J . Phys. Chem. 1985,89, 1064-1066
1064
The relative densities Ap = p - po for these solutions have also been measured. Although the values of A p / m for these systems shown in Figure 6 have some curvature over these concentration regions, they do not show any sharp density transitions. Concentration transitions in the properties of aqueous electrolyte solutions have been discussed by a number of workers."' The earlier volume work has been summarized by V a s l ~ w .More ~ recently Phutela and Pitzer'O have discussed a transition in CaCl, solution near 5 m using osmotic coefficient and apparent molal enthalpy data. Our value of 5.9 f 0.5 m determined from sound speed measurements is in reasonable agreement with this value. Phutela and Pitzer'O suggest that this transition could be related to 2Ca(H20)72++ 4C1-
-
Ca$14(H20)8
+ 6H20
(1)
Mahluddin and Ismall' I have also reported viscosity transitions in concentrated solutions of Ca(N0J2, MgC12, and NiC12. Their reported transition of 3.5 m for these systems is in good agreement with the value of 3.8 f 0.6 m found for MgC12. and earlier studiesg at least support our results and indicate that they are not related to some artifact of the experimental measurements, such as some sound adsorption effect (our system is run at 2.8 MHz). We have no complete answer for the cause of these transitions. They could be related to the hydration (9) Vaslow, F. J . Phys. Chem. 1969, 73, 3745. In "Water and Aqueous Solutions", Horne, R. A., Ed.; Wiley: New York, 1972. (10) Phutela, R. C.; Pitzer, K. S.J. Solution Chem. 1983, 12, 201. (11) Mahluddin, S.; Ismall, K. J . Phys. Chem. 1983, 87, 5241.
structure around the Mg2+and Cl- ions or related to the formation of various ion clusters as suggested by Phutela and Pitzer.Io Since the sound speeds increase for LiCl, MgCl,, and CaCl,, decrease for SrCl, solutions, and go through a near linear transformation for BaCl, solutions, each system may have difference causes. An increase in the sound speed would result in decreases in the adiabatic compressibilities, os, and apparent molal compressibilities, 4K,S.One would infer from a decrease in 4K,S that hydrated water molecules are increased at the transition. This follows from the simple hydration m ~ d e l ' ~that . ' ~ relates changes in the partial molar compressibility to changes in hydration numbers ( A h ) -&KO
Ah = os vs where @S and V , are the compressibility and molar volume for bulk water (&V, = 8.1 X lo4 cm3 mol-' bar-' at 25 "C). This is not what one would expect for reaction 1 which would release water molecules. Further studies of other properties of these solutions are needed to elucidate these transitions. Acknowledgment. The authors acknowledge the support of the Oceanographic (WE-8120659) and Earth Science (EAR-840759) sections of the National Science foundation and the Office of Naval Research (N0001480-G0042) for this study. (12) Millero, F. J.; Ward, G. K.; Lepple, F. K.; Hoff, E.V. J . Phys. Chem. 1974, 78, 1636. (13) Millero, F. J.; Masterton, W. L. J . Phys. Chem. 1974, 78, 1287.
Effects of Proton Exchange on Dlffuslon in Aqueous Solutions of Methanol Allan J. Easteal,* A. Vernon J. Edge, and Lawrence A. Woolf Atomic and Molecular Physics Laboratories, Research School of Physical Sciences, The Australian National University, Canberra, A.C.T. 2601, Australia (Received: October 30, 1984)
Values are reported for tracer diffusion coefficientsof H2I80and 14CH30Hand the average diffusion coefficient (4)obtained by using HTO as tracer in water, methanol, and three water + methanol mixtures at 278 K. Tracer diffusion coefficients of H2l6Oand '?H3OH in methanol at 298 and 323 K are also presented. The assumption that tritium (from HTO) is statistically distributed between H 2 0 and CH30H, previously used to indirectly determine Dm from measurements of DT and DMCH,OH, has been tested. The diffusion data are consistent with either a statistical or near-statistical (*lo%) distribution of tritium. 0H increases with temperature but is significantly smaller than unity even at 323 K, in The ratio ~ 2 ~ s 0 / D ~ 4 C Hin3 0methanol conflict with approximate literature values.
