Si2Cmolecule is bent in an inert gas matrix is surprising; however, molecules like S i c 0 and SiN2 are known to be nonlinear in some sites in some matricesaZ0SiN2in a pure N2 matrix and Sic0 in argon represent cases where almost all molecules are bent as indicated from the relative intensities of the xz and y2lines of their ESR spectra. Although calculations showed that bent structures are unstable relative to the linear arrangement, it is possible to explain this deviation from linearity in terms of a low bending force constant. Thus, a deviation from linearity can be induced by the constraints of the matrix sites. In their study on Sic0 and SiN2,Lembke et aLZomentioned in a footnote that “For an average bond length of 1.5 A, bending S i c 0 by 5 O is equivalent to moving the central atom by 0.07 A. If the bending force constant is assumed to be 0.1 mdyn/A, this corresponds to an energy of 125 cal/mol. This is the same order of magnitude as the energy involved (23 cal/mol) in moving two argon atoms, spaced 4 apart, by 0.07 A.” However, the above discussion does not suggest that Si2C is being bent by the inert gas matrix, but it would be interesting if one proves that this is the case. The force constants (ksic) calculated for S i c 0 and Si2Care similar (5.3 vs. 4.5 mdyn/A) where the value of ksc calculated for S i c 0 was based on vl” = 800 cm-’ (assumed by comparison to vl’ = 750 cm-’ for the first excited electronic state). It would be interesting to know more about the electronic spectrum of Si& and the multiplicity of its ground state. The ground state of C3 is 12,.21Weltner6 pointed out that substituting a silicon for carbon atom in C3would tend to lower the E, orbital energy relative to the strongly bonding II, orbital and would result in a gradual transition from singlet to triplet ground state. Although Sic2has a singlet ground state, one might expect Si$ to have a triplet ground state which may be related to its apparent nonlinearity. A recent failureg to observe electronic spectra of Si& may be related to the different structure and multiplicity of the ground state from those of C3 and Si&. This work also suggests that Si, might exist as a ring in its ground state. Acknowledgment. Funds from the National Science Foundation and the Robert A. Welch Foundation supported this study. Zakya Kafafi acknowledges partial support from a Peace Fellowship sponsored by the U. S. AID. Registry No. Si&, 12070-04-1; Si2I3C,84254-46-6. (19) Schachtschneider, J. M. Technical Report No. 231 and 57, Shell Development Co., Emeryville, CA, 1964. (20) Lembke, R. R.; Ferrante, R. F.; Weltner, Jr., W. J. Am. Chem. SOC.1977, 99,416. (21) Pitzer, K. S.; Clementi, E. J . Am. Chem. SOC. 1959, 81, 4778.