334
J. Phys. Chem. 1986, 90, 334-341
isomers could be present with H, and Ha arising from C4 isomers and H, and H, arising from D4 isomers (cf. assignments in Figure 9). In contrast, the regularly stacked tetramers of 2’-GMP exhibit two H(8) resonances of unequal intensity. This is precisely the result expected for the presence of all isomers, provided that twisting about the C4 axis is fast. For fast twisting and degenerate chemical shifts for isomer pairs with equivalent base-overlap patterns, one time-averaged H(8) resonance should occur for the two C4 isomers and one time-averaged line should also be observed for the four D4isomers. If twisting about the C4axis was slow, as in the case of ordered 5’-GMP,31 then one would have to conclude that the C4 isomers are absent. However, there is no apparent reason why this should be so, and we tend to favor the explanation based on fast tetramer twisting. That twisting should be faster for 2’-GMP than 5’-GMP is not surprising, because we find no evidence for structure stabilizing intertetramer H bonding or Na’ chelation by phosphate oxygens for 2’-GMP. The importance of phosphate position in governing the aggregation properties of alkali-metal G M P salts cannot be overemphasized. Phosphate position also is important in regulating the association of the nucleotide in the presence of organocations like TMA. It is rather remarkable that TMA inhibits the ordered stacking of Na+-directed 2’-GMP tetramers but not 5‘-GMP tetramers. Apparently, ion pairing between TMA and the phosphate oxygens in 2‘-GMP tetramers sterically interfere with their ordered stacking, whereas in the regularly stacked 5’-GMP tetramers the chelation of Na’ by phosphates on adjacent tetramers competes favorably with TMA-phosphate ion pairing. The steric inhibition of regularly stacked 2’-GMP tetramers by TMA also is supported by the results of the mixed nucleotide experiments. Although TMA alone does not inhibit the ordered stacking of 5’-GMP tetramers, inhibition is observed when both (31) The rate of H, 9 H binterchange for ordered Naz(5.’-GMP)(C, isomer twisting) has been estimated to be only 0.3 s-’ by spin-saturation transfer measurements.2’
TMA and 2’-GMP are present. This suggests that TMA-(2’GMP) ion pairs substituted for 5’-GMP units in 5’-GMP tetramers and sterically inhibit ordered stacking of the mixed [(2’GPM),(S’-GMP)+.,] units. There is no evidence for ordered stacking of the mixed tetramers since nonequivalent H(8) environments are not observed by NMR. However, disordered stacking of the rapidly exchanging mixed tetramers most likely occurs, because the time-averaged H(8) resonance of each nucleotide moves to higher field with increasing concentration or decreasing temperature. (TMA),(2’-GMP) does not form ordered self-structures and exhibits little or no tendency toward disordered monomer stacking, as judged from the absence of an appreciable concentration or temperature dependence of the H(8) chemical shift. Therefore, the driving force for mixed tetramer formation is provided not only by the entropy of mixing but also by the interbase H-bond stabilization and disordered stacking enthalpy gained by incorporation of TMA-(2’-GMP) ion pairs into tetramer units. These latter factors are quite important to the overall driving force, because no nucleotide redistribution occurs between Na+-directed 2‘-GMP tetramers and regularly stacked 5’-GMP tetramers. In this case, the H-bond stabilization and stacking forces lie in favor of the symmetrical tetramer units and more than compensate for the entropy of mixing. Note Added in Proof. Led and Gesmar3* have recently investigated twisting in 5’-GMP octamers by 3iPmagnetizationtransfer N M R studies.
Acknowledgment. The partial support of this research through N I H Grant GM-235 16 is greatfully acknowledged. Registry No. Li2(2’-GMP),99309-72-5; Na2(2’-GMP),70347-42-1 ; K2(2’-GMP), 99309-73-6; Rb2(2’-GMP), 99309-74-7; Cs2(2’-GMP), 99309-75-8; (TMA),(Z’-GMP),99309-77-0; Li2(5’-GMP),67553-30-4; Na2(5’-GMP), 5550-12-9; K2(5’-GMP), 3254-39-5; Rb2(5’-GMP), 67553-29-1; Cs2(5‘-GMP),67553-27-9. ( 3 2 ) Led, J. J.; Gesmar, H. J . Phys. Chem. 1985, 89, 583.
Vibrational Spectral Studies of Solutions at Elevated Temperatures and Pressures. 8. A Raman Spectral Study of Ammonium Hydrogen Sulfate Solutions and the HSO,--SO,*- Equilibrium B. S. W. Dawson, D. E. Irish,* and G . E. Toogood Guelph- Waterloo Centre for Graduate Work in Chemistry, Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (Received: July 10, 1985)
Raman spectra of aqueous ammonium hydrogen sulfate solutions spanning a temperature range from 25 to 300 OC,at a pressure of 10 MPa, have been measured. The conversion of sulfate to hydrogen sulfate ion is virtually complete at 300 O C . The relative integrated intensitiesof the 980-cm-I line of SO?-and the 1040-1050-cm-’ lines of HSO, have been measured. The relative integrated molal intensities are almost independent of temperature. From the intensities, the populations of the species SO?- and HSO, have been calculated and thus the change in the degree of dissociation of the acid with temperature has been measured. The equilibrium constant has been partitioned into two terms-the concentration quotient Q, and the activity coefficient quotient Q?.The latter changes with temperature much less than the former. The contributions of each to the standard enthalpy change, AHo, have been estimated. The marked shift of the @-(OH)) vibration of HS04- to lower frequencies as the temperature rises is linked to the changes in hydrogen bonding resulting from changes in the structure of the liquid water and the interaction between water and HS04-.
Introduction Sulfuric acid is of importance in high-temperature aqueous chemistry because the second acid dissociation is related to the base hydrolysis of sulfate.’ The dissociation anstant and related
thermodynamic parameters at 25 O C have been measured by a variety of methods. Early investigations have been reviewed and were shown to yield concordant Values.* More recent studies include heat capacity mea~urements,~ ~pectrophotometry$~ emf,G8
R.C.; Cobble, J. W. Proc. Int. Water Conf., Eng. SOC.West.
