Law, Raoult

Henry s law Raoults law Osmotic pressure Boiling point... 

By assuming EDC and C2H4 form an ideal solution, the mol fraction of ethylene dissolved in the liquid can be estimated, from Raoults Law (see Chapter 8). 

The chemical potential jU, of the components of an ideal mixture of liquids (the components of an ideal mixture of liquids obey the Raoult law over the whole range of mole fractions and are completely miscible) is... 

The standard term p is the chemical potential of the pure component i (i.e. when Xj = 1) at the temperature of the system and the corresponding saturated vapour pressure. According to the Raoult law, in an ideal mixture the partial pressure of each component above the liquid is proportional to its mole fraction in the liquid,... 

The activities of the polymer and monomer of the hypothetical solutions given in Figure 9.6(a) are shown in Figure 9.6(b). While r = 1 corresponds to Raoult law behaviour, strong negative deviations are observed for r = 10, 100 and 1000. 

The Raoult law, the decrease of vapour pressure ps of a solution proportional to the solute concentration is a consequence of the model too. Solute molecules of which the own vapour pressure can be neglected have to be in the holes of the model (Fig. 1 right). Therefore, ps of the solvent decreases corresponding to Raoult s law. Now this effect is reduced by the increase of the sum of pair potentials because the coordina-... 

In more fundamental terms, the solubility of a chemical in water is determined by the activity coefficient in water yw which can be viewed as a "correction factor" to Raoults Law, i.e.,... 

Besides, let us note the automatic observance (certainly with correctly set initial data) and, hence, needlessness of the formalized descriptions in equilibrium modeling of such important regularities of macroscopic system behavior as the Gibbs phase rule, the Le Chatelier-Brown principle, mass action laws, the Henry law, the Raoult law, etc. 

The solvent and the key component that show most similar liquid-ph ase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The activity coefficient of this key approaches unity, or may even show negative deviations from Raoults law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoults law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often a very large number. 

The relation Rpx = P"/x[ is simply a reformulation of Raoult Law when applied to the solvent. Any of the other relations are equivalent to Henry s Law when applied to the solute. Rxx = x [ x[ is also known as the Nernst Distribution Law. 

A comparison between Gy and Gy for the methanol—water system showed that in that case they were close to each other. However, as was already pointed out, the use of a reference state is particularly important for the systems with small deviations from the Raoult law. In such cases, the reference state based on Gy provides results very different from those based on Gjf. 

Glycol mononitrate has aroused a certain amount of interest. Twist and Baughan (109) examined the vapour pressure of the solution of this substance, and of a number of other nitrate esters, and found the deviations from Raoult laws to be of the same order as those observed by Chedin and Vandoni for nitrocellulose [110]. Prior to this work Marans and Zelinski (III] prepared a number of mixed esters of the type XI where R are unsaturated acyls apt to polymerize and thus to give combustible polymers. 

Rgure 8-9. Acetone (1)-chloroform (2) system at 760 mm Hg. Maximum boiling azeotrope formed by negative deviations from Raoult Law (dashed lines). Used by permission. Smith, B.D., Design of Equilibrium Stage Processes, McGraw-Hiil, New York, (1963), all rights reserved. 

In order to better demonstrate whether a system follows Raoult s law, a diagram of the phase equilibrium called T-x-y should be plotted. This plot (Figure 2) shows the equilibrium temperatures at which either a liquid solution will start bubbling (bubble curve) or a vapor mixture starts condensing (dew curve). The two systems with their experimental data and the calculation curve of the ideal solution is shown in Figure 2. In Figure 2, the system of hexane-benzene at the pressure of 101.33 kPa [10] and the system of ethylacetate-benzene [11] show negative deviations from RaoulTs law. 

Example 3 Detv and Bubble Point Calculations As indicated by Example 2a, a binary system in vapor/liquid equilibrium has 2 degrees of freedom. Thus of the four phase rule variables T, P, x, and t/i, two must be fixed to allow calculation of the other two, regardless of the formulation of the equilibrium equations. Modified Raoults law [Eq. (4-307)] may therefore be applied to the calculation of any pair of phase rule variables, given the other two. 

