if at 0° under a pressure p = 1 (for example, under the atmospheric pressure), the volume (for instance, a litre) of a gas or vapour he taken as 1, and therefore v and b be expressed by the same units as p and a. The deviations from both the laws of Mariotte and Gay-Lussac are expressed by the above equation. Thus, for hydrogen a must be taken as infinitely small, and b = 0·0009, judging by the data for 1,000 and 2,500 metres pressure (Note [28]). For other permanent gases, for which (Note [28]) I showed (about 1870) from Regnault's and Natterer's data, a decrement of pv, followed by an increment, which was confirmed (about 1880) by fresh determinations made by Amagat, this phenomena may be expressed in definite magnitudes of a and b (although van der Waals' formula is not applicable in the case of very small pressures) with sufficient accuracy for contemporary requirements. It is evident that van der Waals' formula can also express the difference of the coefficients of expansion of gases with a change of pressure, and according to the methods of determination (Note [26]). Besides this, van der Waals' formula shows that at temperatures above 273( 8a / 27b -1) only one actual volume (gaseous) is possible, whilst at lower temperatures, by varying the pressure, three different volumes—liquid, gaseous, and partly liquid, partly saturated-vaporous—are possible. It is evident that the above temperature is the absolute boiling point—that is (tc) = 273( 8a / 27b - 1). It is found under the condition that all three possible volumes (the three roots of van der Waals' cubic equation) are then similar and equal (vc = 3b). The pressure in this case (pc) = a / 27b2 . These ratios between the constants a and b and the conditions of critical state—i.e. (tc) and (pc)—give the possibility of determining the one magnitude from the other. Thus for ether (Note [29]), (tc) = 193°, (tp) = 40, hence a = 0·0307, b = 0·00533, and (vc) = 0·016. That mass of ether which at a pressure of one atmosphere at 0° occupies one volume—for instance, a litre—occupies, according to the above-mentioned condition, this critical volume. And as the density of the vapour of ether compared with hydrogen = 37, and a litre of hydrogen at 0° and under the atmospheric pressure weighs 0·0896 gram, then a litre of ether vapour weighs 3·32 grams; therefore, in a critical state (at 193° and 40 atmospheres) 3·32 grams occupy 0·016 litre, or 16 c.c.; therefore 1 gram occupies a volume of about 5 c.c., and the weight of 1 c.c. of ether will then be 0·21. According to the investigations of Ramsay and Young (1887), the critical volume of ether was approximately such at about the absolute boiling point, but the compressibility of the liquid is so great that the slightest change of pressure or temperature has a considerable effect on the volume. But the investigations of the above savants gave another indirect demonstration of the truth of van der Waals' equation. They also found for ether that the isochords, or the lines of equal volumes (if both t and p vary), are generally straight lines. Thus the volume of 10 c.c. for 1 gram of ether corresponds with pressures (expressed in metres of mercury) equal to 0·135t - 3·3 (for example, at 180° the pressure = 21 metres, and at 280° it = 34·5 metres). The rectilinear form of the isochord (when v = a constant quantity) is a direct result of van der Waals' formula.
When, in 1883, I demonstrated that the specific gravity of liquids decreases in proportion to the rise of temperature [St = S0 - Kt or St = S0(1 - Kt)], or that the volumes increase in inverse proportion to the binomial 1 - Kt, that is, Vt = V0(1-Kt)-1, where K is the modulus of expansion, which varies with the nature of the liquid, then, in general, not only does a connection arise between gases and liquids with respect to a change of volume, but also it would appear possible, by applying van der Waals' formula, to judge, from the phenomena of the expansion of liquids, as to their transition into vapour, and to connect together all the principal properties of liquids, which up to this time had not been considered to be in direct dependence. Thus Thorpe and Rücker found that 2(tc) + 273 = 1/K, where K is the modulus of expansion in the above-mentioned formula. For example, the expansion of ether is expressed with sufficient accuracy from 0° to 100° by the equation St = 0·736/(1 - 0·00154t), or Vt = 1/(1 - 0·00154t), where 0·00154 is the modulus of expansion, and therefore (tc) = 188°, or by direct observation 193°. For silicon tetrachloride, SiCl4, the modulus equals 0·00136, from whence (tc) = 231°, and by experiment 230°. On the other hand, D. P. Konovaloff, admitting that the external pressure p in liquids is insignificant when compared with the internal (a in van der Waals' formula), and that the work in the expansion of liquids is proportional to their temperature (as in gases), directly deduced, from van der Waals' formula, the above-mentioned formula for the expansion of liquids, Vt = 1/(1 - Kt), and also the magnitude of the latent heat of evaporation, cohesion, and compressibility under pressure. In this way van der Waals' formula embraces the gaseous, critical, and liquid states of substances, and shows the connection between them. On this account, although van der Waals' formula cannot be considered as perfectly general and accurate, yet it is not only very much more exact than pv = RT, but it is also more comprehensive, because it applies both to gases and liquids. Further research will naturally give a closer proximity to truth, and will show the connection between composition and the constants (a and b); but a great scientific progress is seen in this form of the equation of state.