(2) Young, T. F.; Irish, D.E. Annu. Rev. Phys. Chem. 1962, 13, 435. (3) Larson, J. W.; Zeeb, K. G.; Hepler, L. G. Can. J . Chem. 1982, 60,
(1) Murray,
P a , 4lst 1980, 295.
2141.
0022-3654/86/2090-0334!$01 SO10
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 335
Vibrational Spectral Studies of Solutions TABLE I: Parameters of the ur(ar)Band of Sulfate Ion at Selected Compositions and Temperatures" composition/mol kg-' temp/% 0.514 1.11 25 75 100 175 250
981.5 (6.7) (5.3) 980.2 (6.8) (5.5) 977.0 (8.3) (7.2) 975.1 (9.5) (8.6)
982.5 981.1 980.5 978.3 976.5
(6.8) (5.4) (7.0) (5.7) (7.2) (6.0) (8.6) (7.5) (10.2) (9.3)
2.25 982.7 (7.4) (6.2) 980.7 (7.5) (6.3) 979.1 (8.7) (7.7) 977.3 (10.7) (9.9)
"Position (fwhm) (units cm-I; spectral slit width 3 cm-'). The fwhm in the second parentheses are corrected by the procedure of ref 28.
enthalpies of s o l ~ t i o n ssolubility ,~ of Ag2S04in H2SO4 from 25 to 225 O C , I o solubility of C a S 0 4 in H2S04 from 25 to 300 O C , I 1 and c o n d ~ c t i v i t y . l ~ -Pitzer ~ ~ et aL6 have presented a critical analysis of the thermodynamic properties of H2S04. Agreement at elevated temperatures is not considered g 0 0 d . l ~The ~ HS04ion is also of particular interest because it is one of two possible noncomplexing anions known to be thermodynamically stable in high-temperature acidic s01utions.l~~'~ Raman spectroscopy provides a method which complements the classical methods. The vibrational spectrum provides frequencies, intensities, and other band properties which often allow one to identify the species present, their populations, the chemical processes taking place, and their dependence on concentration, temperature, and pressure.17 At the same time, the accuracy with which populations can be measured is considerably less than in, for example, emf measurements, and the lack of knowledge of activity coefficients makes a rigorous transition to thermodynamic parameters virtually impossible. Nevertheless the detailed information about species, equilibrium states, and the degree of dissociation of an electrolyte makes a unique and useful contribution to the subject. Vibrational spectral studies of HS04- and H2S04have been reported by a number of w ~ r k e r s . l * - ~This ~ paper extends our
(4) Young, T. F.; Singleterry, C. R.; Klotz, 1. M. J. Phys. Chem. 1978, 82, 671. (5) Pavlyuk, L. A.; Smolyakov, B. S.; Kryukov, P. A. Izu. Sib. Otd. Akad. Nauk SSSR, Ser. Khim Nauk 1972, No. 3, 3. (6) Pitzer, K. S.; Roy, R. N.; Silvester, L. F. J . Am. Chem. SOC.1977, 99, 4930. (7) Mroczek, E. K. Ph.D. Thesis, Victoria University of Wellington, New Zealand, 1984. (8) SchGn, N. H.; Wannholt, L. Suen. Papperstidn. 1969, 72, 431. (9) Readnour, J. M.; Cobble, J. W. Inorg. Chem. 1969, 8, 2174. (10) Lietzke, M. H.; Stoughton, R. W.; Young, T. F. J . Phys. Chem. 1961, 65, 2247. (11) Marshall, W. I.; Jones, E. V. J . Phys. Chem. 1966, 70, 4028. (12) Ryzhenko, B. N. Geochem. Znt. 1964, 1, 8. (13) Quist, A. S.; Marshall, W. L.; Jolley, H. R. 1.Phys. Chem. 1965,69, 2726. (14) Quist, A. S.;Marshall, W. L. J . Phys. Chem. 1966, 70, 3714. (15) Cobble, J. W. In "Diagrams of Chemical and Electrochemical Equilibria: Proceedings of a NATO Advanced Research Workshop" (22nd CEFA Seminar), Pourbaiw, M., Pourbaix, A,, Eds.; Cebelcor: Brussels, 1981; p 119. (16) Swaddle, T. W.; Fabes, L. Can. J. Chem. 1980, 58, 1418. (17) Irish, D. E.; Brooker, M. H. In "Advances in Infrared and Raman Spectroscopy", Vol. 2, Clark, R. J. H., Hester, R. E., Eds.; Heyden: London, 1978; Chapter 6, p 212. (18) Irish, D. E.; Chen, H. J. Phys. Chem. 1970, 74, 3796. (19) Chen, H.; Irish, D. E. J. Phys. Chem. 1971, 75, 2672, 2681. (20) Young, T. F.; Maranville, L.F.; Smith, H. M. In "The Structure of Electrolytic Solutions", Hamer, W. J., Ed.; Wiley: New York, 1959; Chapter 4, p 35. (21) Balej, J.; Hanousek, F.; Pisarcik, M.; Sarka, K. J . Chem. Soc., Faraday Trans. 1 1984,80, 521. (22) Stopperka, Von K. Z . Anorg. Allg. Chem. 1969, 370, 80. (23) Walrafen, G. E.; Dodd, D. M. Trans. Faraday SOC.1961,57, 1286. (24) Young, T. F.; Walrafen, G. E. Trans. Faraday SOC.1961, 57, 34. (25) Turner, D. J. J . Chem. SOC.,Faraday Trans. 2 1972, 4 , 643. (26) Turner, D. J. J. Chem. Soc., Faraday, Trans. 1 1974, 7, 1346. (27) Goypiron, A.; de Villepin, J.; Novak, A. Spectrochim. Acta, Part A 1975, 31A, 805.
previous studies at 25 0C18,19 to the high-temperature regime. The molal intensities of S042-and HS04- have been measured over a 275-deg temperature range. These values have been used to estimate the concentrations of species and to thus characterize the equilibrium states.