Introduction In solutions comprising water and a lower monohydric alcohol R O H (e.g., methanol, ethanol) rapid proton exchange occurs between the two components. Only the hydroxyl proton of the alcohol can participate in the exchange although both protons are available from the water molecule. The conventional method of measuring the tracer diffusion coefficient of water, namely, use of tritiated water in a diaphragm,cell experiment, gives in these circumstances not simply the tracer diffusion of water but a weighted mean diffusion coefficient DT which is determined by the distribution of the label T between the H 2 0 and the ROH. The Fick's first law expressions for the fluxes of tritiated species are for concentrations ci mol dmm3 J, = -Di(aci/t3x)
(i = T, HTO, ROT)
(1)
because CT
(ac~/ax) =
= CHTO
+ CROT
+
(~CROT/~X)(~CHTO/~X)
(2) (3)
0022-3654/85/2089-1064$01.50/0
= JHTO + JROT Combination of eq 1-4 gives JT
(4)
Because each H 2 0 has two protons available for exchange and ROH only one, tritium exchange occurring on a statistical basis will produce two HTO molecules for each H 2 0 molecule undergoing exchange and one ROT molecule for each ROH, consequently CHTO = ( ~ c w / ( ~ c+ wCA))CT (6) CROT = ( C A / ( ~ C W + C A ) ) C T where the subscripts W and A denote the water and alcohol, respectively.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 1065
Letters For 1 mol of a binary solution the mole fractions of each component Xi ( i = 1, 2) are related to the ci by ci = looop~i/cxiMi i
(7)
with p the density in g cm-3 and M ithe molar mass in g mol-'. Equations 6 and 7 provide CHTO CROT
= (Xw/(Ur,
+ XA))CT
= (XA/(=W + XA))CT
(8)
Because the parenthesized terms in eq 8 are constant substitution in eq 5 gives DT = (1/(2Xw
+ X A ) ) ( ~ W D H T+OXADROT)
(9)
An equation related to eq 9 based on Langevin's equation has been given by Friedman and Ben-Naim.l Hertz and Leiter2 have recently used eq 9 to evaluate h in (HzO CH30H) mixtures and assuming DCH,OT DIVH~OH. by measuring 4 and DIVH~OH This assumption was made presumably on the grounds that since the molecular masses of CH30T and 14CH30Hare very nearly equal the isotope effect for diffusion of these forms of methanol should be negligibly small (provided that the isotope effect is purely a mass effect). (Goldammer and Hertz3 used an equation analogous to eq 9 when considering N M R relaxation times for water in aqueous alcohol mixtures.) A severe limitation on the use of eq 9 to evaluate Dmo is that as the C H 3 0 H content of solutions is increased the contribution of the term XwDmo to 4 becomes smaller, and the uncertainty in h inevitably becomes very large in solutions with small water content. Moreover, the limiting value (&)xsl is the tracer diffusion coefficient of CH30T in almost pure CH30H, so that ( D H T o ! ~can ~ ~ be evaluated only by an extrapolation which becomes mcreasingly unreliable in the compasition region where high precision is needed. Hertz and Leiter reported the notable result
TABLE I: Tracer Diffusion Coefficients4in H 2 0 + CH30H Solutions at 278.15 K mol %
DT
CHSOH 100 80 60 30 0
DI~CH~OH DH,Is~
1.668
1.462 1.067 0.823, 0.6587 1.297
1.152
0.8252 0.5665 0.8814
'The units of D are
eXpt1
calcd
1.617 1.096 0.80, 0.631 1.273
1.617 1.094 0.8045 0.6293 1.273
lo9 m2 s-l.
TABLE 11: Tracer Diffusion Coefficients' in Methanol at Various Temperatures
TI 278.15 298.15 323.15
+
'The units of D are
D14CHjOH
DHz"0
1.668 2.369 3.623
1.462 2.190 3.451
m2s-l.
that temperature have also been obtained. These results will be reported in a future paper. As an adjunct to these experiments, we have measured 4 (using HTO as tracer, and the diaphragm cell technique6) in CH30H and three mixtures at 278 K. In addition, DHZl8Oand DI~CH,OH in pure methanol were measured a t 298 and 323 K.
