There is thus a gap in the middle of this curve (named by the author "principal curve") for which observations are either wanting or untrustworthy; and here the point of inflection would evidently occur. The general aspect of this curve is that of a slightly wavy line, from various points along which the isopyknics radiate; those proceeding from the lowest points being nearly parallel to the axes, and those from the critical point onwards being nearly parallel to the principal curve. Inspection of the diagram leads to some new conclusions. Sarrau's equation gives good results for the higher pressures, but is unusable in the neighbourhood of the curve of liquefaction, since here it allows the isopyknics to pass through and intersect each other. The true course of an isopyknic would probably be that it would bend slightly on approaching the curve of liquefaction and thenceforward run downwards close beside it. Thus all isopy knics should collect into a bundle in this region. Such a course, however, is not indicated by Sarrau's equation. In the neighbourhood of the critical point, the densities of liquid carbonic acid measured by Andreew (Annalen, 110, 1) are much higher than those calculated by Sarrau. Although Andreew's observations are untrustworthy, it is probable that here Sarrau's values are too low. In other cases, too, Sarrau's equation leads to impossible results. By moving along an ordinate in the diagram, we change from one isopyknic to another by simple change of pressure; but by moving along an abscissa the same thing is effected by change of temperature. Thus the passage from one isopyknic to another in a vertical or a horizontal direction gives a conception of the compressibility of the substance, or of its expansion by heat. Now, according to Andrews' conception, everything on the diagram above the curve of liquefactiou, and within the ordinate of so-called "critical temperature," indicates liquid; everything outside these limits, gas. The author believes, however, that the two states are separated, not by the ordinate in question, but by the principal curve, or the curve pv = minimum. Everything below this indicates gas; everything above it, liquid. His reasons are as follows. In the first place, the rate of change of density with pressure (d1 — d)/(p1 − p) when dp and dip, refer to neighbouring isopyknics, changes uniformly from below upwards, whether to right or left of the ordinate of critical temperature. The values of this quotient for different absolute temperatures are given in a table, and in each case they first increase, then reach a maximum, and then begin to decrease. If the curves of equal values of (d1 — d)/(pı — p) are drawn, they are, like the principal curve, convex below and concave above, towards the axis of temperature. So also over the whole diagram this quotient slowly diminishes with increase of temperature. 1 Vi v p2 V2 Pi has con Again, the coefficient of compressibility, K = stantly diminishing values for increase of temperature, when always calculated between neighbouring isopyknics; but constantly increasing values for increasing temperature when the pressure is kept constant. Carbonic anhydride is thus more compressible at high than at low temperatures. And, finally, the coefficient of expansion by heat (d d1) ¡d1(tı t) under different pressures points to no specific difference between the regions on each side of the critical ordinate. In no case, therefore, is any discontinuity observed at this ordinate. It has then no special significance, and the conception of critical temperature as that above which liquefaction of a gas is impossible is erroneous and only an obstacle to progress. The same is true of Mendeléeff's conception (O. E. Meyer, Kinetische Theorie der Gase, p. 64). Andrews' conception was based on the absence of a meniscus at any temperature above 30.92° and the forms of the isothermals. But, as Jamin has pointed out, the absence of the meniscus is simply due to the approximately equal densities of the gas and liquid at the critical point; hence the formation of liquid cannot be seen. These conditions are well seen in the diagram. At the critical point, the isopyknics 04 and 0.5 approach opposite sides of the curve of liquefaction. At higher points, the densities on opposite sides of the principal curve differ still less. The forms of the isothermals also prove nothing. For since the difference between the densities of the liquid and of the saturated vapour above it is exceedingly small above the critical temperature, there is here no cause for the bending which in the lower isothermals denotes liquefaction. This bending is, in fact, due to difference of density. It is commonly asserted that from the critical point upwards there is no latent heat; and it might be objected to the author's view, that if there is no difference of density no heat can be necessary to produce a change of state; there can then be no liquid state above the critical temperature. The author meets this objection by quoting some of his own experiments on the liquefaction of nitrogen (Ann. Phys. Chem. [2], 25, 398), in which the passage of the liquid to the state of gas at the critical point was certainly attended by absorption of heat. Such a change could not be brought about without either absorption of heat or diminution of pressure. It is to be noted that the isopyknic 005, which corresponds nearly with the density of liquid carbonic anhydride at the critical point, comes very close to the upper branch of the principal curve; and when our knowledge of carbonic anhydride is more accurate, it may be found to coincide with it. Every point on this isopyknic from 30.92° upwards, might be regarded as "the critical point." For Andrews' conception, "critical temperature," it would be better to substitute the conception "critical density," or the least density which the substance can have as a liquid. The corresponding isopyknic would then be named "critical isopyknic." The author dwells on the great difficulty in determining the precise conditions under which the meniscus really disappears. Disregard of this has led Cailletet (Abstr., 1880, 604) and Van der Waals to assert that by increased pressure the liquid could be made to dissolve in the gas above it. *This view was first advanced by Ramsay, Proc. Roy. Soc., 30, 323.