The Properties of Dilute Solutions

THE PROPERTIES OF DILUTE SOLUTIONS Vapour Pressures.—When a pure liquid, at a given tempera ture, is put in an evacuated space it gives off vapour until the latter has a definite pressure which is known as the vapour pres sure of the liquid. If a non-volatile substance (i.e., a substance whose vapour pressure is inappreciable) is dissolved in the liquid it is found that the vapour pressure of the latter is thereby lowered. A. Willlner found (1858-6o) that the lowering of the vapour pressure was proportional to the concentration of the dissolved substance. Somewhat later (1886) Francois-Marie Raoult made the fundamental discovery that equal numbers of molecules of different substances, dissolved in the same solvent, produced the same lowering. A little later he found a more gen eral relation, namely, that in dilute solutions the fractional lower ing of the vapour pressure (i.e., the ratio of the observed lowering to the original vapour pressure) was equal to the molar fraction of the dissolved substance. Thus if is the vapour pressure of the pure solvent, p that of the solution and N, the molar fraction of the solute, we have Table I. gives values of these two quantities obtained by Raoult for solutions of aniline, a liquid with a comparatively low vapour pressure, in ether.

Since I being the molar fraction of the solvent), it follows that I I —N„ or p = i.e., the vapour pres sure of the solvent is proportional to its molar fraction. This relation is known as Raoult's law. Its limitations are discussed later.

Elevation of the Boiling Point.

The boiling point of a liquid is the temperature at which its vapour pressure is equal to the pressure of the atmosphere (boiling points are usually stated for the standard pressure of 76cm. of mercury). Since a solution of an involatile solute has a lower vapour pressure than the pure solvent at the same temperature, a greater rise of temperature is required to bring its pressure up to the atmosphere pressure ; so that its boiling point is higher than that of the solvent. Since equal numbers of molecules of different solutes in the same solvent produce the same vapour-pressure lowering, they also cause the same elevation of the boiling point. The magnitude of

the elevation produced by a given number of solute molecules depends, however, on the rate at which the vapour pressure of the solvent increases with the temperature, a quantity which is characteristic of each solvent, and which depends on the heat absorbed in vaporization. Thus every solvent has a character istic molecular elevation of the boiling point, which is usually stated as the elevation produced by one gram-molecule of dis solved substance in 1,000 grams of solvent.

Making use of the laws of energy, J. H. van't Hoff showed in 1887 that the molecular elevation of a solvent, is given by A T = where L, is the heat absorbed in the vaporization of one gram of solvent and T is the absolute temperature at which it boils. The measurements of Raoult, Beckmann, and others showed that, while many solutes gave "normal" molecular ele vations in good agreement with those calculated by van't Hoff, in some cases "abnormal" values are obtained, considerably greater or less than the van't Hoff figures. The study of these "abnormal" cases, as will be discussed later, played a great part in the sub sequent development of the subject. Table II. gives the mole cular elevations of some typical solvents as calculated by the van't Hoff formula, and the average observed elevations produced by "normal" solutes.

Freezing Points of Solutions.

The freezing point of a liquid is the temperature at which the solid form can exist in contact with the liquid. Thus at the freezing point and only at that temperature, can water and ice exist together. If the tempera ture is raised the ice melts to water ; if it is lowered the water freezes. The freezing point of a solution is lower than that of the pure solvent ; thus it is well known that sea water, which contains dissolved salts, freezes at a lower temperature than pure water. As early as 1788, Sir Charles Blagden made measurements of the freezing points of salt solutions and showed that the de pression was roughly proportional to the concentration of the salt.