are ‹polymerized› or ‹associated› to form larger molecules in benzene solution, much as the gas nitrogen dioxide NO_{2} goes over more or less into the gas N_{2}O_{4}, especially at low temperatures, and as hydrogen fluoride at low temperatures has the composition H_{2}F_{2}, while at higher temperatures it is HF. The divergence of the benzene solutions of benzoic acid from the Avogadro-van 't Hoff principle is therefore only an ‹apparent one›, not a real one, inasmuch as the osmotic pressure of the solutions agrees perfectly with that calculated for solutions of a substance (C_{6}H_{5}COOH)_{2}, of molecular weight 244. Such associated molecules (of organic acids, alcohols, phenols, etc.) occur [p019] particularly readily in liquids of small dissociating power, like benzene, and such solutions show marked ‹absorption of heat on dilution›,[25] the dilution being accompanied by a ‹chemical change›. The associated molecules are dissociated more and more completely [(C_{6}H_{5}COOH)_{2} ⇄ 2 C_{6}H_{5}COOH], even in these solvents, as the solutions are diluted. Since dilution results in a ‹chemical increase› in the number of molecules, the osmotic pressure cannot decrease proportionally with the increase of volume in such a case as this. Nor does gas pressure, it must be remembered, decrease proportionally to the volume in the case of gases which show ‹chemical changes› with change of volume, ‹e.g.› in the case of nitrogen tetroxide, for which we have N_{2}O_{4} ⇄ 2 NO_{2}. In still other instances, apparently too high osmotic pressures, or too low molecular weights, have been found by the application of the Avogadro-van 't Hoff Hypothesis to solutions: for instance, the molecular weight of sodium, when dissolved in mercury, was found by Ramsay to vary from 21.6, in dilute, to 15.1 in concentrated solutions. But Cady found that the heat of dilution of sodium in mercury solution is considerable, and by taking this properly into account, Bancroft was able to show that the molecular weight, correctly calculated in a given experiment, is 22.7 (agreeing well with the theoretical weight 23), in place of 16.5, as calculated without making the required allowance for the heat of dilution.[26] These determinations are most instructive in showing that the sources of some of the most important deviations from the van 't Hoff-Avogadro principle, deviations which have been brought forward as arguments against its assumptions, are due, not to any untrustworthiness of the general principle, but to the error of neglecting to observe the limiting conditions of the formulation, or of neglecting to make corresponding corrections for the non-observance thereof.