Results and Discussion The experimental data are listed in Tables I and 11. The probable uncertainties in DidCHIOH and DH21sO should be within &OS% and *0.3%, respectively. The value for DT in pure water is from Mills' who estimated the uncertainty as *0.2%. The uncertainty in the other values for DT is *OS-1%. Equation 9 can be written in the form
(at 298 K) (DHTO)X,,=I = (D14CH~OH)X~=1 which implies that diffusive motions of water and methanol, in methanol, are highly correlated despite the substantial size and mass differences between the two molecules. The work reported here shows that the result expressed by the equality above is an artifact of the procedure which was used to determine DHTo and is at best an approximation. It should also be noted that the same result (as that reported by Hertz and Leiter) has been found, in effectively the same manner, by Kida and Uedaira4 for (HzO + C H 3 0 H ) and (HzO + acetic acid) mixtures at 305 K. The objectives of the present work were to test eq 9 using independently measured values of DT, DMCH,OH,and the tracer diffusion coefficient of water and, hence, to establish whether the tritium distribution departs detectably from the statistical distribution. Also, we wished to establish as accurately as possible the tracer diffusion coefficient of water in pure methanol since its value is not reliably known. Experimental Section We have recently reported5 a very precise and accurate method for measuring the tracer diffusion coeficient of water, using H280 as a tracer in diaphragm cells in combination with isotope ratio mass spectrometry to determine 180/160 ratios in C 0 2 which has undergone enzyme-catalyzed l80exchange with solution samples. The method is currently being applied to measurements of DH2m0 in (HzO + C H 3 0 H ) mixtures at 278 K: values of DI~CH,OH at (1) Friedman, H. L.; Ben-Naim, A. J . Chem. Phys. 1968,48, 120. (2) Hertz, H. G.; Leiter, L. Z . Phys. Chem. (Frankfurt um Muin) 1982, 133, 45. (3) Goldammer, E. V.; Hertz, H. G. J . Phys. Chem. 1970, 74, 3734. (4)Kida, J.; Uedaira, H.; J . Mugn. Reson. 1977, 27, 253. (5) Easteal, A. J.; Edge, A. V. J.; Woolf, L. A. J. Phys. Chem. 1984.88, 6060.
where fw f A
= DHTO/DH~~BO
= DCH,0T/D14CH30H
(11) (12)
f w and f A are measures of the T/H isotope effect for water and methanol diffusion, and they have the valuesf, = 0.9815 and f A = 0.9694 in pure H 2 0 and pure CH30H, respectively. The magnitudes offw and fA are of some interest and they are discussed further below. Either or both offw and f A may vary with mixture composition, but lacking evidence to the contrary we assume that the variation in the values of these parameters with composition is negligibly small. Substitution of the measured diffusion coefficients in eq 10 then yields the calculated values of DT listed in Table I. The coincidence of the experimental and calculated values of 4. at the compasition extremes is of course forced. The significant result is that for the intermediate compositions the agreement is to within the uncertainty in the experimental values. It seems, therefore, that eq 10 is valid and hence eq 9 holds, so that the distribution of tritium between HzO and CH30H is apparently not greatly different from the statistical distribution. Nevertheless, if a nonstatistical distribution is allowed for by replacing XAin eq 10 by zXA, incorporating the weighting factor z, then the agreement between experimental and calculated values of DT is almost equally good for values of z between 0.9 and 1.1. Thus the diffusion data cannot distinguish between a tritium distribution (6) Mills, R.; Woolf, L. A. "The Diaphragm Cell";A.N.U. Press: Canberra, 1968. (7) Mills,R. J . Phys. Chem. 1973, 77, 685.
J . Phys. Chem. 1985,89, 1066-1069
1066
which favors HzO ( z < 1) or C H 3 0 H ( z > 1) and the statistical distribution ( z = 1) unless the distribution is far from statistical. For mixtures of C H 3 0 H and D 2 0 there appears to be some doubt concerning the deuterium distribution, since for the reaction 2CH,OH(l) DzO(1) = ZCHjOD(1) H,0(1)
+
+
values for the equilibrium constant (at 298 K) between 0.81 and 1.4 have been reported! If the value K = 1.09 f 0.02 (from vapor pressure measurements8) is taken to be the most reliable, it is probable that the distribution of tritium between HzO and CH30H is slightly in favor of CH30H. However, in view of the uncertainty in the equilibrium distribution of tritium, it seems inadvisable to utilize measurements of DT and eq 9 to determine DHTo in water-rich solutions, and that method is clearly unsatisfactory for alcohol-rich solutions. Measurements of DH2ls0by the method we have described provides a superior determination of the tracer diffusion coefficient of water throughout the composition range. The isotope effect for diffusion of water has been discussed in detail previ~usly.~In the context of the present work, the important point is that, for ordinary water as solvent, Dm0 is about 2% smaller than DH21s0although the masses of these two tracer molecules are very nearly equal. We have suggestedS that the origin of the smaller value of ho relative to 4 2 8 0 is retardation of the diffusive motion of HTO due to a stronger hydrogen bonding interaction between HTO and surrounding solvent molecules than exists between solvent molecules (or between H2180and solvent, since substitution of I8O for l60in H 2 0 should have an insignificant effect on hydrogen bond strength5). However, an alternative explanation would attribute the difference to changes in the coupling of translational and rotational motion consequent on the substitution of T for H. The situation appears to be similar for diffusion of isotopically substituted species in ordinary methanol: DCHIOT is about 3% smaller than D I ~ ~(A ~similar , ~ difference ~ . in diffusion coefficients has been found' for HzO and HTO diffusion in water.) The self-diffusion coefficients of C H 3 0 H (in C H 3 0 H ) and CH30D (in CH30D) show differences reflecting clearly the effect of the different moments of inertia about the principal axis.9 It (8) Kooner, Z. S.;Phutela, R. C.; Fenby, D. V. Aust. J . Chem. 1980,33, 9, and work cited therein.
