1.14.70: Solutions: Neutral Solutes: Inter-Solute Distances
At its simplest a solution comprises one liquid component is vast excess, the solvent, and another, the solute, which is dispersed in the solvent. The solvent is more than just a useful medium in which to disperse the solute although one might argue that a key role is to inhibit associations of the solute molecules. In an even cursory examination of the properties of solutions, a key consideration is the distance between solute molecules. An interesting calculation offers insight into the dependence of solute-solute distances on solute concentration [1]. For a simple non-ionic solute ( e.g. urea) in aqueous solution at concentration \(\mathrm{c}_{j} \mathrm{~mol dm}^{-3}\), the average solute-solute distance \(\mathrm{d}\) is given by equation (a) where \(\mathrm{N}_{\mathrm{A}}\) is the Avogadro number.
\[d=\left(N_{A} \, c_{j}\right)^{-1 / 3} \nonumber \]
At \(\mathrm{c} = 10^{-2} \mathrm{~mol dm}^{-3}\), \(\mathrm{d} = 5.5 \mathrm{~nm}\). If the solute is a 1:1 salt where 1 mole of salt yields two moles of solute ions, \(\mathrm{d} = 4.4 \mathrm{~nm}\). With increase in solute concentration, the mean distance between solute molecules decreases.
An interesting feature of aqueous solutions is worthy of comment. If a given water molecule is hydrogen bonded (indicating strong cohesion) to four nearest neighbour water molecules, that water molecule exists in a state of low density-high molar volume. In other words cohesion is linked to low density, a pattern contrary to that encountered in most systems. Nevertheless in reviewing the properties of aqueous solutions and water, one must be wary of overstressing the importance of hydrogen bonding. Indeed liquid water has a modest viscosity which is not the conclusion would draw from some models for liquid water which emphasize the role of water-water hydrogen bonding.
Footnote
[1] R. A. Robinson and R. H. Stokes, Electrolyte Solutions, Butterworths, London 2nd. Edn. Revised, 1965.