Boyle's law, the ‹osmotic pressure of the solution increases›. Similarly, when a solution is cooled until freezing occurs, provided the solute does not crystallize out with the solvent, the concentration of the solute is again increased, and therefore the ‹osmotic pressure› of the solution is also increased. Van 't Hoff recognized the relations existing between the freezing, boiling and vaporization of solutions, on the one hand, and the changes of their osmotic pressures on the other. By developing rigorously the ‹relations between the lowering of the vapor tension, the raising of the boiling-point, the lowering of the freezing-point› of a solvent by a solute ‹and the osmotic pressure of the solution›, he made it possible[21] to use [p018] extensive experimental material,[22] on the elevation of boiling-points and the lowering of freezing-points and of vapor tensions, to determine the osmotic pressures of solutions. The theory of the relation of osmotic pressure to gas pressure is fully confirmed by these measurements, for those cases to which it may properly be applied, namely, to sufficiently dilute solutions and such as have only negligible heats of dilution, ‹i.e.› in which dilution does not involve chemical changes. «Apparent Exceptions.»—Instead of discussing the vast amount of material of this kind, which agrees with van 't Hoff's theory, we may consider, more profitably, typical cases of ‹apparent exceptions›. The most important instance of this kind, the case of solutions of compounds which undergo ‹electrolytic dissociation or ionization›, will be separately discussed in the next chapter, and we shall find that van 't Hoff's great generalization is a vital element in the evidence of this important form of dissociation. Of other apparent exceptions, we may note the fact that some solutes seem to give "abnormally" ‹low› osmotic pressures[23] in certain solutions. For instance, benzoic acid, in benzene solutions, gives only a little more than half as great an osmotic pressure as it does in aqueous solutions of the same concentration and temperature, and as would be calculated on the basis of the Avogadro-van 't Hoff Hypothesis for a compound of the formula C_{6}H_{5}COOH and the molecular weight 122. But a rigorous study[24] of the distribution of benzoic acid between water and benzene, when solutions of the acid in the two solvents are shaken together until equilibrium is established (Chapter VIII), has proved that the distribution is strictly in accord with the assumption that benzoic acid, in aqueous solution, has the molecular weight 122 and the composition C_{6}H_{5}COOH, and that, in benzene solution, it has the molecular weight 244 and the composition (C_{6}H_{5}COOH)_{2}; only a ‹small part› of the acid (C_{6}H_{5}COOH)_{2} is decomposed in benzene solution into the simpler molecules, of the composition C_{6}H_{5}COOH. In other words, the simpler molecules C_{6}H_{5}COOH