Chapter: Molecular Weight Of Substances In Solutions

Molecular Weight Of Substances In Solutions, Summary

The freezing point of a solvent, is lowered by a dissolved substance and the depression, D. is proportional to the amount of substance w in 1 kgm. of solvent. The molecular lowering, Δ for the molecular weight M, in 1 kgm. of solvent, is constant for all substances (except electrolytes, and associated substances) in a given solvent, when the solution is dilute. Thus, it follows that w : M = D : Δ, or M = w Δ / D

The boiling point of a solvent is raised by a dissolved substance, and the same laws hold as for the freezing point: M=w E / D where E is the molecular elevation of boiling point and D is the observed elevation.

The vapour pressure of a liquid is lowered by a dissolved substance. If n gm. mol. of the substance are dissolved in N gm. mol. of solvent, and if f₀, f are the vapour pressures of the pure solvent and solution, respectively, then (f₀ - f) / f₀ = n / (N + n).

The above relations enable one to determine the molecular weight of a substance in solution.

The osmotic pressure of a dissolved substance is related to the concentration and temperature of the solution in the same way as the pressure of a gas.

Colloidal solutions show only small differences from the freezing- and boiling-points of the solvent, and small osmotic pressures. The colloidal substance has, therefore, a high molecular weight. Ultra-microscopic particles of colloidal gold (1.86 x 10^-7 cm. diameter) and silicic acid, etc., are shown by X-rays to be crystalline aggregates.

On Arrhenius's theory of electrolytic dissociation, the abnormally high values of the osmotic pressure, depression of freezing point, relative lowering of vapour pressure and elevation of boiling point, are due to the increase in number of the dissolved molecules by ionisation. If D, Δ are the observed and theoretical (for no ionisation) values of these, then α = (D - Δ) / Δ (x - 1), where x is the number of ions formed from one molecule of electrolyte, and α is the degree of ionisation. On this theory, the same value of α should be obtained from the conductivity ratio, Λ / Λ_∞. On the new theory of strong electrolytes, these are practically completely ionised at all concentrations in dilute solutions (< 0.01N), and the variations of osmotic pressure etc., and of Λ, are referred to interionic attraction. The value α then has no meaning and is replaced by osmotic and conductivity coefficients, f₀ and f_c (not to be confused with the vapour pressures). Arrhenius's theory, however, is very nearly true for a weak electrolyte, since then the interionic attractions are weak and the electrolyte is only partly ionised.

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