Experimental Section Spectra were recorded with a digitally driven Jarrell-Ash 25- 100 1.O-m double Czemy-Turner monochromator with an RCA 3 1034 photomultiplier and SSR Model 1105/ 1120 photon-counting system. Spectra were excited with the 514.5-nm line of a Spectra-Physics argon ion laser Model 165-08 operating at 800 mW. Instrument control and data collection were performed with a Commodore 2001 computer interfaced to the spectrometer and to a H P 7470A plotter. Band fitting of overlapping lines was performed with a BNDFT program3' operating on an IBM 4341 computer. Spectra of the high-temperature samples were obtained by using the furnace assembly described p r e v i o ~ s l y . ~Pressures ~ were maintained at 10 MPA; no vapor phase was present. The spectral slit width (6 cm-I) and geometry of the optical assembly was maintained constant. For temperatures of 25 and 50 "C, samples were sealed in thin-walled capillary tubes and held in a thermostated copper block. The data of Table I were recorded with 100-pm slits (3 cm-l) and calibrated with the 1031.49-cm-' neon line. All solutions were prepared with Analar-grade reagents; anhydrous sodium sulfate and ammonium hydrogen sulfate were heated for 2 h at 105 "C and cooled in a desiccator prior to use, while sodium perchlorate was stored in a desiccator. Distilled, deionized water was used. We have chosen to use the temperature-independent composition variable molality (mol kg-' of water) rather than molarity for this work. The composition ranges studied were up to 2.9 m sodium sulfate and 8.7 m ammonium hydrogen sulfate; the molality of the internal standard, sodium perchlorate, was kept at about 0.3. All samples were filtered through 0.6-pm Polyvic BD Millipore filters before injection into the Raman cells. Results and Discussion Sodium Sulfate. The tetrahedral sulfate ion generates four Raman bands, nominally at 451 (v2, e), 618 (v4, f2), 981 ( v I ,a'), and 1104 cm-' ( v 3 , f2). Our primary concern is with the intense, polarized symmetric stretching mode of vibration, v,(al). The integrated band depolarization ratio from a 1.1 m solution of N a 2 S 0 4was 0.0006; thus the band profile is essentially that of the isotropic component. The positions and the full widths of this band, measured at one-half the peak height (fwhm) for temperatures spanning the range 25 to 250 "C and with a spectral slit width of 3 cm-I, are reported in Table I. The effect of the finite slit width has been removed by using eq 2 of Tanabe and H i r a i ~ h i . The ~ ~ band positions (25 "C) are 0.5- to 1.5-cm-' higher than values given by Dean and W i l k i n ~ o n . ~(Note ~ an error in the latter paper; uo should read 980.75 cm-I.) The band positions increase with increasing concentration and decrease with increasing temperature. This decrease correlates with a lower force constant or a longer bond length. As the temperature rises the hydrogen-bonded structure of liquid water is weakened35 and the anion-water hydrogen bonds are also weakened and distorted. The mean bond length appears to be increased when the strength of this anion-solvent interaction is diminished. The Raman band is simultaneously broadened, indicating shorter mean lifetimes in a particular vibrational state. Fujita and K i m ~ r suggest a ~ ~ that the v, mode of sulfate ions in aqueous solutions is modulated by (28) Ikawa, S.; Yamada, M.; Kimura, M. J . Raman Spectrosc. 1977, 6, 89. (29) Zarakhani, N. G.; Vinnik, M. I. Zh. Fir. Khim. 1963, 37, 503. (30) Giguere, P. A.; Savoie, R. Can. J . Chem. 1960, 38, 2467. (31) Jarv, T.; Bulmer, J. T.; Irish, D. E. J. Phys. Chem. 1977, 81, 649. (32) Irish, D. E.; Jarv, T.; Ratcliffe, C. I. Appl. Spectrosc. 1982, 36, 137. (33) Tanabe, K.; Hiraishi, J. Spectrochim. Acta, Part A 1980, 36A. 341. (34) Dean, K. J.; Wilkinson, G. R. J . Mol. Struct. 1982, 7 9 , 293; also see J . Raman Spectrosc. 1983, 14, 130.
(35) Ratcliffe, C. I.; Irish, D. E. J . Phys. Chem. 1982, 86, 4897. (36) Fujita, K.; Kimura, M. J . Raman Spectrosc. 1981, I I , 109.
336 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986
Dawson et al.
TABLE II: Molal Intensity Values for SO4*- and HSOr in the Temperature Range 298-573 K temp/K no. of points JSOP' r2 no. of points 298 5 0.636 f 0.022 0.999 323 6 0.661 f 0.007 1.oo 373 6 0.644 f 0.006 1.000 7 423 6 0.630 f 0.019 0.999 8 473 6 0.633 i 0.013 0.999 8 523 5 0.615 i 0.049 0.994 7 573 7 0.637 i 0.015d
r,
Jwso.-'
0.663 0.647 0.652 0.672 0.638
i 0.012 i 0.009
0.995 0.998 0.998 0.999 0.997
f 0.009 f 0.005 f 0.009
0.655 f 0.013d
"Values for Na2S04relative to NaC104 as internal standard. bRegression coefficient. CValues for NH4HS04 relative to NaCIO, as internal standard where the molal concentration of HSOL was determined from the difference (m(NH4HS04,analytical) - WI(SO,~-, measured)). Mean values
a very low-frequency mode, probably associated with the hydrogen bond making and breaking in water. Such a mode would be degraded at 300 O C . The first requirement for a quantitative analysis of the Raman band profiles of the acidic solutions was to establish the molal scattering coefficients (called molal intensities of species i to emphasize that the concentration is in mol kg-] of water and abbreviated J,) at each temperature of interest for the vl(al) symmetric stretching band of the sulfate ion. With these values available it will be assumed that the concentration of species i, m,, can be obtained from the relative integrated band intensities of species i, I,, from the equation I, = Jim,. A low concentration (about 0.3 m ) of NaC104 was added to each Na2S04solution to provide an internal intensity standard, viz. the vl(al) symmetric stretching band of C104-at 935 cm-'. The use of Clod- as an internal standard is justified because perchlorate ions do not interact strongly with metal ions in solution and thus competing equilibria can frequently be neglected. We have also recently shown that perchloric acid continues to be a strong acid to at least 200 OC for concentrations as high as 3 mol water per mol of HC104.37 Solution density decreases with increasing temperatures when pressure is held constant. However, it is not necessary to correct intensities for density changes because the correction applies equally to the intensity from the sample and the intensity from the standard and thus cancels in the ratio. In independent experiments the integrated intensity of the 935cm-' line of C104- from a 0.52 m solution was found to be independent of pressure (better than 1%) over the range 3 to 13.5 MPa, and independent of temperature over the range 25 to 250 "C. Thus the standard appears to be good and the populations inferred from the relative intensities correctly correspond to constant pressure experiments. Overlap between the two bands of interest, 981 and 935 cm-I, is minor and was easily resolvable with the BNDFT program. The C104- band envelope consists of two bands, the vl(al) fundamental and a lower-frequency shoulder which has been tentatively assigned to an overtone of the v2(e) bending mode of ClO,, which occurs at 462 cm-', and which can be in Fermi resonance with the fundamental ~ ~ ( a , For ) . ~this ~ study, as for all past quantitative studies, the area of the entire perchlorate band envelope was employed. Intensities were measured for four or five compositions at five temperatures ranging from 25 to 250 OC. Spectra of Na2S04solutions could not be obtained at 300 or 250 O C for the 2.88 m sample because of precipitation of NazS04(s). The solubility of Na2S04 drops sharply above 240 "C, where a high-temperature solid phase becomes stable relative to the saturated solution.38 For each temperature the relative intensities I were plotted against sulfate molality and the molal intensity values, JSo4z-,were obtained by linear regression. The values are presented in Table 11. Within experimental error the molal intensity is independent of temperature. The slope ( d J / d T ) , = -1.34(10e4) 5.7(10-5). The regression coefficient is -0.76. This temperature independence was also observed from (NH4),S04solutions over the temperature range 25 to 85 "C by Hayes et al.39
*
(37) Ratcliffe, C. I.; Irish, D. E. Can. J . Chem. 1984, 62, 1134. (38) Schroeder, W. C.; Gabriel, A,; Partridge, E. P. J. Am. Chem. SOC. 1935, 57, 1539.
