The partial molar volumes of aqueous metal cations: their prediction and relation to volumes of activation for water exchange

Abstract

. J. Chcm. 61, 473 (1983).Partial molar volumes V" of the Fe", ~i " , Fe3', ~r " , ~h " , and M(NH,),0HZ3' (M = Cr, Co, Rh, Ir) aqueous ions have been obtained by extrapolation from density measurements at 298.15 K on the perchlorate salt solutions containing added HCIO, where ncccssary to suppress hydrolysis or oxidation. The values for thcsc high-spin aqua-ions and others in the literature can be represented satisfactorily for ionic chargcs z = I through 4 by whcre ?:,, is thc absolute partial molar volume in cm3 mol-' of MT'(aq) rclativc to ?:,, = -5.4 cm' mol-' for H'(aq), and r-is the Shannonradius in pm of M" with coordination number n,. Volumcs of activation AV,,:Vor watcr exchange correlate inversely with V" within the series ~" ( a q ) and M ( N H~) ~O H~" (~~) at least, allowing predictions of AV,,:!: to be made from V" or the above equation. The physical origin of these correlations is considcrcd. Our interest in the precision measurement of volume properties of aqueous metal ions stems from the observation (1, 2) that volumes of activation AV,," for the exchange of coordinated water on M2+(aq), M(NH3),OH:+(aq), and possibly M3+(aq) seem to correlate inversely with the apparent molar volumes 4, or partial molal volumes at infinite dilution V0 of the respective aqueous ions within each of these series. If this observation has any general validity, the transition states volumes must be much less sensitive to the nature of M than are either AV,,* or vO, i.e., the transition states must resemble each other relatively closely within a series despite some differences in reaction mechanism which AV,," is thought to reveal (1). Furthermore, the correlations themselves would permit prediction of unknown AV,," values from known V0 data (or vice-versa). Finally, if a physically meaningful model is available for the prediction of VO, we have the prospect of predicting AV,,*, and so arguably the mechanistic predisposition of a metal aqua-ion, from basic principles and quantities.The establishment and subsequent application of such correlation and models. however. require values of V0 that are . * accurate to within 2 dm3 mol-I or better. Good modern data are available for aqueous Mn2+, Co2+, and ~i " (3-7), but for Fe2+(aq) there exist only older V0 values which range from -17.7 to -26.4 cm3 mol-' (8-10) (relative to v0 = 0 for H+(aq)), possibly because of the rapidity of aerial oxidation of Fe2+(aq) in the absence of added acid (1 1). For Fe3+(aq), the V0 value cited in Millero's comprehensive review (10) can be traced back to density data of precision no better than 1 part in 10" which implies uncertainties in the derived molar volume of at least + 2 cm3 mol-I at 0.05 mol L-I; solution densities reproducible to about 2 parts in lo6 are now routinely measurable. In any case, addition of substantial amounts of acid is necessary to suppress hydrolysis and polymerization of iron(111) (pK, -2).[I] Fe3+(aq) + H 2 0 S H+ + Feo~"(aq) S polymers Suppression of hydrolysis is also important for Rh3+(aq), -3), for which n...

Towards Binuclear Polyaminocarboxylate MRI Contrast Agents? Spectroscopic and MD Study of the Peculiar Aqueous Behavior of the LnIII Chelates of OHEC (Ln=Eu, Gd, and Tb): Implications for Relaxivity

“…This approach also enabled us to calculate the partial molar volume of an electrostricted water molecule (V , which corresponds well with the volume of an electrorestricted water molecule in the first coordination sphere of an aqua ion. [39,40] Chem. Eur.…”

“…[39,40] From these volumes we can calculate the reaction volume of isomerization (DV 0 = + +10 AE 5 cm 3 mol…”

Pressure dependences of the electrode potentials of some iron(III/II) and cobalt(III/II) couples in aqueous solution

“…Absolute molar volumes are available, or can be calculated, for all the reactants and products of reactions [4] and [5] (17)(18)(19),~ so that the corresponding volumes of reaction AVO at infinite dilution, 25.0°C, and 0.1 MPa can be derived: AVO = -49.1 cm3 mol-' for reaction [4] and + 12.8 cm3 mol-' for reaction [5]. An approximate correction of these to ionic strength 0.28 rnol kg-' can be made as described elsewhere (19) .0 cm3 mol-', respectively).…”

“…An approximate correction of these to ionic strength 0.28 rnol kg-' can be made as described elsewhere (19) .0 cm3 mol-', respectively). It should be borne in mind that the values of AV measured electrochemically are in effect averages over the pressure range taken, so that, if an assumed linear dependence of E, on P conceals a nonlinearity such as is observed for reaction [4] at I = 1.0 rnol kg-', AV at 0.…”

Reflections on the outer-sphere mechanism of electron transfer

“…Stranks' calculations (6) appeared to give hvcALci for a single-electron mechanism in excellent agreement with the observed value, whereas AVCALCZ for a two-electron step was 12 cm3 mol-' more negative. These numbers, however, incorporate hvDHi with the sign reversed, and an estimated AVO of -9.3 cm3 mol-' for the hypothetical formation of 2~1 " as compared with -2.4 cm3 mol-' from a model now available (42), so that the experimental AV: falls between the theoretical values for the one-and two-electron paths. At least, AV; rules out an inner-sphere mechanism.…”