Properties of water solutions. The effective molality

Abstract

Textbooks and research articles referring to properties of water solutions commonly state that Raoult’s law requires the diminution of vapor pressure of solutions of non-volatile solutes to be proportional to the mole fraction of solutes and that most solutions do not obey the law. This is wrong; twice. First: Raoult expressed concentrations in moles of solute per 100 mol of solvent, not in molar fractions; the two quantities are not related linearly. Second: The decrease in vapor pressure is linearly related to the effective molality of solute particles in adherence with the law as originally stated by Raoult and with the same slope for all solutes. In water solvent, molality is currently defined as moles of solute-derived particles in 55.509 mol (1.000 kg) of solvent. If a solute binds strongly with some water molecules, the bound waters become part of the solute and move as one unit with it, as noted by Einstein in 1906. Bound waters are no longer serving as solvent and are not available for binding with any additional solute. Hence, there are fewer than 55.509 mol of solvent and the effective molality of solutes changes accordingly. The importance of this was pointed out in 1912 by Arrhenius, in 1921 by Scatchard and in 1947 by Robinson. Neither they nor anyone else yet provided measures of these changes. The present work does so. Linearity is maintained up to the point where one half of the total water is bound. Past this, additional solute must remove water equally from free and from bound waters and linearity with the effective molality is no longer possible.