I 720
X6
920
820
1020
1120
1220
1 0
RAMAN SHIFT / c m - '
250
350
450
550
650
R A M A N SHIFT / crn-'
Figure 1. Upper panels: Raman spectra (isotropic X I ; anisotropic X6) of the 720-1320-cm-' region of 3.8 m NH4HS04at 300 OC. Lower panel: the 250-700-cm'l region showing the fit to two symmetrical
bands.
Ammonium Hydrogen Sulfate Solutions. The hydrogen sulfate ion can be described in terms of C3usymmetry if the O H group is considered as a point mass (a distorted five-atom tetrahedron); otherwise it will have C, or CIsymmetry. The normal modes of vibration will span the following representations for the two cases C3uand C, respectively:
+ 3e (R, ir) (R, ir) + 4a" (R, ir)
I'(C3u)= 3a1 (R, ir) I'(C,) = 8a'
Of the 12 normal modes (C,), three belong to OH group vibrations: 0-H stretching contributes weak, broad Raman intensity in the 2900-cm-' region (overlapping with the spectrum of water and Hag'); S-O-H bending gives infrared intensity at 1340 cm-'; the S-O-H torsional mode is expected at lower f r e q u e n c i e ~ .Three ~~ of the nine remaining 0'-SO, skeletal modes will become degenerate under C,, symmetry and only six bands, coincident in the infrared and Raman spectra, are then predicted. The vibrational spectrum of the hydrogen sulfate anion in aqueous solution is obscured by bands of sulfate produced by (39) Hayes, A. C.; Kruus, P.; Adams, W. A. J . Solution Chem. 1984, 13, 61.
Vibrational Spectral Studies of Solutions
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 337
TABLE 111: Raman Shifts (an-’), fwhm, Depolarizations, and Assignments of Bands of the Hydrogen Sulfate Ion N H 4 H S 0 4 solid4I this work, 25 OC,” 1.3 m
* 1052 (17) 1039 (35) 869 (45)
*
*
200 O C , ” 1.3 m
* 1054 (13) 1049 (30) 854 (42)
*
*
25 OC, 3.8 m 1191 (96) dp 1050 (20) p 1034 (52) p 899 (56) p
*
*
i,
(fwhm), p 300 OC, 3.8 m 1195 (102) dp 1043 (13.5) p 1035 (33) p 831 (69) p 585 (40) p 422 (71) p
assignments under C,” symmetry
K H S 0 4 molten ref 43 ref 44 1360-1 390’ 1230 wp
vas SO, stretch, e us SO3 stretch,
al
1050 p
us S-(OH)
stretch, a l 6, SO, deformation, a , ti,,
SO3 deformation, e
840 wp 590 wp 420 wp
assignments under C, symmetry
D
1240 dp 1205 p 1046 p
3510
do-H)
a’
I194 dp
s-0 s-0 6, S-0-H us s-0
a” a’ a’ a’ a’ a‘ a” a‘ a’ a” a”
Yas
us
823-844 p 585 p 417 p
1044 p 1022 p 883 p 610 p 589 dp 576 447 p 418 dp 407 145
S-OH 6,O-s-0 V,
Pw
PI
so3 so3
6,O-S-OH 6,, 0-S-OH
A, O H
OThis is a sample of many data for six concentrations and four temperatures, obtained for the population analysis which follows. The entire spectrum was not measured. The values are from band fitting the contour. The peak maximum is very close to the higher frequency for the 1052-1039-~m-~doublet. Regions designated * have bands of overlapping with the bands of HSOC. bThis band is identified from infrared sDectra. CTheanalysis of Dhamelincourt et aL4I based on frequencies for the crystal and depolarization ratios for the molten salt. They did not tabulate frequencie; for the molten salt.
