Lewis fugacity rule

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 ... 

To use Equation (13), it is first necessary to calculate the true fugacity coefficient (ft. This calculation is achieved by utilizing the Lewis fugacity rule... 

The Lewis fugacity rule is used for calculating the fugacity coefficients of the true species, and (2) the second virial co-... 

The limits of the Lewis fugacity rule are not determined by pressure but by composition the Lewis rule becomes exact at any pressure in the limit as y( - 1, and therefore it always provides a good approximation for any component i which is present in excess. However, for a component with small mole fraction in the vapor phase, the Lewis rule can sometimes lead to very large errors (P5, R3, RIO). 

L termination, 62-63 Lewis fugacity rule, 144-145 Liquid-liquid equilibria in binary systems, 184-190 in ternary systems, 194-203 phase diagram, 196-202... 

An ideal liquid solution must obey Raoult s Law and the Lewis Fugacity Rule (just like an ideal gas solution). 

Fig. 11.6. A binary system (solution) that obeys the Lewis Fugacity Rule. The solution can be liquid, solid, gas, or supercritical fluid, although generally this rule is used for the latter two.

This relationship, the Lewis Fugacity Rule, is a kind of variation of Dalton s Law, and has been widely used to estimate fugacities in gas mixtures (Prausnitz, 1969). 

Although the Lewis Fugacity Rule is generally used for gas or supercritical solutions, it is particularly interesting to see what results when a condensed phase in equilibrium with such a phase is considered, just as we first considered Dalton s Law and then a condensed phase in equilibrium with a solution obeying Dalton s Law. 

Comparison of equations (11.19) and (11.26) shows that for solutions that obey the Lewis Fugacity Rule. , ... 

Fig. 11.7. Normalized fugacities in a binary system obeying the Lewis Fugacity Rule. Figure 11.6 is converted to this diagram by dividing the fugacity of each component by the fugacity of the pure component. The mole fraction axis can now be used for the original system or for a phase equilibrated with it.

This leads to the easiest approach to understanding activities. The activity of a constituent is the ratio of the fugacity of that constituent to its fugacity in some other state, which we called a reference state. We then showed through consideration of the Lewis Fugacity Rule, which is an extension of Dalton s Law, that for ideal solutions of condensed phases, the activity of a constituent equals its mole fraction, if the reference state is the pure constituent at the same P and T. Deviations from ideal behaviour are then conveniently handled by introducing Henryan and Raoultian activity coefficients. 

Moving one step closer to reality, the Lewis Fugacity Rule (described in Chapter 11) is frequently used to approximate the behavior of real gas mixtures... 

Fig. 16.4. Solubility of liquid decane in nitrogen gas at 50°C, calculated from Henry s Law coefficient and decane fugacities based on ideal gas and Lewis Fugacity Rule approximations and the virial equation. Experimental data are solid dots. After Prausnitz (1969)...

This is the Lewis fugacity rule, and is seen to be true if Amagat s law is true. So fluids can mix ideally volumetrically, but might still be nonideal mixtures. Note that it assumes the additivity of the molar volumes of all components of... 

But it is not necessary to set / " = 1 bar, just convenient in many cases. Another option, fairly common in geochemistry though not in chemistry, is to let /° = and to define the standard state pressure as the system pressure. In this case, we compare the fugacity of i with the fugacity of pure / at the same T and P. If the Lewis fugacity rule ( 8.1.3) holds, this is the same as using the mole fraction of i, but normally this wiU be only approximately true. 

Volumetric ideal mixing (Equation 10.4) is also called Amagat s law, which we saw was connected to the Lewis fugacity rule in Chapter 8. 

Find the fugacity and fugacity coefficient of gaseous species / as a pure species and in a mixture using tables, equations of state, and general correlations. Identify the appropriate reference state. Write the Lewis fugacity rule, state the approximation on which it is based, and identify the conditions when it is likely to be valid. 

This approximation is known as the Lewis fugacity rule and will be discussed in more detail shortly. 

This approximation is known as the Lewis fugacity rule. It approximates all interactions in the mixture as being identical to the i-i interaction and simplifies calculations significantly because the pure species fugacity coefficient does not depend on the other species in the mixture but rather depends only on T and P (e.g., compare the complexity of Examples 7.2 and 7.4). 

As a first approximation, we can use the Lewis fugacity rule and base the fugacity coefficient on the pure species value, as discussed in Section 7.3. This approach treats all the interactions as the same i-i interactions). The advantage of this approach is that mixing rules are not needed, and it is mathematically much... 

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