Equilibrium pressures

If we vary the composition of a liquid mixture over all possible composition values at constant temperature, the equilibrium pressure does not remain constant. Therefore, if integrated forms of the Gibbs-Duhem equation [Equation (16)] are used to correlate isothermal activity coefficient data, it is necessary that all activity coefficients be evaluated at the same pressure. Unfortunately, however, experimentally obtained isothermal activity coefficients are not all at the same pressure and therefore they must be corrected from the experimental total pressure P to the same (arbitrary) reference pressure designated P. This may be done by the rigorous thermodynamic relation at constant temperature and composition ... 

Two other examples will sufhce. Methane physisorbs on NaCl(lOO) and an early study showed that the symmetrical, IR-inactive v mode could now be observed [97]. In more recent work, polarized FTIR rehection spectroscopy was used to determine that on being adsorbed, the three-fold degeneracies of the vs and v modes were partially removed [98]. This hnding allowed consideration of possible adsorbate-adsorbent geometries one was that of a tripod with three of the methane hydrogens on the surface. The systems were at between 4 and 40 K so that the equilibrium pressure was very low, about 10 atm. 

As a final example, similar spectroscopy was carried out for CO2 physisorbed on MgO(lOO) [99]. Temperatures were around 80 K and equilibrium pressures, as low as 10 atm (at higher temperatures, CO2 chemsorbs to give surface carbonate). Here, the variation of the absorbance of the infrared bands with the polarization of the probe beam indicated that the surface CO2 phase was highly oriented. 

Now, considering process XVII-93, where P is the equilibrium pressure of the adsorbate, we have... 

Getting I 1998 New determination of the bismuth l-ll equilibrium pressure—a proposed modification to the practical pressure scale Metroiogica 35 119... 

For an absorption system in which the solute is highly soluble in the solvent, such that the equilibrium pressure of the solute over the absorbing liquid is very low, we may write ... 

If Uvo or more systems are connected together (such as a pipe length with an orifice plate, two or more vessels connected with pipe or duct, or a compartmented vessel) and an explosion develops in No. 1 area, which generally may be at equilibrium pressure with compartments No. 2 and 3 in equilibrium with No. 2, it can cause a pressure rise in front of the dame front in the unburnt gases in the interconnecting spaces (pipe, compartment). The increased pressure in compartment or area No. 1 becomes the starting pressure for an explosion in com-... 

P = intial pressure. - equilibrium pressure. AP- change in pressure... 

The equilibrium constant for a chemical system can be used to calculate the partial pressures of the species present at equilibrium. In the simplest case, one equilibrium pressure can be calculated, knowing all the others. Consider, for example, the system... 

You must distinguish carefully between initial pressures (P0) and equilibrium pressures. 

What is the equilibrium pressure of hydrogen sulfide if those of hydrogen and sulfur gases are 0.103 atm and 0.417 atm, respectively ... 

If we start with hydrogen and oxygen, equilibrium is attained after most of the hydrogen and oxygen have united to form water. More important, though, the partial pressures at equilibrium are the same as those obtained beginning with pure H20. The equilibrium pressures are fixed by the temperature, the composition, and the total pressure they do not depend upon the direction from which equilibrium is approached. The balanced equation does not indicate the concentrations (or partial pressures) at equilibrium. 

Although we have no way of determining the moisture content of the individual components, it is not difficult to measure a property which is directly related to it and is common to all the components—the equilibrium pressure of water vapor. It seems logical, therefore, to use it as an index of moisture, as suggested by Makower and Myers (20). 

An example is the complex with argon which can be kept indefinitely in an ordinary bottle, although the equilibrium pressure of argon over the crystal amounts to several atmospheres at room temperature. Powell31 named these complexes "clathrate compounds, which according to him are those compounds "in which two or more components are associated without ordinary chemical union but through complete enclosure of one set of molecules in a suitable structure formed by another. ... 

The fact that both heats of formation and equilibrium pressures of the hydrates of spherical molecules correctly follow from one model must mean that the L-J-D theory gives a good account of the entropy associated with the motions of these solutes in the cavities of a clathrate. That the heat of formation of ethane hydrate is predicted correctly, whereas the theoretical value of its vapor pressure is too low, is a further indication that the latter discrepancy must be ascribed to hindered rotation of the ethane molecules in their cavities. 

Since the molecules of SFt and propane only fit into the larger cavities, their equilibrium hydrates must have identical compositions. From the experimental value of the equilibrium pressure, pp = 1.48 atm for propane... 

It is essentially a phase diagram which consists of a family of isotherms that relate the equilibrium pressure of hydrogen to the H content of the metal. Initially the isotherm ascends steeply as hydrogen dissolves in the metal to form a solid solution, which by convention is designated as the a phase. At low concentrations the behaviour is ideal and the isotherm obeys Sievert s Law, i.e.,... 

PCT diagrams of AB2 (electrode alloys) /H systems reflect multiphase or nonideal behaviour [54], This is illustrated in Fig. 19, in which both the equilibrium pressure and the open—circuit equilibrium voltage, Er are plotted for Zr()5Ti05 Vo.sNij Fe02Mn02. 

The isotherms represented in Fig. 1 give a general idea of the equilibria in the Pd-H system under different p-T conditions. Most experimental evidence shows, however, that the equilibrium pressure over a + /3 coexisting phases depends on the direction of the phase transformation process p a-p > pp-a (T, H/Pd constant). This hysteresis effect at 100°... 

The nickel-hydrogen system has not been studied in such detail. The isotherm at 25°C is presented in Fig. 3 on the basis of the results obtained by Baranowski and Bochenska (11a). The /3-phase of nickel hydride appears when H/Ni exceeds 0.04 at an equilibrium pressure of 3400 atm. The characteristic H/Ni ratio in the /3-phase then amounts to 0.6. 

Letp be the ordinary equilibrium pressure in a system composed of a condensed phase and its vapour, and let, r, Y be the specific volumes of these phases, respectively, under a pressure p. We now assume that these values are altered to p r Y, when the condensed phase alone is exposed to a pressure P + p. 

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