dissociation; band parameters are also sensitive to temperature, concentration, and the cation. In earlier work the spectrum of a 50 mol % solution of NH4HS04at 93 “ C was recorded to reveal the important features, because for this system bands of S042are strongly suppressed, and the NH4+cation is similar in many respects to water.I8 The spectrum of HS04- in aqueous 3.8 m NH4HS04solution at 300 O C is presented in Figure 1. All bands of S042-are suppressed and thus bands of the HSO, are clearly revealed. This spectrum consists of six lines and, in the absence of corresponding infrared data, these can be correlated with the C,,model (Table 111). There are several noteworthy features. The two lowest frequency bands have very symmetrical line shapes and there is no indication of the lifting of degeneracy (as has been observed in both infrared and Raman spectra of solutions at 25 OC,@ and of solids41) which would have indicated a symmetry as low as the C, point group. The assignment of the 585-cm-’ line to v3(al)is consistent with the observed depolarization ratio, which is lower than that of the 422-cm-l band, and is also consistent with the observations of Clark and Woodward42based on comparison with the spectrum of (CH,Hg)SO;, and of Dhamelincourt et aL41 who studied solid and molten NH4HS04. The S-(OH) band shifts 50 to 70 cm-’ lower in frequency as the temperature is raised from 25 to 300 “ C (Figures 2 and 3). At temperatures less than 150 OC the band shifts downward by a few wavenumbers as the concentration is increased, but above 150 OC this concentration dependence is reversed-1 2 cm-’ upward for 0.65 to 7.2 m at 300 OC. This band occurs in the range 823-844 cm-l for the molten salt, KHS04;43,44 it shifts to lower values (823 cm-I) on heating in the presence of S2072-.44A similar shift to lower wavenumbers on heating has also been observed for the N-(OH) band of nitric acid45and, on decreasing water content, for the C1-(OH) band of perchloric acid.)’ In crystals the %(OH) bond length is greater than the S-0 length and is sensitive to the cation and structure.46 It appears that HS04-binds more strongly to water, through the S-0-H--OH2 hydrogen bond, than it does to other HS04- or cation units. These hydrogen bonds lengthen
0
100
200
Tomporaturo
300
/‘c
Figure 2. The dependence of the position (in cm-I) of the S-(OH) stretching vibration on temperature and composition.
700
800
900
1000
1100
1200
1300
RAMAN S H I F T / CM-’ (40) Chen, H. MSc. Thesis, University of Waterloo, Ontario, Canada, 1968. (41) Dhamelincourt, P.; Palvit, G.; Noel, S . Bull. SOC.Chim. Fr. 1971, 8, 2849. (42) Clarke, J. H. R.; Woodward, L. A. Trans. Faraday SOC.1968, 64, 1041. (43) Walrafen, G. E.; Irish, D. E.; Young, T. F. J . Chem. Phys. 1962, 37, 662. (44) Fehrmann, R.; Hansen, N. H.; Bjerrum, N. J. Inorg. Chem. 1983,22, 4009. (45) Ratcliffe, C. I.; Irish, D. E. Can. J . Chem., in press. (46) Pringle, G. E.; Broadbent, T. A. Acta Crystallogr. 1965, 19, 426.
Figure 3. Raman spectra of the sample 4.10 m N H 4 H S 0 4 , 0.388 m NaC10, at the temperatures indicated.
the 0 - H bond and shorten the S-(OH) bond causing the S-(OH) force constant to increase and the band is thus observed at the higher frequencies. As the temperature rises the hydrogen bonding is weakened (both between water molecules35and between water and HS04-) and the 0-H bond shortens, the S-(OH) bond lengthens and the band position of the S-(OH) vibration decreases. This decrease can also be realized by replacing the water in the
Dawson et al.
338 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 surrounding medium by similar anions or by cations, e.g. K'. Even in the molten salt the OH group of the HS04- is interacting strongly with other HS04- or K+ ions, and the strength of this interaction is diminished by raising the temperature. However for the aqueous solutions the upward shift with increase of the NH4HS04molality at 300 "C suggests that the proximity of the ammonium cation can cause shortening and strengthening of the S-(OH) bond, both in solution and in the crystal.41 The intense band at ca. 1050 cm-I (SO3 stretching mode) is clearly asymmetrical and can be resolved into two components. The components shift downward by a few wavenumbers on increasing the molality and shift upward on increasing the temperature. Thus as the S-(OH) bond lengthens, the S-0 bonds shorten and become stronger. The lower frequency band component is in the range of 2.0 to 1.5 times as broad (fwhm) as the high-frequency component. The fwhm of both bands increase with increasing concentration and decrease with increasing temperature. In acidic media at 25 "C the increase in the fwhm of the uI(al) band of has been shown to be directly proportional to the hydronium c o n ~ e n t r a t i o n . 'This ~ ~ ~dependence ~ was linked to the change in the fwhm of the 1050-cm-' band and explained in terms of the proton transfer occurring in these s y ~ t e m s . ' ~ At * ' ~elevated ~~~ temperatures other processes contribute to the fwhm, making this a complex property. It is difficult to obtain unique band fits48 and in the subsequent population analysis the total band intensity under the contour was used as a measure of the HS04- population and was found to be directly proportional to the HS04- concentration. This is justification for assigning both components to the HS04- species, as done in earlier ~ o r k . ' ~The . ~suggestion ~ of Turner25that the two bands reveal two kinds of differently aquated HS04- in equilibrium is refuted because one of the pair would be expected to disappear at higher temperatures where the water-to-molecule ion hydrogen bond would be broken. Dhamelincourt et aL4]suggested that the 1044-cm-I band arises from the 6,(SOH) angle bending mode, coupled to the u,(S03) stretching mode at 1022 cm-l. 1044 cm-l is low for such a mode and leaves the infrared-active 1340-cm-' band (shifted on deuteration to 983 cm-l 40 ) unaccounted for. The assignment of this doublet is not obvious, using the C3, model. Although an overtone or combination cannot be excluded, the slight nonequivalence of the three S-0 bonds (giving C, symmetry) could yield two different, but closely coupled, symmetric S-0 vibration^.^^ A splitting arising from proton transfer may also be a possibility. This point requires further theoretical consideration. The 1 195-cm-I band is virtually all anisotropic scattering (Figure l), indicating e (or a") symmetry. In summary the observed number of balids at 300 OC is less than the number predicted for a six-atom species with C, symmetry. Both our depolarization measurements and those reported by Fehrmann et al.44do suggest that both of the lower bands are polarized, despite their failure to exhibit shoulders or other evidence of splitting. Thus the number of polarized bands is greater than the number predicted for a five-atom species with C3,symmetry; the doublet structure of the 1043-cm-I band also suggests a lower symmetry. Thus the symmetry perturbation produced by the hydrogen atom must be small in the molten and solution states. Possibly the rapid torsional motions of the O H group at temperatures where the hydrogen bond strength is greatly diminished randomize the position of the hydrogen atom to give an effective C,,symmetry to the molecule and the degeneracies are not lifted. Further work on these band shapes is required. Raman spectra of a sample of 4.10 m NH,HS04, containing 0.388 m NaC10, to provide the internal standard, obtained at three temperatures, 50, 150, and 300 OC, are presented in Figure 3. The asymmetric 935-cm-I band of C104- is clear and requires no discussion. The intensity of the band at 98 1 cm-I, from S042-, decreases as the temperature rises and the intensity of bands at 1040-1050 cm-I, due to HS04-, increases with temperature, (47) Ikawa, S . ; Yamada, M.; Kimura, M. J . Raman Spectrosc. 1977, 6, 89.
