Fugacity of gases

The fugacities of gases such as CO2 and O2 can be buffered (Fig. 2.1 see Chapter 14) so that they are held constant over the reaction path. In this case, mass transfer between the equilibrium system and the gas buffer occurs as needed to maintain the buffer. Adding acid to a C02-buffered system, for example, would be likely to dissolve calcite,... 

SOLVEQ is a program for computing PC multicomponent homogeneous chemical equilibria in aqueous systems. For a given temperature and total composition of a homogeneous aqueous solution, it computes the activities of all aqueous species and the saturation indices of solids and the fugacities of gases. 

The limiting behavior ensures that the fugacities of real gases approach those of the ideal gas in the limit of low pressure. Since at low pressures the fugacity and pressure become the same, it should be clear that fugacities will be expressed in the same units as pressure, Pa, MPa, atm, Torr, etc. 

Figure 6.4 Fugacity coefficients of gases in terms of the reduced pressure and temperature. Based on data taken from B. W. Gamson and K. M. Watson, Natl. Petrol. News, Tech. Sec. 36, R623 (Sept. 6, 1944).

Activity is a dimensionless quantity, and / must be expressed in kPa with this choice of standard state. It is inconvenient to carry f° = 100 kPa through calculations involving activity of gases. Choosing the standard state for a gas as we have described above creates a situation where SI units are not convenient. Instead of expressing the standard state as /° = 100 kPa, we often express the pressure and fugacity in bars, since 1 bar = 100 kPa. In this case, /0 — 1 bar, and equation (6.92) becomes4... 

With the standard state expressed in this manner, the activity of the gas becomes the fugacity expressed in bars. We will usually follow this convention as we work with activities of gases. An added convenience comes from being able to relate fugacity to pressure through the fugacity coefficient [Pg.284]

When dealing with an ideal mixture of gases (that do not behave ideally themselves), the fugacity of gas X is given by... 

The fugacity of species B in an ideal solution of gases is given by the Lewis and Randall rule... 

The feed stream consists of 60 mole percent hydrogen, 20% nitrogen, and 20% argon. Calculate the composition of the exit gases, assuming equilibrium is achieved in the reactor. Make sure that you take deviations from the ideal gas law into account. The equilibrium constant expressed in terms of activities relative to standard states at 1 atm may be assumed to be equal to 8.75 x 10 3. The fugacity of pure H2 at 450 °C and 101.3 MPa may be assumed to be equal to 136.8 MPa. 

In the simplest class of geochemical models, the equilibrium system exists as a closed system at a known temperature. Such equilibrium models predict the distribution of mass among species and minerals, as well as the species activities, the fluid s saturation state with respect to various minerals, and the fugacities of different gases that can exist in the chemical system. In this case, the initial equilibrium system constitutes the entire geochemical model. 

Fixed-activity and sliding-activity paths (Sections 14.2-14.3) are analogous to their counterparts in fugacity, except that they apply to aqueous species instead of gases. Fixed-activity paths are useful for simulating, for example, a laboratory experiment controlled by a pH-stat, a device that holds pH constant. Sliding-... 

Having determined the distribution of species in solution, we can also calculate the fugacity of the various gases with respect to the fluid. For any gas An in the database that can be composed from the component set, we can write a reaction,... 

Analogous examples of nonuniqueness can be constructed using any mineral or gas of intermediate oxidation state. Buffering the fugacity of N2(g) or S02(g), for example, would be a poor choice for constraining oxidation state, since the gases can either oxidize to NO3 and SO4 , respectively, or reduce to NH4 and H2S(aq) species. 

Most applications in materials science are carried out under pressures which do not greatly exceed 1 bar and the difference between/and/ is small, as can be seen from the fugacity of N2(g) at 273.15 K [15] given in Figure 2.11. Hence, the fugacity is often set equal to the partial pressure of the gas, i.e./ p. More accurate descriptions of the relationship between fugacity and pressure are needed in other cases and here equations of state of real, non-ideal gases are used. 

In mixtures of real gases the ideal gas law does not hold. The chemical potential of A of a mixture of real gases is defined in terms of the fugacity of the gas, fA. The fugacity is, as discussed in Chapter 2, the thermodynamic term used to relate the chemical potential of the real gas to that of the (hypothetical) standard state of the gas at 1 bar where the gas is ideal ... 

Equation 2.63 is valid for any homogeneous or heterogeneous reaction. The only difference is in the definition of activities. For a species in a perfect gas-phase mixture a = pi/p°, where pi is the partial pressure of species i andp° is the standard pressure (1 bar). For a real gas-phase mixture a =f/p°, where is the fugacity of i. The fugacity concept was developed for the same reason as the activity to extend to real gases the formalism used to describe perfect gas mixtures. In the low total pressure limit (p -> 0), fi = pi. 

A few gases may be involved in some enzyme reactions, e.g., C02 and 02 as used by carbonic anhydrase and produced by catalase, respectively. If the presence of such dissolved gases affects rates and equilibria at ordinary pressure, their importance will increase at higher pressure. Henry s law says that the partial pressure of a gas above a solution is proportional to its mole fraction in the solution. At high pressure it is more correct to speak of the fugacity / of a gas, instead of partial pressure, in the same sense that one uses activity instead of concentration in solution calculations. In dilute solutions, the fugacity of the dissolved gas is given by... 

Now that we have obtained expressions for the fugacity of a real gas and its temperature and pressure coefficients, let us consider the application of the concept of fugacity to components of a mixture of real gases. 

As the evaluation of Equation (10.86) requires a great deal of data, and as adequate data are available for only a few mixtures of gases, it is useful to have approximate relationships that can be used to estimate the fugacity of components in a solution of gases. 

Then, Kp can be obtained at any pressure at which the fugacities of the pure gases are available. 

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