Vapour pressure constants

The constant of integration i, which depends on the composition of the substance, is caUed the vapour pressure constant or the chemical constant ( 10. VIIIL). 

The important constant i was called by Nemst the chemical constant, since it has a characteristic value for every pure substance Fowler and Sterne s name, vapour pressure constant, has not found much favour. 

It is not sufficient even for an approximate calculation to know the form of the function L for a limited range of temperature (see p. 407). The value of the constant C depends to a considerable extent on the form of the function L at very low temperatures. For the calculation of C it is therefore necessary to know the values of the specific heats at very low temperatures. These have recently been determined in Nemst s laboratory for a number of solid substances, but unfortunately almost exclusively for substances which volatilise only at very high temperatures. Iodine is apparently the only substance whose vapour pressure and specific heats at low temperatures are both known. In this case the vapour pressure constant c can therefore be calculated with a certain degree of approximation. The calculation is as follows ... 

We shall show in the next paragraph that the vapour pressure constants play an important part in the calculation of chemical equilibria in gases. The first problem which Nernst had to solve after the discovery of his theorem was therefore the calculation of at least the approximate value of C for as many simple substances as possible. For this purpose he made use of the theorem of corresponding states, and assumed further that the specific heat of solid and liquid bodies diminishes to a small but finite value (viz. nx 1 5, where n is the number of atoms in the molecule) as the temperature is lowered. On the evidence of the measurements published up to that time he also assumed that the molecular specific heat of gases and vapours is a linear function of the temperature which approaches the value 3-5-l-7ixl-5 at very low temperatures. In this way he arrived at the vapour pressure formula... 

The integration constant need not be zero, and will in general have a finite value varying from case to case. The value of C cannot be calculated from thermal quantities. We can calculate this constant, however, for every reaction, as Nernst has shown, by adding the vapour pressure constants of the reacting substances. 

The integration constant of this equation left undetermined by thermodynamics is therefore the sum of the vapour pressure constants of the individual reacting substances. In this way it is possible in principle to calculate chemical equilibria at all temperatures from thermal quantities (calorimetric measurements) and vapour pressure measurements with the individual reacting substances. 

The equilibrium constant can therefore be calculated for all temperatures when the vapour pressure constant, the heat of reaction at a given temperature, and, finally, the temperature coefficients of the specific heats (and hence 2a) are given. For the formation of water vapour from the elements, the calculation is as follows ... 

Considering the somewhat daring assumptions made with regard to the variation of the specific heats, the agreement is excellent. Nernst has calculated many other chemical equilibria in this way from the vapour pressure constants and thermal quantities, and has obtained a complete confirmation of his theory. 

By the method used on p. 416 for pure gas reactions, Nernst has shown that the integration constant can again be expressed as the sum of the vapour pressure constants of the individual volatile reacting substances. In most of the more important heterogeneous reactions only a single gas takes part in the reaction, as, for example, in the dissociation of carbonates, hydroxides, ammoniates, salt hydrates, and, further, in reactions between metals and oxygen or the halogens. In these cases the condition for equilibrium simplifies to... 

WiCHTERLE J, and Linek J., Antoine Vapour Pressure Constants of Pure Compounds, Academia, Prague, 1971. 

Chemical Constants [j ) and Vapour Pressure Constants i ) of some Monatomic Elements ... 

Table 10.4 gives values of j for various diatomic substances. Again the table includes values of the vapour pressure constant i which will be considered later (c/. chap. XIV, 2). 

Thus if we know the heat of evaporation, the specific heats and the vapour pressure we can calculate the vapour pressure constant i. 

Vapour pressure constants have also been evaluated for a modified expression of the reduced Frost-Kalkwarf equation [1395], but this type of expression is useful only where limited experimental data are available. Unfortunately, a full statistical analysis of all these alternative expansions of p(T) has not been performed. 

Table B.l. Vapour pressure constants for some precursors...

This correlation is of importance when the appropriate relative humidity is calculated for stability testing by keeping the mean partial vapour pressure constant and increasing the temperature to the testing temperature of 30°C. 

Up to the testing temperature 30°C, by keeping the partial vapour pressure constant, the relative humidity decreases to 16.3%. This RH value is lower compared to the standard long-term testing condition for hot and dry climates, 30°C/35% RH. In other words, testing at 30°C/35% RH represents a higher humidity than the real condition measured in the open air. 

The influence of the constant term i is connected purely with the entropy. If i becomes larger, the vapom pressure becomes greater also. Scrutiny of the formulae reveals several points of interest. As the mass of the molecules or atoms increases, the vapour-pressure constant increases also. This is because a greater mass leads to a more fine-grained quantization of the translational energy in the gas phase. There are thus relatively more possibilities of existence as... 

Far better results can be expected from multi-source techniques where each of the constituent metals is heated in a separate crucible. The composition of the deposited film will then be determined by the relative vapour pressures and hence by the relative heating rates applied to the various sources. The heating rates of each of the sources has to be controlled independently. Furthermore, in order to keep the ratio of the vapour pressures constant during the entire evaporation process, one has to be able to correct quickly for any deviation from the desired vapour pressure. 

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