(48) Perram, J . W . J . Phys. Chem. 1968, 49, 4245.
R A M A N SHIFT ( C M - ' )
Figure 4. Computer band resolution of Raman spectra of NH,HSO4 solutions: (A) 2.01 M NH4HS04,0.363 M NaCIO,, 100 OC; (B) 7.23 m NH,HSO,, 0.409 M NaCIO,, 100 OC; (C) 4.10 m NH4HS04,0.388 m NaCIO,, 100 "C; (D) 4.10 M NH4HS04,0.388 m NaCIO,, 300 O C .
consistent with the shift of the point of equilibrium to favor the HSO,. The 830-cm-' band is seen to be shifted from a markedly higher value at 25 OC. In addition to its intrinsic interest, described above, this shift makes measurement of the intensity of the standard more accurate at higher temperatures. At the highest temperature, where S042-has a very low concentration, the 1195-cm-' band of HS04- is clear; at the lowest temperature the band of SO4*-at 1104 cm-I overlaps the 1195-cm-' band. The results of BNDFT analysis for three compositions at 100 OC and one composition at 100 and 300 OC are shown in Figure 4. Up to eight component Lorentzian-Gaussian bands are requird to fit the spectrum: two for the ul(al) C104- band, two for the .,(al) and V3(f2)SOd2- bands, and four bands of HS04-. Successful deconvolution was achieved for temperatures greater than 100 OC and less concentrated than 6 m. Outside of this range the overlap between the 935-cm-' band and the ca. 895-cm-I band was too severe. The essential intensity ratios could, however, be obtained by using N H 4 H S 0 4solutions without NaC104 present. Representative line positions and fwhm values are presented in Table 111. Populations, Equilibria, and Thermodynamics. The overall dissociation equilibrium is defined as HSO,-
F?
Haq++ S042-
for which the degree of dissociation, a , is a = mso42-/~Nnbnso4
(1)
and the thermodynamic dissociation constant K2 is given by K2 = =
QmQy
a2m -Q3
1-a
(2)
(3)
where Q, is the concentration quotient (concentrations in mol kg-') and Q, is the activity coefficient quotient. The molalities of free sulfate ion in eq 1 were calculated from the relative integrated intensities of the 980-cm-I band in the different solutions through the relationship %Ob'-
=
z980/JS0,2-
(4)
The concentrations of HS04- were obtained by subtracting the molality of SO4*-from the total analytical molality of salt ~ H S O = ~ -~ N H ~ H S-Omsob2~
(5)
Plots of the relative integrated intensity of the 1040-1050-cm-' bands of HS04- against mHsO4- were linear for each temperature and thus JHSOb-values were obtained from the slopes; these are presented in Table 11. These values are essentially temperature independent:
(dJ/dT), = -5.3(10-5) f 9.2(10-5); regression coefficient of -0.313
Vibrational Spectral Studies of Solutions
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 339
TABLE I V Values of the Degree of Dissociation, a, of NH4HS04
compn, mol ka-' 0.655 1.32' 2.01 3.09 4.10 5.05 5.23" 5.88 7.23 8.61
289" K 323O K 373 K 423 K 473 K 523 K 573 K 0.456 0.445
0.339 0.299
0.400 0.377
0.285 0.284
0.400
0.280
0.360 0.351
0.292 0.275
0.128 0.149 0.122 0.120 0.134 0.129 0.158 0.130 0.142
0.049 0.071 0.056 0.064 0.057 0.064 0.064 0.065 0.061
0.021 0.038 0.029 0.030 0.032 0.035 0.048 0.031 0.053 0.053
I( 0.4
0.0
0.012 0.022 0.023 0.009 0.013 0.026
0.019 0.004 0.011 0.015 0.015 0.014 0.028 0.021
0.014 0.023 0.025
-
I
I
I
I
F
D L
g"
"No internal standard used; see text. 0.6
1
t
a
I
I
I
11.C
I
100
0
0 25
0 50 100
250
X
8
300
Figure 6. The degree of dissociation vs. the temperature for 4.10 M NH4HS0,.
a 150
0.5
200
Temperature /*C
0.2 -4
-
m 0
O00
1
2
3
4
.
5
Concentration / mol
6
7
8
'
m 0
~
-6
-
kg-'
Figure 5. The degree of dissociation vs. the concentration at the indicated
temperatures. The average J values for the 980-cm-' lines of S042-(0.637 f 0.015) and the 1040-1050-~m-~ lines of HS04- (0.655 f 0.013) are, within the standard deviations, equal to each other. This is further justification that the two bands at ca. 1040 and 1050 cm-' are correctly assigned to HS04-. For NH4HS04samples at 25 and 50 OC, for which the S-(OH) vibration occurs in the region 895 to 898 cm-I, the band areas overlapped severely and were difficult to obtain by computer resolution when Clod- (935 cm-l) was present. However, the degree of dissociation can be obtained from the ratio of intensities of the 980- and 1040-1050-~m-~ pair of bands, R, once the ratio of J values is known. Thus
~so~~-/~H = s(Iso,z-/ZHSO,-) o,(JHso~-/Jso,~-) = RJ (6) Taking Ji from Table I1 (extrapolating as necessary), values of a were calculated from a = RJ/(1
C
+ RJ)
(7)
obtained by introducing eq 6 and 5 into eq 1. Values of a for the complete temperature and composition range are presented in Table IV. For six temperatures the values of a are shown plotted against concentration in Figure 5. There is clearly considerable scatter but some facts are apparent. A rapid decline in a occurs between 25 and 150 OC; above this temperature range the change in CY with increasing temperature is small (Figure 6). Above 0.5 m values of a become almost composition independent for temperatures greater than 100 "C and even for 5 0 O C for compositions greater than 1 m (Table IV). For temperatures greater than 200 OC the data suggest that a increases with increasing composition, but this inference may not be valid considering the low values and the experimental error. The values of a at 25 and 50 O C from this analysis are closer to those given by Young et aLZ0than those of Irish and Chen.'* The latter attributed less intensity to the sulfate and bisulfate bands because a small intensity was attributed to the H,0+.S042-ion pair. The presence of such a species is not negated here, but over
-
-8
-10
0.01
A
a001
150.C
200.C
I
1
0
2
1
1
1
4 6 8 Concantrotion mol kg'
6
10
Figure 7. In Q, vs. concentration for the temperatures indicated. The -yH2SOI is included for comparison.
