J. Chem. Soc., Faraday Trans. I, 1982, 78, 1629-1631 The Self-diffusion Coefficient of Sulphuric Acid BY KENNETH R. HARRIS^ Diffusion Research Unit, Research School of Physical Sciences, Australian National University, Canberra, A.C.T. 2600, Australia Received 3rd August, 1981 The self-diffusion coefficient, D, of sulphuric acid has been measured at 15.1 and 25 OC to a maximum pressure of 194 MPa using the n.m.r. steady-gradient spin+cho method. The pressure dependence of D is similar to that of methanol, (aD/i3p)T being negative, and dissimilar to that of water, where (aD/dp)T passes from positive to negative values at low temperatures. The purpose of this note is to report measurements of the pressure dependence of the self-diffusion coefficient, D, of sulphuric acid at temperatures in the region of the freezing point.The molecules of sulphuric acid are believed to be extensively associated by hydrogen bonds and the low diffusion coefficients observed are consistent with this. Of other hydrogen-bonded liquids, only water and methanol have been intensively studied: the pressure dependence of D for sulphuric acid is similar to that of methanol, but differs from that of water. EXPERIMENTAL The diffusion coefficients were measured using the n.m.r. steady-gradient spin-echo method. The apparatus used and the technique followed have been described previously.'* The precision and accuracy of the results are estimated to be k 1.5 and f 3%, respectively. The sulphuric acid sample was confined in a glass, Kovar and 3 16 stainless-steel bellows cell, sealed with a cap made from half a Swagelok union and a ball bearing, also of 316 stainless steel.This cell and the combined gradient coil and r.f. coil probe were contained in the pressure vessel. Temperatures and pressures were measured with an accuracy of k0.03 K and k 0.3 MPa, respectively. The Pt resistance sensors and Heise bourdon tube pressure gauge had been calibrated at the National Measurement Laboratory, CSIRO, Sydney. The sulphuric acid was prepared from concentrated (98 %) aqueous sulphuric acid solution (Ajax Chemicals, Sydney: AnalaR grade). Sulphur trioxide was distilled into a sample of the acid to form a dilute oleum solution which was titrated against more of the concentrated acid until the electrical conductivity was a minimum.This titration was done in a mixing chamber attached to one side of the conductance cell to which the burettes were fitted. The conductance cell had been calibrated at 25 OC with a 0.1 demal aqueous KCl solution prepared from fused, recrystallized KCl and conductivity water. The cell electrodes were platinized and the frequency dependence in the measurement range 0.3-2 kHz was negligible. Conductivities were measured with a Leeds and Northrup Jones-Dike bridge. The temperature of the oil thermostat was controlled within the limits k 3 mK. The cell constant was 35.77 f 0.01 cm-l. The minimum conductivity was found to be (1.0428 & 0.0005) x 1 0-2 S cm-' at 25 O C . Gillespie et aZ.3 have reported a value of (1.0432 k 0.0005) x lop2 S cm-l for this quantity, which corresponds to a water composition of 0.002 mol kg(so1ution)-'.A sample of acid of this conductivity was taken for the diffusion measurements, though it undoubtedly absorbed moisture during the time taken to rinse, fill and seal the n.m.r. cell. From measurements of t Present Address: Chemistry Department, Chelsea College, Manresa Road, London SW3 6LX. 16291630 SE LF-D I FFU S I ON COEFFICIENT 0 F SU L P HU R I C A c I D the rate of absorption of acid samples exposed to the air, the maximum amount of water contamination was estimated to be a mole fraction of 0.0002. The results are listed in table 1 and are shown plotted against pressure in fig. 1. TABLE 1 .--SELF-DIFFUSION COEFFICIENTS OF SULPHURIC ACID 15.10 0.09 23.8 51.0 98.8 149.5 24.6 50.7 100.9 151.1 193.7 25.00 0.09 45.4 41.6 39.3 33.8 29.2 65.7 61.9 59.4 50.3 43.8 41.5 20 1 1 I I 1 100 200 p/MPa FIG.1.