184
CONDENSATION
It would follow from the law of corresponding states that in this formula the value of / is the same for all substances, the molecules of which do not associate to form larger molecule-complexes. In fact, for a great many substances, we find a value for f, which differs but little from 3, e.g., ether, C02, benzene, benzene derivatives, chloric ethyl, ethane, &c. As the chemical structure of these substances differs greatly, and association, if it takes place, must largely depend upon the structure of the molecule, we conclude from this approximate equality that the fact of this value of f being equal to about 3 is characteristic for normal substances in which, consequently, association is excluded. Substances known to associate, such as organic acids and alcohols, have a sensibly higher value of /. Thus M. Estreicher (Cracow, 1896) calculates that for fluor-benzene/varies between 3'07 and 2'94 ; for ether between 3'0 and 3T ; but for water between 3'2 and 3'33, and for methyl alcohol between 3'65 and 3-84, &c. For isobutyl alcohol/even rises above 4. It is, however, remarkable that for oxygen /has been found almost invariably equal to 2'47 from Olszewski’s observations, a value which is appreciably smaller than 3. This fact makes us again seriously doubt the correctness of the supposition that /= 3 is a characteristic for nonassociation. It is a general rule that the volume of saturated vapour decreases when the temperature is raised, while that of the co-existing liquid increases. We know only Critical one excep^on to this rule, and that is the volume of water below 4° C. If we call the liquid volume vi, and the vapour vv, vv - vi decreases if the temperature rises, and becomes zero at Tc. The limiting value, to which vi and vv converge at Tc, is called the critical volume, and we shall represent it by vc. According to the law of corresponding states the values both of vijvc and vv/vc must be the same for all substances, if T/Tc has been taken equal for them all. According to the investigations of Sydney Young, this holds good with a high degree of approximation for a long series of substances. Important deviations from this rule for the values of vvjvi are only found for those substances in which the existence of association has already been discovered by other methods. Since the lowest value of T, for which investigations on vj and vv may be made, is the value of T8; and since T3/Tc, as has been observed above, is not the same for all substances, we cannot expect the smallest value of vilvc to be the same for all substances, But for low values of T, viz., such as are near T3, the influence of the temperature on the volume is but slight, and therefore we are not far from the truth, if for normal substances we take the minimum value of v/vc as being equal for all normal substances, and put it at about -j. Moreover, the influence of the polymerization (association) on the liquid volume appears to be small, so that we may even attribute the value ^ to substances which are not normal. The value of vvlvc at T = T3 differs widely for different substances. If we take y>3 so low that the law of Boyle-Gay-Lussac may be applied, we can calculate v3/vc by means of the formula provided h be known. According to 4s J-c the observations of Sydney Young this factor has proved to be 3'77 for normal substances. In consequence ^ — 3-77 ^ —. A similar formula, but with another value Vc j»3 i-c of Jc, may be given for associating substances, provided the saturated vapour does not contain any complex molecules. But if it does, as is the case with acetic acid, we must also know the degree of association. It can, however, only be found by measuring the volume itself. Matthias has remarked that the following relation
OF
GASES
exists between the densities of the saturated vapour and of the co-existing liquid RuIe of the and that, accordingly, the curve which represents the densities at different temperatures possesses a rectilinear diameter. According to the law of corresponding states, a would be the same for all substances. Many substances, indeed, actually appear to have a rectilinear diameter, and the value of a appears approximatively to be the same. In a Memoire presente a la societe royale a Liege, 15th June 1899, Matthias gives a list of some twenty substances for which a has a value lying between 0'95 and L05. It had been already observed by Sydney Young that a is not perfectly constant even for normal substances. For associating substances the diameter is not rectilinear. Whether the value of a, near 1, may serve as a characteristic for normal substances is rendered doubtful by the fact that for nitrogen a is found equal to 06813, and for oxygen to O'S. At T = Tc/2, the formula of Matthias, if pv be neglected with respect to pi, gives the value 2 + a for pijpc. The heat required to convert a molecular quantity of liquid coexisting with vapour into saturated vapour at the same temperature is called molecular latent Latent heat. It decreases with the rise of the temperaheat. ture, because at a higher temperature the liquid has already expanded, and because the vapour into which it has to be converted is denser. At the critical temperature it is equal to zero on account of the identity of the liquid and the gaseous states. If we call the molecular weight m and the latent heat per unit of weight r, then, according to the law of corresponding states, mr/T is the same for all normal substances, provided the temperatures are corresponding. According to Trouton the value of mr/T is the same for all substances if we take for T the boiling-point. As the boiling-points under the pressure of one atmosphere are generally not equal fractions of Tc, the two theorems are not identical; but as the values of pc for many substances do not differ so much as to make the ratios of the boiling-points under the pressure of one atmosphere differ greatly from the ratios of Tc, an approximate confirmation of the law of Trouton may be compatible with an approximate confirmation of the consequence of the law of corresponding states. If we take the term boiling-point in a more general sense, and put T in the law of Trouton to represent the boiling-point under an arbitrary equal pressure, we may take the pressure equal to pc for a certain substance. For this substance mr/T would be equal to zero, and the values of mr/T would no longer show a trace of equality. At present direct trustworthy investigations about the value of r for different substances are wanting • hence the question whether as to the quantity mr/T the substances are to be divided into normal and associating ones cannot be answered. Let us divide the latent heat into heat necessary for internal work and heat necessary for external work. Let r represent the former of these two quantities, then :— r = r +p(vv-vi). Then the same remark holds good for mr/T as has been made for mr/T. The ratio between r and that part that is necessary for external work is given in the formula, r _T dp P(vv - vt) p dT By making use of the approximate formula for the vapour tension : — Nap. log. - =/ Pc T ,,-Lc p{v» - vi) J T'
we find
