Fugacity and partial pressure

The fugacity and partial pressure of a gas are related in the same way as activities and concentrations in solution. Interaction of molecules with each other in a real gas diminishes the reactivity of an individual gas shghtly, creating an effective partial pressure called the godly. As the gas pressure approaches zero, the pressure and fugacity are equal. The interference effect on gases in the atmosphere, however. 

Since Eqs. (5) and (6) are not restricted to the vapor phase, they can, in principle, be used to calculate fugacities of components in the liquid phase as well. Such calculations can be performed provided we assume the validity of an equation of state for a density range starting at zero density and terminating at the liquid density of interest. That is, if we have a pressure-explicit equation of state which holds for mixtures in both vapor and liquid phases, then we can use Eq. (6) to solve completely the equations of equilibrium without explicitly resorting to the auxiliary-functions activity, standard-state fugacity, and partial molar volume. Such a procedure was discussed many years ago by van der Waals and, more recently, it has been reduced to practice by Benedict and co-workers (B4). 

Solubility normally is measured by bringing an excess amount of a pure chemical phase into contact with water at a specified temperature, so that equilibrium is achieved and the aqueous phase concentration reaches a maximum value. It follows that the fugacities or partial pressures exerted by the chemical in these phases are equal. Assuming that the pure chemical phase properties are unaffected by water, the pure phase will exert its vapor pressure Ps (Pa) corresponding to the prevailing temperature. The superscript S denotes saturation. In the aqueous phase, the fugacity can be expressed using Raoult s Law with an activity coefficient y ... 

For nonideal elementary reaction mixtures, the chemical activities and fugacities, respectively, must replace the concentrations and partial pressures in the above equations. 

Unless otherwise stated, concentrations and partial pressures, instead of activities and fugacities, respectively, are used here and in all following equations, for simplicity. 

The content of CO2 in snrface waters is often presented as the fugacity (or partial pressure) in solution, j Oj- example of this application is that the difference in the fugacities of CO2 between the atmosphere and the ocean is often used in gas... 

The result just obtained is applicable to any liquid-vapor equilibrium, irrespective of the behavior of the gas phase or the solution if, however, these are assumed to be ideal, equation (34.21) can be greatly simplified. For an ideal gas mixture, the fugacity /<, or partial pressure, of any constituent is proportional to its mole fraction n <, at constant temperature and total pressure ( 5b) it can be readily seen, therefore, that... 

Instead of using the difference in fugacities as the driving forces in the rate expressions, concentrations and partial pressures are commonly used. Again, dynamic equilibrium is assumed to exist at the interface and the rate of transfer across the interface is omitted in this and subsequent developments. The rate of mass transfer of component f from the liquid to the vapor phase is given by... 

When it comes to physical meaning, parameters in the thermodynamic model sometimes have meanings that are difficult to relate to the real world, as we have seen, particularly in the case of standard states. The example most relevant here is oxygen fugacity, another measure of the state of oxidation of systems, which we will consider in a later section. Oxygen fugacity is often used as a parameter in systems which contain no O2, just as water contains no free electrons. Still, there are other. systems where fugacity approximates partial pressures, and this is a link to reality that... 

It is also apparent (Fig. 6.29) that Kp correlates with the octanol-air partition coefficient, Moa. and this would follow from the fact that pl can be expressed as a linear function of Kq - In the equilibrium distribution of a compound between the vapor phase and octanol, the fugacity or partial pressure of the compound in... 

Mass transfer is always directed towards the medium with lower fugacity or partial pressure. In connection with this disequilibrium of the underground water-gas system is determined either from the degree of water saturation by component i relative to the rmderground gas, i.e., from the ratio pjp., or using disequilibrium index log p./p.)-equilibrium the saturation state is equal 1 and the index, zero. If the saturation state is greater than I (index less than 0), water is oversaturated relative the subsurface gas, if it is less (the index greater than 0), water is undersaturated. 

Equations such as those for the equilibrium constant, the reaction quotient and the Nemst equation are written mostly in terms of concentrations and partial pressures. This is correct only for very dilute solutions or ideal gases. In general, the amount of active material present appears to be less than the nominal amount measured in the customary units (in moles per litre, or in atmospheres). In order to retain the form of the equations used here and yet increase precision, thermodynamics replaces the concentration terms by the activity, which is an effective concentration, and the pressure by the fugacity, which is an effective pressure. Thus, the equilibrium constant for the reaction... 

Henry s law owes its name to William Heniy, the British chemist who reported the linearity between solubility and partial pressure in the early 1800s. The empirical observation of linearity was made independently of thermodynamics and took the force of a physical law. It is not a new physical principle, however, and the constant it introduces is fully accounted for by thermodynamics. To establish the relationship between formal quantities introduced earlier and Henry s law constant, we return to the general expression for the fugacity of a species in a mixture in eq. fio.it I. Applying this equation to the infinite dilution limit, we have... 

Use the fugacity coefficient and partial pressure of O2 to evaluate its fugacity in states 1 and 2 likewise, find the fugacity of CO2 in state 2. [You calculated the fugacity of the H2O in part (f) ]... 

All the discussion and equations in this chapter up to this point apply to solids, liquids, or gases. The rest of this section is restricted to ideal solutions of ideal gases for which we can replace the fugacities by partial pressures, ft = y,P. 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

Driving Force Gas moves across a membrane in response to a difference in chemical potential. Partial pressure is sufficiently proportional to be used as the variable for design calculations for most gases of interest, but fugacity must be used for CO9 and usually for Hg... 

The heart of the question of non-ideality deals with the determination of the distribution of the respective system components between the liquid and gaseous phases. The concepts of fugacity and activity are fundamental to the interpretation of the non-ideal systems. For a pure ideal gas the fugacity is equal to the pressure, and for a component, i, in a mixture of ideal gases it is equal to its partial pressure yjP, where P is the system pressure. As the system pressure approaches zero, the fugacity approaches ideal. For many systems the deviations from unity are minor at system pressures less than 25 psig. 

Where R is the gas constant, T the temperature (K), Fthe Faraday constant and H2 is the relative partial pressure (strictly, the fugacity) of hydrogen in solution, which for continued evolution becomes the total external pressure against which hydrogen bubbles must prevail to escape (usually 1 atm). The activity of water a jo is not usually taken into account in elementary treatments, since it is assumed that <7h2 0 = U nd for dilute solutions this causes little error. In some concentrated plating baths Oh2 0 I O nd neither is it in baths which use mixtures of water and miscible organic liquids (e.g. dimethyl formamide). However, by far the most important term is the hydrogen ion activity this may be separated so that equation 12.1 becomes... 

Dalton s law is based on the assumption of ideal gases so that each behaves independently and exerts the same partial pressure as it would il alone in the container. The Lewis and Randall rule assumes that the fugacitv of the gases is independent so that the gas has the same fugacity coefficient as it would have at the same total pressure when other gases were not present. 

As mentioned above, activities are correctly represented by fugacities and not by partial pressures. Hence, the correct form of Eq. (22) is ... 

Po is the standard pressure and px is the partial pressure of component X. Rearrangement of Eq. (56) leads to a third-order equation in t, which can be solved iteratively. Notice that the pressures used in Eq. (55) should actually be replaced by activities, implying that they should be corrected by their respective fugacity coefficients, which are of importance when dealing with methanol and water. We leave it as an exercise for the reader to judge the influence of such effects, utUizing the relation between pressure and activity given in Eq. (39) of Chapter 2. 

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