-Self-diffusion coefficient of sulphuric acid as a function of pressure. DISCUSSION The properties of liquid sulphuric acid indicate that it is highly associated. Like water, it has a high boiling point (317 "C), dielectric constant (100 at 25 "C), and surface ten~ion.~ The entropy change on freezing (4.54 R)5 is similar to that of many alcohols, and the viscosity (24.54 mPa s at 25 "C)6 is also high. On the basis of X-ray diffraction measurements' of the solid structure, which is monoclinic, it has been suggested that each molecule is linked by hydrogen bonds to four others, there being two 0-0 distances, 0.264 and 0.287 nm. The bonded molecules form layers within the crystal.This is consistent with the high melting point, 10.371 0C.4K. R. HARRIS 1631 It has been observed that some salts, e.g. NH,HSO,, have negative Jones-Dole viscosity B coefficients in sulphuric acid solution.6 Sulphuric acid as a solvent is similar to water, glycol and other polyhydric alcohols in this respect, but dissimilar to methanol and other monohydric alcohols.* If this is interpreted to mean that such ions distort or break up the hydrogen bonding between solvent molecules, thereby increasing the fluidity, then it might be expected that a similar effect could be produced by the application of pressure. Such an increase in the fluidity, and therefore the self-diffusion coefficient, is well documented in the case of water9-13 close to and below the melting temperature (i.e.< 30 "C). On the other hand no such effect is observed in the case of methanol,l49 l5 where the lowest temperature investigated was 29 K above the freezing point,15 but (aD/@), was still clearly negative along this isotherm (ca. - m2 s-l MPa-l). The measurements reported here show no anomaly in the pressure dependence of D for sulphuric acid at the temperatures investigated. Due to freezing of the sample on the application of pressure, it was not possible to approach the freezing temperature more closely than 4.7 K. The freezing pressure at 15.1 "C was ca. 50 MPa and the higher pressure points lie in the supercooled region. The results suggest that the structure of sulphuric acid is quite different from that of water, though both are highly associated liquids. It may be that the liquid retains some of the planar association present in the solid.In this respect it is interesting that it is H30+ and NH,+ ions which have been observed to produce negative viscosity B coefficients. These are of course ions which can hydrogen bond with solvent molecules and so interrupt linkages between them. Further interpretation of these diffusion measurements requires high-pressure density data which are not yet available. K. R. Harris, R. Mills, P. J. Back and D. S. Webster, J. Magn. Reson., 1978, 29, 473. K. R. Harris, Physica (Utrecht), 1978, 93A, 593; 1978, 94A, 448. R. J. Gillespie, J. V. Oubridge and C. Solomons, J. Chem. SOC., 1957, 1804. R. J. Gillespie, Rev. Pure Appl. Chem., 1959, 9, 1. J. E. Kunzler and W. F. Giauque, J. Am. Chem. Soc., 1952, 74, 3472. R. J. Gillespie and S. Wasif, J. Chem. Soc., 1953, 215. J. Padova, Nonaqueous Electrolyte Solutions, in Water and Aqueous Solutions, ed. R. A. Home (Wiley-Interscience, New York, 1972), chap. 4. L. A. Woolf, J . Chem. SOC., Faraday Trans. 1, 1975, 71, 784. ' R. Pascard, C.R. Acad. Sci., 1955, 240, 2162. lo C. A. Angell, E. D. Finch, L. A. Woolf and P. J. Back, J. Chem. Phys., 1976, 65, 3063. l1 T. DeFries and J. Jonas, J. Chem. Phys., 1977, 66, 5393. l 2 K. Krynicki, C. D. Green and D. W. Sawyer, Faraday Discuss. Chem. Soc., 1979, 66, 199. l3 K. R. Harris and L. A. Woolf, J . Chem. SOC., Faraday Trans. I , 1980, 76, 377. l4 J. Jonas and J. A. Akai, J . Chem. Phys., 1977, 66, 4946. R. L. Hurle, Thesis (Australian National University, Canberra, 1981). (PAPER 1/1218)