Ideal gas solution

Like molecules of an ideal gas, solute particles are widely separated in very dilute solutions and do not interact significantly with one another. For very dilute solutions, osmotic pressure, tt, is found to follow the equation... 

As a first guess, use ideal gas solution for pressure. (Also try some neighboring pressures.) My solution is... 

Once again, the ideal gas solution is seriously in error. 

With eight equations (Eqs. h-o) and eight unknowns, this problem can be solved, though the solution is a trial-and-error process. In general, a reasonable first guess for the pressure in the nonideal gas problem is the ideal gas solution, which was... 

From the Maxwell-Stefan theory for multicomponent diffusion, Taylor and Krishna (1993) developed the following scheme to estimate the matrices of zero-flux multicomponent mass-transfer coefficients from binary-pair mass-transfer coefficients, Fy. These are obtained from correlations of experimental data, with the Chan and Fair (1984) correlations being the most widely used. For an ideal gas solution ... 

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

This work was done by mixing two or more liquid components in known proportions, then equilibrating the liquid with its own vapor and measuring the composition of the vapor. Because the total vapor pressure (also measured) was relatively low (generally well below one atmosphere) the vapor behaved as an ideal gas solution, and the partial pressures of the components could be calculated from their compositions using Dalton s Law. Of the many systems investigated, a very few were found to exhibit a particularly simple relationship between the vapor partial pressures and the liquid composition. In these systems, for all compositions, the partial pressures of the gas constituents were found to be a linear function of their mole fractions in the liquid. That is, in the binary system A-B,... 

From (4-61), with the assumptions of the idea) gas law and an ideal gas solution, vapor enthalpy is simply... 

The empirical equations for are applicable at reduced temperatures from 0.5 to 1.3. When the vapor is an ideal gas solution obeying the ideal gas law and the liquid solution is ideal, p"l is the ideal K-value. 

Solution. Both product temperatures and pressures are equal to those of the feed. Because the components are similar in molecular structure and the pressure is 1 atm, all streams entering and leaving the process are ideal gas solutions that follow the ideal gas law. Therefore, (17-9) can be used to compute the minimum rate of work. Note that the temperature of the surroundings To is also the ambient temperature, which is taken as SStFR. 

If all streams enter and leave the process as gases at the same temperature and pressure and form ideal gas solutions and follow the ideal gas law, (— IVmi ) in (17-9) is equal to AB. If all streams enter and leave the process as liquids at the same temperature and the same low pressure, (- Wmj ) in (17-11) is equal toAB. Otherwise AB must be calculated from entering and leaving stream enthalpies and entropies. 

It is convenient to represent the departure from both types of ideality (ideal gas law and ideal gas solution) by defining the following mixture fugacity coefficients. 

Let us assume that in a sufficiently diluted solution molecules of the dissolved components are so disconnected between themselves by the solvent that their interaction may be disregarded. To such solutions are applicable the laws of infinitely diluted solutions, which are analogous to the laws of ideal gas solution. 

According to the theory of state of ideal gas solution, change of the free enthalpy of each component i at constant temperature depends only on its partial pressure according to Equation... 

In the final state, pressure is lower and the compressibility factor is expected to be even closer to i. In both states, therefore, the compressibility factor is sufficiently close to i to assume ideality. Nonetheless, the ideal-gas solution overestimates the final temperature by 8 °C. 

For illustration purposes, we have also included in these graphs the properties of two limiting cases, a solute in the ideal solution (IS), that is, the pure solvent, and the ideal gas solute (IG). These cases are very convenient references because they encompass two extreme molecular asymmetries, that is, nonzero intermo-lecular interactions with null solute-solvent asymmetry, and zero solute-solvent interactions, respectively. As the solute-solvent interactions become less repulsive, (3/7/3x )r,p, x) > 0 approaches its value for the ideal gas solute, (9p/3x )r,p,ixi =... 

There is only one kind of ideal gas solution, as discussed above, but there are two kinds of ideal liquid and solid solutions. 

The partial pressure variable, x , in Eq. (11) for the gas, g, in an ideal gas solution provides a convenient correspondence to the mole fraction, Xy > for solute, in an ideal liquid solution. The basis for the correspondence between flie partial pressxure of an ideal gas, x , and the mole fraction of a solute, Y y, in an ideal solution, Xy > comes from Lewis concept of escaping tendency. 

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