Сн. В. Stefan has lately shown that when a liquid exists under the pressure of its saturated vapour, and whilst a meniscus is distinctly visible, there must nevertheless be a gradual transition between the gas and the liquid at the boundary. The diagram represents this perfectly. For although the gas and liquid are both under the same pressure, and the points on the diagram corresponding with the two states are immeasurably close together, these points are still on opposite sides of the principal curve, and between them all the isopyknics for intermediate densities must pass down. A particle of liquid, then, to reach the other side of the curve must pass through all these intermediate states. A meniscus is, however, visible because the transition layer is exceedingly thin. Сн. В. Specific Gravities of Mixtures of Ethylic Alcohol and Carbonic Anhydride. By A. BLÜMCKE (Ann. Phys. Chem. [2], 30, 243-250). The author has determined the specific gravities of mixtures of alcohol and carbonic anhydride at different temperatures and pressures, by a slightly modified form of the method already described (Abstr., 1885, 215). The following are the results, the figures in column p denoting the percentages of carbonic anhydride in the mixtures: The specific gravity thus reaches a maximum for 80 per cent. of carbonic anhydride under 55 atmospheres pressure, and for 70 per cent. under 66 atmospheres. No relation between the specific gravities of the constituents and that of the mixture has been discovered. A table is also given showing the increase of volume produced in alcohol by addition of carbonic anhydride. If the new volume of 1 c.c. of alcohol, V = 1 + na, where n equals the number of c.c. of gaseous carbonic anhydride at 0° and 760 mm., the value of a is approximately constant for mixtures containing less than 50 per cent. of carbonic anhydride; and for a mixture of this strength = 0·00199 at 04°, 0.00210 at 11°, and 0.00221 at 25°. For greater proportions of carbonic anhydride, a increases, especially at the higher temperatures. The author's values for the specific gravity of liquid carbonic anhydride (p = 100 in the table) at the liquefying pressure are different from those observed by Andreew (Annalen, 110, 1) and those calculated by Clausius' and Sarrau's equations. Andreew found 0.947 at 0°, 0.849 at 17°, 0·783 at 25°. These measurements were however made by compressing carbonic anhydride in glass tubes and calculating the uncondensed gas on the basis of Boyle and Marriott's law, which does not hold near the critical temperature. The author's results are also different from those recently obtained by Cailletet and Matthias (Abstr., 1886, 758), namely, 0.908 at 0°, 0·842 at 10°, 0·748 at 20°. The carbonic anhydride used by the author may have been slightly impure. CH. B. Dissociation of Sodium Phosphate and the Measure derived from the Vapour-tension of the Chemical Attraction of the Water of Crystallisation. By W. MÜLLER-ERZBACH (Ber., 20, 137-141).—The results of two series of experiments made with disodium hydrogen phosphate show that within the limits of temperature of 13° and 62° the chemical attraction between sodium phosphate and its water of crystallisation has a constant or nearly constant value. With a considerable rise of temperature, the attraction must become slighter, owing to the increased distance of the components, so that the greater dissociability of strongly heated salts is readily explained. The behaviour of water absorbed by alumina (Ann. Chim. Phys. [2], 28, 695) makes it probable that greatly diminished chemical affinity will be found only at a temperature considerably above 62°. N. H. M. Solubility of Solid Substances, and the Changes in Volume and Energy accompanying Solution. By F. BRAUN (Ann. Phys. Chem. [2], 30, 250-274).-Let p be the pressure, t temperature, V volume, and E total internal energy, all in absolute units, of the mixture of a solid salt with its saturated solution; and let dQ be the quantity of heat added for an infinitesimal change of p and t; then where J = mechanical equivalent of heat. Let r be the mass, v specific volume, m coefficient of compression, a coefficient of expansion by heat, and u internal energy per unit mass, of the solution; and let P, P, μ, a, and w be the similar magnitudes for the solid salt. Then v is directly changed by the pressure, and indirectly by the further solution (or deposition) of salt. Hence dv/dpdv/òp + dv/dy. ô7/ôp, when is a magnitude depending on the amount of salt initially in solution, and the partial differential coefficients refer only to the first part of the change; so also for drôt, du/op, and duôt. The total change of V due to pressure alone will then be where the mass of salt which dissolves in 1 gram of solution when the pressure is increased by unity, and traction of this salt in dissolving. In a similar way, coefficient of con where 7 mass of salt which dissolves in l'gram of solution saturated at t°, when the temperature is raised 1o. Again since at pressure p, Eur + wp, at p + dp, the total internal energy E+E/cp.dp, by partial differentiation with respect to p and to t, and putting dy/dp =xe and dy/dt = xŋ, we find, Here we may write u-w + xòu!dy = — -JA, where = the heat absorbed when 1 gram of salt dissolves in its nearly saturated solution, neglecting external work. Then by substitution in the first equation, and putting pêv/ep + du/op + T &v/ôt = 0, and pèp/èp + òw/&p + T dø/ôt = 0, since dQ/T must be an exact differential, we get finally ε(Jλ - ρνφ) = Τνηφ. In this expression -pvp/JL, the latent heat of solution at pressure p, including external work. This equation shows that-first, substances which dissolve in their nearly saturated solutions with development of heat and diminished volume, must have their solubility increased by pressure; second, substances which dissolve either with absorption of heat or with increased volume, must be partly precipitated by pressure. Other interesting relations follow from it. Sorby (Proc. Roy. Soc., 12, 538), reasoning from the change of melting point by pressure, has already been led to experiment in this direction, and found for sal ammoniac, which dissolves with increased volume, diminished solubility at high pressures; but for sodium chloride, copper sulphate, potassium sulphate, and potassium ferroand ferri-cyanide, which dissolves with contraction, increased solubility at high pressures. Möller also (Ann. Phys. Chem. [1], 117, 386), has made similar experiments; his results partly contradict those of Sorby. In one In the experimental part of his work, the author has used a castiron block pierced lengthwise by two narrow communicating channels, which could be closed by steel screws with copper washers. of these pressure was produced by a copper plunger, forced in by a screw and lever; the other contained the solution or mixture experimented on. The pressure applied, about 900 atmospheres, was |
