Transport of Water by Group 1 and 2 Ions with t-Butyl Alcohol as Reference Substance: Comparison with Raffinose and Dioxan

Abstract

Measurement of the transport of water with respect to the second solvent component in a binary aqueous mixture gives the Washburn number, $w_{\text{W}} = (n_{\text{W}} )_{ + } t_{ + } - (n_{\text{W}} )_{ - } t_{ - }$, in a transport number determination, where the ions move in opposite directions, and give the Erdey–Grúz number, $\Upsigma n_{\text{W}} = (n_{\text{W}} )_{ + } + (n_{\text{W}} )_{ - }$, in a diffusion experiment, where the ions move in the same direction. Here n _W and t are the number of water molecules and transport number, respectively, of the anion or cation. Combination of the results of these two experiments allows unambiguous determination of values for the solvent transport numbers, $n_{\text{W}}$, of the individual ions. While the values of $n_{\text{W}}$ depend on the cosolvent, at high dilutions of the second component the highest value of $n_{\text{W}}$ found, $N_{\text{W}}$, should approach the number of water molecules transported by the ion in pure water, $N_{\text{W}}^{0}$. New data for alkali-metal, alkaline-earth metal, hydrogen and halide ions in dilute mixtures of t-butyl alcohol with water are presented. Values of $N_{\text{W}}$ rounded to whole numbers thus found are: 12 (Li⁺), 10 (Na⁺), 6 (K⁺), 5 (Rb⁺), 5 (Cs⁺), 1 (H⁺), 13 (Ca²⁺), 16 (Sr²⁺) and 15 (Ba²⁺). Factors influencing preferential solvation are briefly discussed. Detailed recalculations of $n_{\text{W}}$ in the raffinose–water system from literature data also allows resolution of a problem with the Onsager Relations.

Appendix

1.1 The Raffinose–Water System: Recalculation and Discussion of n _w; the Onsager Relations

In 1959, Miller [17] analyzed the mutual diffusion coefficients, D _ij , for a number of aqueous ternary systems to test the ORR, which require, for the phenomenological coefficients $L_{ij}$ of the solute components, that $L_{23} = L_{32}$. Two systems studied by Dunlop [21] had a raffinose concentration of 0.015 mol·dm⁻³ and KCl concentrations of either 0.1 or 0.5 mol·dm⁻³. Lacking activity data for the raffinose–water system, Miller assumed a value of $\partial \ln y_{3} /\partial c_{2}$ = 0.25 mol⁻¹·dm³; here y and c are the activity coefficient of KCl and concentration of water on the molar scale. $L_{23}$ and $L_{32}$ values were then in good agreement at 0.1 mol·dm⁻³ KCl but not at 0.5 mol·dm⁻³ KCl.

Now [13]:

$$ \Upsigma n_{\text{S}} = L_{23} /L_{33} , $$

(17)

and, as required by the ORR, $= L_{32} /L_{33}$.

If we put:

$$ (\Upsigma n_{\text{W}} )_{23} = ( - y_{1} /y_{2} )L_{23} /L_{33} \,{\text{and}}\,(\Upsigma n_{\text{W}} )_{23} = ( - y_{1} /y_{2} )L_{32} /L_{33} , $$

(18)

the ORR in turn require that (Σn _w)₂₃ = (Σn _w)₃₂.

Miller’s 1959 analysis gave $\Upsigma n_{\text{W}} \approx$ 10 at 0.1 mol·dm⁻³ KCl, and in combination with w_w values this figure gives n _w, for example, of 16 for Li⁺, 10 for Na⁺ and 4 for Cl⁻ [13].

Miller et al. [18] later repeated Dunlop’s measurements on the 0.5 mol·dm⁻³ KCl system. The new D _ij values from both the Goüy and Rayleigh methods were in good agreement with Dunlop’s, and the authors concluded that if the ORR were to be obeyed the value previously assumed for $\partial \ln y_{3} /\partial c_{2}$ was in error. If that is so, the earlier values for D _ij in the 0.1 mol·dm⁻³ KCl system are unreliable and we shall not consider them further.

