A third case arises when a mixed gas is in equilibrium with immiscible pure liquid or solid phases. The vapor pressure of each condensed phase is then unaffected by the existence of the mixed vapor phase. Each pure condensed phase communicates only with its own partial pressure. This results in a total pressure that is the sum of the two vapor pressures, as illustrated above for ideal gas mixing pi = njRTA t, and [Pg.100]

A closed container of water is a two-phase system in which molecules of water are in a gas phase in the space above the liquid phase. Moving randomly above the liquid, some of these molecules strike the walls and some go back into the liquid, as shown in Figure 21. An equilibrium, in which the rate of evaporation equals the rate of condensation, is soon created. The molecules in the gas exert pressure when they strike the walls of the container. The pressure exerted by the molecules of a gas, or vapor, phase in equilibrium with a liquid is called the vapor pressure. You can define boiling point as the temperature at which the vapor pressure equals the external pressure. [Pg.418]

A consequence of the second law of thermodynamics is that the chemical potential of any component in equilibrium phases at a particular temperature or pressure is the same in all phases. For a pure compound the chemical potential is the Gibbs energy per mole of the substance. The following equation results for a condensed phase in equilibrium with the gas phase. [Pg.6]

Substance A in the condensed phase is in equilibrium with its own vapour at temperature T, A is the only species in the gas phase. Now an inert gas is introduced into the system so that the total pressure rises from P° to P , Assuming that the inert gas behaves ideally with A and does not dissolve in the condensed phase, choose the correct one from the following [Pg.141]

The vapor pressure, Pvp, of a liquid or solid is the pressure of the compound s vapor (gas) in equilibrium with the pure, condensed liquid or solid phase of the compound at a given temperature [5-9]. Vapor pressure, which is temperature dependent, increases with temperature. The vapor pressure of chemicals varies widely according to the degree of intermolecular attractions between like molecules The stronger the intermolecular attraction, the lower the magnitude of the vapor pressure. Vapor pressure and the Henry s law constant should not be confused. Vapor pressure refers to the volatility from the pure substance into the atmosphere the Henry s law constant refers to the volatility of the compound from liquid solution into the air. Vapor pressure is used to estimate the Henry s law constant [equation (2.4)]. [Pg.39]

Let us consider now the pressures, p°, of vapor, in equilibrium with the condensed phase I, on the one hand, and p , in equilibrium with the reference bulk phase, having the same structure as the k-th sublayer of boundary phase a, on the other hand. Assuming the vapor phase as an ideal gas, one can write [Pg.161]

It is conventional to define fugacity so that in the limit of a dilute gas, it becomes the pressure. Thus fugacity has units of pressure. When one deals with condensed phases and with gases in equilibrium with condensed phases, it becomes convenient to introduce a unitless generalization of fugacity, which is called activity. The activity is defined by [Pg.65]

The fugacity of a pure liquid or solid can be defined by applying Eq. si.4 to the vapor in equilibrium with the substance in either condensed phase. Usually, the volume of the vapor will follow the ideal gas equation of state very closely, and the fugacity of the vapor may be set equal to the equilibrium vapor pressure. The thermodynamic basis of associating the fugacity of a condensed [Pg.26]

The design of purification processes involving the removal of impurities by condensation from pressurized gas streams requires phase equilibrium data which are often not available. The objective of this paper is to examine several methods of predicting the composition of a gas phase in equilibrium with an essentially pure condensed phase when only the properties of the pure components are known and to compare these predictions with the limited experimental data for the system hydrogen-methane at low temperatures. [Pg.413]

Water molecules in an aqueous solution continually escape into a surrounding gas phase, and simultaneously water molecules condense back into the liquid phase, the two rates becoming equal at equilibrium. The gas phase adjacent to the solution then contains as much water as it can hold at that temperature and still be in equilibrium with the liquid. The partial pressure in the gas phase exerted by the water vapor in equilibrium with pure water is known as the saturation vapor pressure, P ,. [Pg.84]

