Real gases, fugacity activity coefficients

Most complex phenomena are made tractable using cases that are far simpler than the real phenomena. Examples of this type of approach abound in many areas of sci-ence/engineering starting with the ideal gas law for predicting fluid properties. This ideal case is then considered as the basis, and the deviations from this ideal case (fugacity/activity coefficient) represent the behavior of the real system. In the case of turbulence, two classes are defined. 

The fugacity, considered as the thermodynamically effective pressure /, equals the measured pressure p exactly in the case of ideal gases only. In the case of real gases both values differ by the so called activity coefficient Yj the value of which depends on the given state of the gas ... 

Ideal A/B mixtures that can be described by Raoult s law do not exist in practice. Generally, mixtures that have a more or less pronounced real behavior are encountered. The deviations from ideal behavior are taken into account by correcting factors known as activity coefficients y in the case of the liquid phase or fugacity coefficients 0 in the case of the gas phase (Equation 2.3.2-10 see also Section 3.3.2) ... 

In these equations addends J rdnic, and i T-lny. characterize deviation of the solutions from ideal and the work, which is necessary to expend in order to squeeze 1 mole of component i of the ideal solution into real solution. Activity coefficients can be greater or smaller than 1. When pressure of a gas solution or concentration of dissolved substances tends to 0, fugacity coefficients or activities coefficients approach 1. Even in diluted real solutions charged ions and dipole molecules experience electrostatic interaction, which shows up in a decrease of activities coefficient. Only in very diluted solutions this interaction becomes minuscule, and fugacity and activities values tend to values of partial pressure and concentration, respectively. Table 1.3 summarizes calculation formulae for activities values of groxmd water components under ideal and real conditions. 

That basic strategy is illustrated in Table 6.1. First we define an ideal mixture whose properties we can readily determine. Then for real mixtures we compute deviations from the ideality as either difference measures or ratio measures. In one route the ideality is the ideal-gas mixture, the difference measures are residual properties, and the ratio measure is the fugacity coefficient. In the other route the ideality is the ideal solution, the difference measures are excess properties, and the ratio measure is the activity coefficient. 

The form taken by the equilibrium constant depends on the type of expression which is substituted in the above equation for the purpose of expressing the chemical potentials in terms of the composition this in its turn dex>ends on additional physical knowledge concerning whether or not the real system in question may be approximately represented by means of a model, such as the perfect gas or the ideal solution. If the system does not approximate to either of these models it is still possible, of course, to formulate an equilibrium constant in terms of fugacities or in terms of mole fractions and activity coefficients. However, this isapurely formal process the fugacities and activity coefficients are themselves defined in terms of the chemical potentials and therefore the knowledge contained in equation (10 1) is in no way increased, but is obtained in a more convenient form. 

Thus for liquid-liquid reactions, a similar approach is used as for real gas equilibria as discussed above in Section 4.2.2. For gas-phase reactions, we use the ratio of the fugacity to the standard pressure po (=fi o) instead of the activity O , and the fugacity coefficient activity coefficient /j (= Oj/jq). Thus we have an ideal gaseous system for j)=pi, that is, ideal liquid system for a = Xi, that is, /i = 1. 

The activity coefficient of a gas is also known as the fugacity coefficient and is sometimes denoted by (pi instead of by y,. If the value of the activity coefficient of a real gas is greater than unity, the gas has a greater activity and a greater chemical potential than if it were ideal at the same temperature and pressure. If the value of the activity coefficient is less than unity, the gas has a lower activity and a lower chemical potential than if it were ideal. 

In the gas phase, the activity a, =fjp , where is the fugacity of the component at T (not necessarily T = 298 K) and / = 1 bar, the standard state pressure. This is a dimensionless term. Similarly, if a,- is set to for a real solution, where is the molar fraction and is the related dimensionless activity coefficient for the ith component, all a/s and thus K remain dimensionless quantities. 

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