Estimation of $\partial \ln y_{3} /\partial c_{2}$. Table 10 shows values of the Gibbs energy of transfer on the molal scale, $\Updelta G_{t}^{0} (m)$, for various chlorides from water to glucose– and sucrose–water mixtures. At 5 % the values for KCl are the same within experimental error, whether the transfer is to solutions of the mono- or disaccharide. The corresponding values for 10 % solutions are also close (identical if the values from Wang et al. [22] are preferred). This is also found for solutions of sodium chloride. $\Updelta G_{t}^{0} (m)$ thus appears to depend on the weight-fraction of the sugar, or, more likely, on the weight or closely related volume fraction of water [44]. We now assume that this dependence extends to the trisaccharide raffinose. $\Updelta G_{t}^{0} (m)$ for KCl in the interval 0–5 % raffinose, which includes the concentrations studied by both Miller [17, 18] and Longsworth [10], can then be taken as the mean of the values for the 5 % mono- and disaccharide solutions. This makes $\partial \ln y_{3} /\partial c_{2} =$ 0.03 mol⁻¹·dm³, very different from the value assumed by Miller.

Table 10 Gibbs energies of transfer on the molal scale, from water to carbohydrate–water systems, $\Updelta G_{\text{t}}^{ 0} (m)/$J

Miller et al. [18] list four sets of values for the D _ij based on different experiments or treatments of the data. The values of $\partial \ln y_{3} /\partial c_{2}$ required for the $L_{ij}$ to satisfy the ORR range from 0.04 mol⁻¹·dm³ for the values recalculated from Dunlop’s measurements to −0.05 mol⁻¹·dm³ for the newer measurements. Our estimate of 0.03 mol⁻¹·dm³ from the activity measurements is within this range and close to that found from Dunlop’s data, with which it gives (Σn _w)₂₃ 5.9 and (Σn _w)₃₂ = 5.3.

If the condition that (Σn _w)₂₃ = (Σn _w)₃₂ is imposed, then the values of Σn _w found from the sets of D _ij listed by Miller et al. [18] range from 6.1 to 4.5. We adopt the mean of these, i.e. 5.3, as Σn _w, which is also close to the mean value of 5.6 estimated from the e.m.f. data in Table 10.

We have also recalculated the w _w from Longsworth’s data [10], extrapolating w _w against c rather than c ^1/2 to obtain values at infinite dilution. His values were obtained in 1, 1.5, and 2 % raffinose solutions, but appear not to depend on the raffinose concentration.

The revised values of n _w calculated from these Σn _w and w _w are given in Table 9. We have assigned rough error limits by considering the changes that would occur if (a) extreme values of Σn _w, i.e. 4.5 and 6.1, and (b) Washburn’s results for w _w in 5 % raffinose at 25 °C instead of Longsworth’s, were used. This gives ±2.0 (Li⁺), ±1.3 (Na⁺), ±0.8 (K⁺, NH₄ ⁺, Cl⁻) and ±0.2 (H⁺).

The n _w values for the cations in the raffinose–water system are appreciably lower than those calculated earlier [13]. While the new value for Li⁺ is close to the values found in the TBA–water and dioxan–water systems (Table 9), the values for both Na⁺ and K⁺ are lower, and raffinose is less useful as a reference molecule than might have been expected.

In view of the provenance of these values, only the briefest discussion is justified. There is evidence for weak complex formation between the alkali-metal ions and mono- and oligosaccharides in solution, with stabilities generally in the order Na⁺ > K⁺ > Li⁺ [45]. In crystalline adducts of sucrose (L), for example NaLCl·2H₂O, the 6-coordinated Na⁺ ion binds through O(4),O(6), and O(6′) of the sucrose molecule [46]. The low n _w values of Na⁺ and K⁺ could therefore be consistent with the effect of weak complex formation on the equilibrium distribution, but against this, the movement under a potential gradient of large raffinose-containing solvates would not be favored compared with that of aqueous solvates. We cannot therefore decide whether complex formation explains the low n _w for Na⁺ and K⁺.

Another possible explanation lies in the strong interaction of the hydrophilic groups of carbohydrates with water, which result in marked negative deviations of the binary systems from Raoult’s Law [47, 48]. Thus the carbohydrate molecule may disrupt the ionic solvates, partly through its own strong steric demands and partly by competing with them for water, partially desolvating them. The weaker the ion–water interaction, the larger the desolvation of the aqueous solvate, hence the marked lowering compared with N _w of the n _w for Na⁺ and K⁺ compared with that for the strongly interacting Li⁺; further desolvation by a carbohydrate molecule adjacent to the solvate would be expected on flow.