Clausius (in 1880), taking into consideration the variability of a, in van der Waals' formula, with the temperature, gave the following equation of condition:—
(p + a / T(v + c)2 )(v - b) = RT.
Sarrau applied this formula to Amagat's data for hydrogen, and found a = 0·0551, c = -0·00043, b = 0·00089, and therefore calculated its absolute boiling point as -174°, and (pc) = 99 atmospheres. But as similar calculations for oxygen (-105°), nitrogen (-124°), and marsh gas (-76°) gave tc higher than it really is, the absolute boiling point of hydrogen must lie below -174°.
[35] This and a number of similar cases clearly show how great are the internal chemical forces compared with physical and mechanical forces.
[36] The property of palladium of absorbing hydrogen, and of increasing in volume in so doing, may be easily demonstrated by taking a sheet of palladium varnished on one side, and using it as a cathode. The hydrogen which is evolved by the action of the current is retained by the unvarnished surface, as a consequence of which the sheet curls up. By attaching a pointer (for instance, a quill) to the end of the sheet this bending effect is rendered strikingly evident, and on reversing the current (when oxygen will be evolved and combine with the absorbed hydrogen, forming water) it may be shown that on losing the hydrogen the palladium regains its original form.
[37] Deville discovered that iron and platinum become pervious to hydrogen at a red heat. He speaks of this in the following terms:—‘The permeability of such homogeneous substances as platinum and iron is quite different from the passage of gases through such non-compact substances as clay and graphite. The permeability of metals depends on their expansion, brought about by heat, and proves that metals and alloys have a certain porosity.’ However, Graham proved that it is only hydrogen which is capable of passing through the above-named metals in this manner. Oxygen, nitrogen, ammonia, and many other gases, only pass through in extremely minute quantities. Graham showed that at a red heat about 500 c.c. of hydrogen pass per minute through a surface of one square metre of platinum 1·1 mm. thick, but that with other gases the amount transmitted is hardly perceptible. Indiarubber has the same capacity for allowing the transference of hydrogen through its substance (see Chapter [III].), but at the ordinary temperature one square metre, 0·014 mm. thick, transmits only 127 c.c. of hydrogen per minute. In the experiment on the decomposition of water by heat in porous tubes, the clay tube may be exchanged for a platinum one with advantage. Graham showed that by placing a platinum tube containing hydrogen under these conditions, and surrounding it by a tube containing air, the transference of the hydrogen may be observed by the decrease of pressure in the platinum tube. In one hour almost all the hydrogen (97 p.c.) had passed from the tube, without being replaced by air. It is evident that the occlusion and passage of hydrogen through metals capable of occluding it are not only intimately connected together, but are dependent on the capacity of metals to form compounds of various degrees of stability with hydrogen—like salts with water.
[38] It appeared on further investigation that palladium gives a definite compound, Pd2H (see further) with hydrogen; but what was most instructive was the investigation of sodium hydride, Na2H, which clearly showed that the origin and properties of such compounds are in entire accordance with the conceptions of dissociation.
Since hydrogen is a gas which is difficult to condense, it is little soluble in water and other liquids. At 0° a hundred volumes of water dissolve 1·9 volume of hydrogen, and alcohol 6·9 volumes measured at 0° and 760 mm. Molten iron absorbs hydrogen, but in solidifying, it expels it. The solution of hydrogen by metals is to a certain degree based on its affinity for metals, and must be likened to the solution of metals in mercury and to the formation of alloys. In its chemical properties hydrogen, as we shall see later, has much of a metallic character. Pictet (see Note [31]) even affirms that liquid hydrogen has metallic properties. The metallic properties of hydrogen are also evinced in the fact that it is a good conductor of heat, which is not the case with other gases (Magnus).