Real gases fugacity

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

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. 

That is, as the pressure approaches zero, the fugacity approaches the pressure. Figure 10.5 indicates the relationship between P and/for ideal and real gases. The standard state for a real gas is chosen as the state at which the fugacity is equal to 0.1 MPa, 1 bar, along a line extrapolated from values off at low pressure, as indicated in Figure 10.5. The standard state for a real gas is then a hypothetical 0.1 MPa standard state. 

The ratio of the fugacity/2 at the pressure P2 to the fugacity/i at the pressure Pj can be obtained by graphical or numerical integration, as indicated by the area between the two vertical lines under the isotherm for the real gas in Figure 10.6. However, as Pi approaches zero, the area becomes infinite. Hence, this direct method is not suitable for determining absolute values of the fugacity of a real gas. 

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. 

MPa). Also, a pressure, usually near 1 bar, will exist at which the real gas has a fugacity of unity. bar also real gas at zero pressure. (See Exercise 1, this chapter.) (0.1 MPa). Also, a pressure of the real gas will exist, not zero and not that of unit fugacity, with an entropy equal to that in the standard state. (0.1 Mpa). V =(RT/P°). 

In defining activities in a real gas mixture, the partial pressure of each component is replaced by its fugacity, fx... 

Fugacity is a thermodynamic property related to the deviation of the p—V—T properties of the gas from those of an ideal gas. At very low pressures, the fugacity of a real gas tends to its partial pressure... 

In the absence of experimental measurements, it is usual to calculate the fugacities of components in a real gas mixture using the Lewis and Randall rule... 

Fugacity may be defined as a substitute for pressure to explain the behaviour of real gas and activity may be defined as the substitute for the concentration to explain the behaviour of a non-ideal solution. 

Accdg tp Ref 2, fugacity is a quantity which measures the true escaping tendency of a gas, a sort of idealized pressure. If primes and double primes refer, respectively, id an ideal gas and a real gas, then dF V dp = RTdlnp, and dF" = v"dp = RTdlnf,... 

The first term on the right-hand side is the idea gas limit, and the remaining -logarithmic terms express the successive virial corrections for the real gas behavior. It is evidently most convenient for this problem to choose the standard state pressure as P° = 0, where all gases are ideal. With this choice, we can write the relationship between fugacity and pressure as... 

Note that fugacity simply replaces pressure in an ideal gas equation to form a real gas equation. Fugacity has pressure units. Equation 15-4 merely states that at low pressures the fluid acts like an ideal fluid. 

One method of calculating fugacity and hence y is based on the measured deviation of the volume of a real gas from that of an ideal gas. Considet the case of a pute gas The ftee energy F and chemical potential /i changes with pressure according to the equation... 

Gas (g). The standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

Fugacity, /, corresponds to a pressure, P whilst f, the fugacity of a component, i, behaves in a similar way to partial pressure, both adjusted to represent the departure from ideality. / therefore plays the same role for a real gas as pressure, P does for an... 

It has already been mentioned that the state of an ideal gas at the temperature of the system and the pressure of 1 atmosphere is most frequently chosen as the standard state of gases. The idea of such an ideal gas can be explained by the imagination of a real gas which is first expanded to zero pressure and then by means of isothermal compression compressed to 1 atm. into the region of the ideal gas. As with an ideal gas pressure equals fugacity, we can substitute in equation (V-8a) p° = f° — 1, whereby the following equation is obtained ... 

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