Gases equilibria with

At the same time, there is no crude physical controversy in this approach. The largest pores are those which are obtained at given Pc by capillary condensation. Gas filled pores, that is, pores with larger radii than those corresponding to Eq. (3) do not exist, and water-filled pores do not conduct gas. Equilibrium with the gas outside the membrane is established. 

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

It must also be realized that this thin surface region is in a very turbulent state. Since the liquid is in equilibrium with its vapor, then, clearly, there is a two-way and balanced traffic of molecules hitting and condensing on the surface from the vapor phase and of molecules evaporating from the surface into the vapor phase. From the gas kinetic theory, the number of moles striking 1 cm of surface per second is... 

If we consider the case of a gas in adsorption equilibrium with a surface, there must be no net free energy change on transporting a small amount from one region to the other. Therefore, since the potential represents the work done by the adsorption forces when adsorbate is brought up to a distance x from the surface, there must be a compensating compressional increase in the free energy of the adsorbate. Thus... 

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

Nearly all experimental eoexistenee eurves, whether from liquid-gas equilibrium, liquid mixtures, order-disorder in alloys, or in ferromagnetie materials, are far from parabolie, and more nearly eubie, even far below the eritieal temperature. This was known for fluid systems, at least to some experimentalists, more than one hundred years ago. Versehaflfelt (1900), from a eareflil analysis of data (pressure-volume and densities) on isopentane, eoneluded that the best fit was with p = 0.34 and 8 = 4.26, far from the elassieal values. Van Laar apparently rejeeted this eonelusion, believing that, at least very elose to the eritieal temperature, the eoexistenee eurve must beeome parabolie. Even earlier, van der Waals, who had derived a elassieal theory of eapillarity with a surfaee-tension exponent of 3/2, found (1893)... 

Wlien H has reached its minimum value this is the well known Maxwell-Boltzmaim distribution for a gas in themial equilibrium with a unifomi motion u. So, argues Boltzmaim, solutions of his equation for an isolated system approach an equilibrium state, just as real gases seem to do. Up to a negative factor (-/fg, in fact), differences in H are the same as differences in the themiodynamic entropy between initial and final equilibrium states. Boltzmaim thought that his //-tiieorem gave a foundation of the increase in entropy as a result of the collision integral, whose derivation was based on the Stosszahlansatz. 

As noted above, an isothemi plots the muiiber of molecules adsorbed on the surface at some temperature in equilibrium with the gas at some pressure. Adsorption gives rise to a change in the free energy which, of... 

Check. The number of free particles with all momenta p in equilibrium with a gas bath of volume v at temperature T is the translational partition fiinction Z>. Since the fraction of particles with energy E is exp (-... 

The column (or line entry) headed a gives the volume of gas (in milliliters) measured at standard conditions (0°C and 760 mm or 101.325 kN dissolved in 1 mL of water at the temperature stated (in degrees Celsius) and when the pressure of the gas without that of the water vapor is 760 mm. The line entry A indicates the same quantity except that the gas itself is at the uniform pressure of 760 mm when in equilibrium with water. 

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). 

There is a parallel between the composition of a copolymer produced from a certain feed and the composition of a vapor in equilibrium with a two-component liquid mixture. The following example illustrates this parallel when the liquid mixture is an ideal solution and the vapor is an ideal gas. 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

In the first step, in which the molecules of the fluid come in contact with the adsorbent, an equihbrium is established between the adsorbed fluid and the fluid remaining in the fluid phase. Figures 25-7 through 25-9 show several experimental equihbrium adsorption isotherms for a number of components adsorbed on various adsorbents. Consider Fig. 25-7, in which the concentration of adsorbed gas on the solid is plotted against the equilibrium partial pressure p of the vapor or gas at constant temperature. At 40° C, for example, pure propane vapor at a pressure of 550 mm Hg is in equilibrium with an adsorbate concentration at point P of 0.04 lb adsorbed propane per pound of silica gel. Increasing the pressure of the propane will cause... 

The smallest expanders usually use oil with a viscosity at 38° C (100° F) of 60 to 100 SSU, and large machines up to 500 SSU. If the oil is kept in a totally enclosed system in contact with hydrocarbon or another partly soluble gas, which would dissolve and reduce the viscosity of the oil, then a compensating higher viscosity should be used so that the working viscosity after ultimate equilibrium with such gas is suitable for the bearings. 

Y = Mol fraction of one component (solute) at any point in the gas phase Y = Mol fraction gas phase composition in equilibrium with a liquid composition, X... 

Poor glycol reconcentration (exit gas dew point is 5-15°F higher than dew point in equilibrium with lean glycol concentration)... 

Enhancement of gas storage capacity through adsorption occins when the overall storage density is increased above that of the normal gas density at a given pressure. The adsorbed phase has a greater density than the gas phase in equilibrium with it. However, enhancement in a storage system of fixed volume can only happen if a greater amount of gas is adsorbed compared to the volume of gas displaced by the adsorbent volume. 

LPG (liquefied petroleum gas) Petroleum gas stored or proeessed as a liquid in equilibrium with vapour by refrigeration or pressurization. The two LPGs in general use are eommereial propane and eommereial butane supplied to produet speeifieations, e.g. BS 4250. (These, or mixtures thereof, eomprise LPG for the purpose of the Highly Flammable Liquids and Liquefied Petroleum Gas Regulations 1972.)... 

PRESSURE SYSTEM Defined in the Pressure System Safety Regulations 2000 as a system containing one or more pressure vessels of rigid construction, any associated pipework and protective devices the pipework with its protective devices to which a transportable gas container is, or is intended to be, connected or a pipeline and its protective devices which contains or is liable to contain a relevant fluid, but does not include a transportable gas container. Here relevant fluid is steam any fluid or mixture of fluids which is at a pressure of >0.5 bar above atmospheric pressure, and which fluid or a mixture of fluids is a gas, or a liquid which would have a vapour pressure of >0.5 bar above atmospheric pressure when in equilibrium with its vapour at either tlie actual temperature of the liquid or 17.5°C or a gas dissolved under pressure in a solvent contained in a porous substance at ambient temperamre and which could be released from the solvent with the application of heat. 

With a sparingly-soluble gas a much-higher partial pressure of that gas is in equilibrium with a solution of a given concentration than is the case with a highly soluble gas. 

Cg = concentration of soluble gas in equilibrium with gas of partial pressure Pg... 

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