The Clapeyron equation can be simplified to some extent for the case in which a condensed phase (liquid or solid) is in equilibrium with a gas phase. At temperatures removed from the critical temperature, the molar volume of the gas phase is very much larger than the molar volume of the condensed phase. In such cases the molar volume of the condensed phase may be neglected. An equation of state is then used to express the molar volume of the gas as a function of the temperature and pressure. When the virial equation of state (accurate to the second virial coefficient) is used, [Pg.234]

For a gas at temperature T and pressure P containing a single condensable vapor A with mole fraction y>A and vapor pressure pXiT), Raoult s law [j a/ = Pa( )1 provides the basis for a number of definitions. If Raoult s law is satisfied, the vapor is saturated (or equivalently, the gas is saturated with A) if VaP < Pa(T), the vapor is superheated. If A is saturated and either the temperature is decreased or the pressure is increased, A will begin to condense. If liquid A is in contact with a gas phase and the system is at equilibrium, the A vapor in the gas must be saturated. [Pg.278]

If the temperature of the system is increased, the number of liquid molecules with sufficient energy to escape into the gas phase will increase, but the number of gas molecules available to condense will not immediately be affected. Therefore, the rate of evaporation will exceed the rate of condensation until the number of molecules in the gas phase builds up, and a new and higher vapor pressure results. (If all the liquid evaporates, no equilibrium is possible.) [Pg.395]

The dew-point temperature of a gas (vapor) may be found using a method similar to that for bubble-point temperature estimation. Again, suppose a gas phase contains the condensable components A, B. C. .. and a noncondensable component G at a fixed pressure P. Let y/ be the mole fraction of component i in the gas. If the gas mixture is cooled slowly to its dew point, Tdp, it will be in equilibrium with the first liquid that forms. Assuming that Raoult s law applies, the liquid-phase mole fractions may be calculated as [Pg.260]

The solar condensation sequence The processes of vaporization and condensation are of major importance in the solar nebula. In order to systematize this process, Grossman (1972) used thermodynamic equilibria to calculate the composition of phases in equilibrium with a gas with cosmic element concentrations, at a pressure of 10 3 atm, and as a function of temperature. This work has subsequently been developed by others and is systematized in Lewis (2004). It is worth noting that in detail it is likely that the assumption of equilibrium conditions will not [Pg.42]

The adsoiption isotherm is obtained by gradually increasing the pressure. The smallest pores are filled first the gas then condenses in successively larger pores until a saturated vapour pressure level is reached at which the entire porous volume is saturated with liquid. By measuring, from Pq, the quantities of gas that remain adsorbed for decreasing relative pressure levels, the desorption isotherm is obtained. Equation (1.4) is used to ascertain, for each equilibrium pressure value, the dimension of the pores in which the liquid is in equilibrium with the vapour phase. [Pg.20]

The design engineer (a) converts the volumetric flow rate of the feed stream to a molar flow rate using the ideal gas equation of state, an approximate relationship between the pressure, temperature, volumetric flow rate, and molar flow rate of a gas (Chapter 5) (b) specifies a condenser temperature of IS C (c) calculates the mole fraction of MEK in the vapor product using Raoult s law—an approximate relationship between the compositions of liquid and vapor phases in equilibrium with each other at a specified temperature and pressure (Chapter 6) and (d) calculates the molar flow rates of the vapor and liquid products from nitrogen and MEK balances (input = output). The results follow. [Pg.151]

This concept of an ideal solution is of value because it represents the simplest kind of condensed mixture that has any pretense to physical reality although most solutions are not ideal [by the definition in equation (31)], there exist some real mixtures which are ideal, and many other solutions approach ideal behavior as they become dilute. In most cases the constants a,- in equation (31) are empirically found to have little, if any, pressure dependence, oc a (r). When the gas in equilibrium with the condensed phase is ideal f = pi), equation (31) reduces to Raoult s law, Xi p,. [Pg.534]

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