curve for In
the wide temperature range of this study the inclusion of a band from such a species was not necessary to achieve computer fits within experimental error. We have thus chosen to describe the chemistry in terms of the simple dissociation reaction defined previously. The activity coefficient quotient is unknown for the compositions and temperatures of interest and extended Debye-Hiickel equations cannot be assumed at such high concentrations. Thus our data cannot rigorously lead to estimates of K 2 . However, if we assume values of K2 from the literature it is of interest to examine the trend of Q, with composition and temperature. The fitted values of K2 of Lietzke et a1.I' (their eq 10 and Table I) have been assumed for this purpose. Mroczek' has recently measured K , by the emf method and has critically compared the existing data. Between 100 and 150 O C his values are somewhat smaller than those of Lietzke et al. H e recommends the data of Lietzke et al. above 150 OC and we have used them across the range for consistency. Values of Q, were then calculated by dividing K, by the measured Q, values. Values of -In K,, -In Q,, and -In Q, are presented in Table V. In Figure 7 -In Q, is plotted against concentration for three temperatures. The stoichiometric In activity coefficients of HZSO4 are shown on the same figure for reference.49 Again care must be taken not to overinterpret the results, in view of uncertainty in the data. A few facts can be inferred. Q, is small (less than 0.05 over most of the range). Values decrease with increasing concentration. The lowness of the values confirms the large departure from ideal solution behavior. Powellsohas critically assessed the procedures (49) Staples, B. R. J . Phys. Chem. Rex Data 1981, IO, 119
340
Dawson et al.
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986
TABLE V: Values of the Concentration Quotient, Q , and the Activity Coefficient Quotient, Q ,
-In -In
Qm,
Q, 200 "C 473 K
250 "C 523 K
6.41 2.17
8.15 2.23
9.28 2.94
3.36 3.52
4.94 3.65
6.24 4.14
7.31 4.91
3.38 3.50
5.02 3.57
6.37 4.01
6.83 5.39
25 O C 298 K
50 O C 323 K
100 O C 373 K
150 O C 423 K
0.655
1.39 3.19
2.17 3.13
4.39 2.49
1.32
0.75 3.82
1.78 3.52
compn, mol kg-'
2.01
300 O C 573 K
7.60 6.52
3.09
0.21 4.37
1.05 4.25
2.98 3.90
4.29 4.29
5.88 4.50
8.31 3.91
9.86 4.26
4.10
0.07 4.5 1
0.77 4.53
2.47 4.41
4.27 4.3 1
5.42 4.96
7.28 4.94
7.58 6.54
2.33 4.55
3.80 4.79
5.06 5.32
5.69 6.53
6.78 7.34
5.05 5.23
-0.33 4.91
0.57 4.73
5.88 7.23
-0.38 4.96
0.14 5.16
8.61
-0.49 5.07
0.1 1 5.19
4.575"
4.38 6.00
1.86 5.02
5.298"
6.72 7.40
2.18 4.70
3.67 4.91
5.17 5.20
6.81 5.41
6.78 7.34
1.77 5.1 1
3.43 5.15
3.83 6.55
5.52 6.70
5.18 8.94
3.37 5.21
3.68 6.70
5.20 7.02
5.53 8.59
10.375"
12.221"
8.584"
6.878'
14.11Sa
"-In K , values from the smoothed equation of ref 10. bCalculated from In K2 (ref 10) - In Qm TABLE VI: Coefficients and Their Sum for Eq 9 and 10 concn. mol kg-l temp, range coeff 0.655, 6 data
25-250
a b c
rrms 1.32, 6 data
25-250
a b c
rrms 3.09, 5 data
25-200
a b c
rrms
4.10, 6 data
25-250
a b c
rrms
ref IO, 9 data
25-225
In
Q,
In
Q,
+ 17.4616 -(2.3710 f 0.801)10-2 -(4.1044 f 1.24)103 0.239
-5.6098 -(1.2743 f 0.237)10-2 +(2.5799 f 0.367)IO' 0.0705
+17.5824 -(2.9053 f O.225)1Ow2 -(3.7974 f 0.349)lO' 0.0671
+11.9726 -4.1 796( -1.21 75( IO')
+O. IO69 -(2.0236 f 0.776)10-2 +(1.7141 f 1.09)lO' 0.139
+12.3231 -(2.2161 f 0.755)10-2 -(3.0154 h 1.06)103 0.135
+12.4300 -4.2397( 10-2) -1 .3013(10')
+7.8005 -(2.9834 f 0.628)10-2 +(0.3185 f 0.973)103 0.187
+4.5291 -(1.2386 f 0.642)10-* -(1.6071 f 0.994)103 0.191
+12.3296 -4.22 20( 10-2) -1.2886( IO') +9.9513 -(3.9242 f 0.495)10-, -(0.8267 f 0.740)103 0.139
a b c
rrms
for the simultaneous evaluation of AHo and K20from enthalpimetric titrations. His results indicate the strong dependence of both AHo and K O on the equation used for the activity coefficient expression. Our results reinforce this point. In particular, assumptions concering the value of Y ~ must~ be carefully ~ ~ con~idered.~' From knowledge of the dependence of K2 on temperature it is possible to evaluate the standard enthalpy change for the process, AH', from the van't Hoff equation
(!s)p=s
(8)
Raman spectroscopy provides only Q, and thus there is no rigorous (50) Powell, H. K. J. J . Chem. Soc., Dolton 1973, 1947. (51) Riddell, J. D.; Lockwood, D. J.; Irish, D. E. Can. J . Chem. 1972, 50,
2951.