seems therefore that the differences between DCH,OT and Di%H,OH in methanol are due to a stronger coupling of translational and rotational motion between C H 3 0 T and C H 3 0 H than when the molecules are identical. A significant feature of the results in Table I1 is the magnitude of DH2180 relative to DI~CH,OH in pure CH30H. It is clear that 42.l~ is substantially smaller over the temperature range 278-323 K, in contrast to the results found by Hertz and Leiter2 at 298 K and Kido and Uedaira4 at 305 K. The diameter of the water molecule (considered as a hard sphere) diffusing in pure water is about 20% smaller than for CH30H diffusing in pure methanol and its mass is about 50% less. It seems therefore that the effective size of a water molecule diffusing at very low concentration in methanol is substantially larger at 278 K than the effective size of a methanol molecule. The ratio D I ~ ~ , o decreases ~ / D ~with ~ I ~ ~ increasing temperature, but at 323 K DI~CH,OH is still 5% larger than DH2ls0and even at this temperature it seems that H 2 0does not diffuse in C H 3 0 H as single water molecules but rather as a solvated species. Conclusions The tracer diffusion coefficient of water in binary mixtures with water as one component, in which proton exchange between the components occurs, cannot be reliably determined from measurements using HTO as tracer. In particular, the limiting tracer diffusion coefficient at vanishingly small concentration of water is virtually indeterminate by that method. The tracer diffusion coefficient of water can, however, be accurately determined by using Hzi80as a tracer. The magnitude of the ratio D I ~ ~ H , o ~ / +and ~ Iits B temperature O dependence, for methanol as solvent, indicate that HzO is strongly solvated by CH30H particularly at low (278 K) temperature, and probably even at temperatures considerably in excess of 323 K. Acknowledgment. We are indebted to Mr. Z. Roksandic and the Research School of Biological Sciences, The Australian National University, for the mass spectrometric measurements. Registry No. CHIOH, 67-56-1; H20, 7732-18-5. (9) Easteal, A. J.; Hurle, R. L.; Woolf, L. A. J . Chem. SOC.,Faraday Trans. 1, in press.
Pressure and Temperature Dependence of Tracer Diffusion Coefficients of Methanol, Ethanol, Acetonitrile, and Formamide in Water Allan J. Easteal* and Lawrence A. Woolf Atomic and Molecular Physics Laboratories, Research School of Physical Sciences, The Australian National University, Canberra, A.C.T . 2601, Australia (Received: November 15, 1984)
Tracer diffusion coefficients (0)for methanol, ethanol, acetonitrile,and formamidein water have been determined at temperatures between 278 and 313 K and pressures up to 360 MPa. D for the alcohols has a similar pressure dependence at constant temperature to that for water itself, viz. it initially increases with increasing pressure (at low temperature), but the effect of pressure is considerably more pronounced than for water. For acetonitrile, D decreases monotonically with increasing pressure and at 278 K varies in almost identical fashion as D for formamide at 278 K and pressures above 20 MPa. Formamide shows the additional feature that D decreases very rapidly with pressure in the 0.1-20-MPa region.
Introduction Self-diffusion coefficients of liquids typically decrease with increasing pressure at anstant temperature, so that the ratio D/Do (where Do and D are diffusion coefficients at 0.1 MPa and pressure p , respectively) decreases monotonically with increasing pressure. The pressure dependence of tracer diffusion coefficients has the 0022-3654/85/2089-1066$01.50/0
same form, for those cases (e.g. for solutes in n-hexanel) which have been investigated. The tracer2 and self-diffusion3 coefficients of water are anom(1) Dymond, J. H.; Woolf, L. A. J . Chem. SOC.,Faraday Trans. 1 1982, 78, 991.
0 1985 American Chemical Society