By equation (31.5), the activity of the solvent is equivalent to fi/fi where fi is the fugacity in a given solution and / is numerically equal to that in the standard state, i.e., pure liquid at 1 atm. pressure at the given temperature. Hence, it is seen from equation (34.1) that for an ideal solution the activity of the solvent should always be equal to its mole fraction, provided the total pressure is 1 e m. In other words, in these circumstances the activity coefficient ui/ni should be inity at all concentrations. For a nonideal solution, therefore, the deviation of ai/Ni from unity at 1 atm. pressure may be taken as a measure of the departure from ideal (Raoult law) behavior. Since the activities of liquids are not greatly affected by pressure, this conclusion may be accepted as generally applicable, provided the pressure is not too high. 

Estimate the vapor pressure of the two components in a regular solution for which cAh/(RT) = 1 and = 0.4 given that the vapor pressure of pure component A is 15.0 kPa and that of pure B, 20.0 kPa. Also calculate the Raoult law activity coefficients. Repeat the calculation for the case that cAh/(RT) = -1. 

Fig. 1.9 Vapor pressure for a hypothetical regular solution for which cAh(RT = 1 plotted against the mole fraction of component B. The vapor pressure of pure component B is 26.7 kPa, and that of component A, 20.0 kPa. The broken lines show Raoult law behavior.

Using Wilson s parameters for the carbon tetrachloride-acetonitrile system, estimate the Raoult law activity coefficients for each component in a equimolar solution. Then estimate the molar Gibbs energy of mixing. 

From the theory for regular solutions, the Raoult law activity coefficient for component B in a solution of A and B is... 

Table 1.4 Raoult Law and Henry Law Activity Coefficients for Dilute Solutions of Methanol in...

This is the form of the Gibbs-Duhem equation needed to relate the activity of component B in solution to that of component A. Choosing the Raoult law activity for the solvent A, and the Henry law activity for the solute B, equation (1.13.4) may be rewritten as... 

It should be noted that the values of quickly become non-unity and are greater than one. This is indicative of strong attractive solute-solvent interactions and negative deviations from Raoult law behavior. In the case of the methanol water system for which positive deviations from Raoult s law is observed (table 1.4), the Hemy law activity coefficients are less than one. 

Use an interpolation method to obtain the values of the mole fraetion of CCI4 in the vapor and the total vapor pressure for values of the mole fraetion in the liquid phase equal to 0.2, 0.4, 0.6, and 0.8. Then calculate the vapor pressure and the activity coefficient of each component for the same values. Finally estimate the molar Gibbs energy of mixing on the Raoult law scale at these four points. 

Calculate the Raoult law activity coefficients of both components and plot them as a function of the mole fraction of acetone. Determine the range of composition with respect to acetone that the solution can be regarded as regular. Calculate the enthalpy parameter for acetone-chloroform interactions on the basis of a one-parameter least-squares fit of the data in this range using an appropriate plot. 

Calculate the Raoult law and Henry law activity coeiScients for methanol on the mole fraction scale. 

The symmetrical ideal behavior is equivalent to the well-known Raoult law. Suppose that a mixture of A and B is in equilibrium with an ideal-gas phase let PA be the partial pressure of A. The chemical potential of A in the gas phase is... 

To integrate this we must know of some relation between p and n This is given by the approximate Raoult Law, namely, that—... 

Non-ideal Solution A solution formed by mixing two liquids is said to be non-ideal if it does not obey Raoults law or the interactions of A and B molecules in the solution are not similar to those of pure A and pure B or D V 1 0 and... 

Taking 80°C as the normal boiling point of the mixture, applying Raoults law,... 

The next step for the calculation of the number of theoretical trays is to make a material balance around the tower bottom (it can also be started from the tower top). The concentrations of the components in the ascending vapor stream are calculated from equilibrium equation (Dalton Raoult laws) for the existing mixture composition in the tower bottom (5.3). 

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