sum (= In K ) +12.1202 -4.1960( -l.2484( IO')
-5.3414 -(1.8250 f 0.806)10'2 +(2.8559 f 1.25)IO' 0.240
way to evaluate the standard enthalpy change. However, it was were reasonably previously noted that plots of In Q, against T 1 linear52and thus similar plots were made for this system; near linearity was also observed. Figure 8 reveals that In Q, decreases with increasing temperature with a slope similar to In K2 vs. temperature. In contrast the In Q, change very little with temperature. This suggests that the temperature dependence of Q., makes only a small contribution to AHo. To explore this further, for each of four compositions the Robinson equations3was fitted to the Q, and Q, values
+ blT + c l T ' In Q, = u2 + b2T + c 2 T '
In Q, = ul
(9) (10)
( 5 2 ) Irish, D. E.; Jarv, T. Appl. Spectrosc. 1983, 37, 50. (53) Blandamer, M . J.; Burgess, J.; Robertson, R. E.; Scott, J. M . W. Chem. Rev. 1982, 82, 259.
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 341
Vibrational Spectral Studies of Solutions
TABLE VII: Contributionsto AHo from the Dependence on Temperature of In Q , and In Q ,
compn, mol kg-' 0.655
1.32
298 K 25 "C -37.2 16.6 -20.6 -30.9 10.1
3.09
4.10
ref 10" ref lob
-20.8 -29.2 8.7 -20.5 -24.7 4.2 -20.5 -22.1 -20.5
AH,/kJ mol-l from In Q, AH,/kJ mol-l from In Q, AHo/kJ mol-' from the sum 323 K 373 K 423 K 473 K 50 OC 100 OC 150 OC 200 O C -39.6 -44.9 -50.9 -57.7 16.5 6.7 -1.2 -10.0 -26.1 -38.2 -52.1 -67.7 -32.5 -36.2 -40.4 -45.2 6.3 -2.1 -11.7 -22.5 -26.2 -38.3 -52.1 -67.7 -31.8 -37.7 -44.4 -51.9 5.8 -0.6 -7.9 -16.2 -26.0 -38.3 -52.3 -68.1 -28.6 -37.2 -47.0 -58.2 2.6 -1.0 -5.1 -9.7 -26.0 -38.2 -52.1 -67.9 -27.2 -38.6 -51.5 -66.2 -26.0 -38.2 -52.2 -67.9
523 K 250 O C -65.3 -19.8 -85.1 -50.4 -34.5 -84.9
-70.5 -14.8 -85.3 -82.4
'These values of AHo have been calculated from the coefficients given in Table VI, obtained by fitting the Robinson equation to the data of ref 10. bThese values of AHo are quoted in ref 10.
I
I
I
1
200
100
Temperature / "C Figure 8. In Q,, In Q,.,,and , In K2 vs. temperature. The points are experimental data; the lines have been drawn from eq 9 to 1 1 .
by application of the program package LINWOOD54 by linear least-squares; the program provides both statistics and plots to indicate whether residuals are normally distributed and how they are distributed over the fitted values of the dependent variable. The solid lines in Figure 8 have been drawn in accordance with the resulting equations; the coefficients are given in Table VI. The experimental values of In K2 obtained from measurement of the solubility of Ag2S04by Lietzke et al.1° were fitted by the same program: In K2 = a
+ bT + c T 1
(11) The coefficients a, b, and c differ from those reported by Lietzke et a1.I0 but are preferred here for consistency. Because In K2 = In Q, In Q., (12)
+
it follows that a l + a2 should equal a, b, + bZshould equal b, and cI c2 should equal c. Because of scatter in the data the correspondence is not perfect but the relations do apply within the uncertainties in the coefficients (Table VI). The contribution to W from each of Q, (eq 9) and Qr (eq 10) can now be evaluated from the relations
+
AH,,, = R(b1
- c,)
(13a)
and
AH., = R(b2P - ~
2 )
(13b)
respectively. AHo is given by the sum
+ AH,,
The resulting values are collected in Table VII. One can see that the consistency of the calculation is as good as can be expected, given the small data base and the experimental error. Several conclusions can tentatively be drawn for this reaction: (1) In Q, is a slowly varying function of temperature; (2) below about 100 O C the contribution of Q, to AHo is endothermic whereas at higher temperatures it is exothermic; (3) the contribution varies with temperature and is zero at a temperature near 100 O C ; (4) the "apparent AH" values obtained by fitting In Q, to temperature are within at least 30% of the correct thermodynamic values, the closeness being obviously sensitive to the temperature selected. Very recently Kruus et al.55reported a mean AHcvalue (concentrations were expressed as mol L-I solution) of -37 f5 kJ mol', obtained from Raman intensities of NH4HS04 solutions measured for the temperatures 25, 55, and 85 OC. As far as we know this is the first report of the temperature dependence of Q., for a reaction. Raman spectroscopy is particularly well suited for measuring Q,, although, as with any technique, it has its limitations: base line error; band overlap; uniqueness of a signal to a particular species; appropriateness of the molar intensity obtained from a completely dissociated salt for estimation of the species concentration in acid media; the inertness of the internal standard; the limited sensitivity. Despite these limitations it appears that Raman spectroscopy can make some unique contributions which will lead to a deeper understanding of thermodynamic nonideality and complement the information obtained by other techniques. Future work will be directed at collecting data for optimum concentrations with improved precision for many more temperatures.
Acknowledgment. This research was supported by grants from the Natural Sciences and Engineering Research Council of Canada. D. E. Irish expresses his thanks to Dr. T. M. Seward and members of the Geochemistry Division, D.S.I.R., Petone, New Zealand for their contributions and hospitality during sabbatical leave when this manuscript was finalized.
(14)
Registry No. NH4HS04, 7803-63-6; H2SO4, 7664-93-9; HS04-, 14996-02-2.
(54) Wood, F. S. University of California, Berkeley, CA. Daniel, C.; Wood,F. S. "Fitting Equations to Data, Computer Analysis of Multifactor Data for Scientists and Engineers": Wiley: New York, 1971.
(55) Kruus, P.; Hayes, A. C.;Adams, W. A. J. Solution Chem. 1985, 14, 117.
AHo = AH,
