Equilibrium coefficients for

At low temperatures, using the original function/(T ) could lead to greater error. In Tables 4.11 and 4.12, the results obtained by the Soave method are compared with fitted curves published by the DIPPR for hexane and hexadecane. Note that the differences are less than 5% between the normal boiling point and the critical point but that they are greater at low temperature. The original form of the Soave equation should be used with caution when the vapor pressure of the components is less than 0.1 bar. In these conditions, it leads to underestimating the values for equilibrium coefficients for these components. 

When a recovery well is located within a contaminant plume and the pump is started, the initial concentration of contaminant removed is close to the maximum level during preliminary testing. As the pump continues to operate, cleaner water is drawn from the plume perimeter through the aquifer pores toward the recovery well. Some of the contaminant is released from the soil into the water in proportion to the equilibrium coefficient. For example, if the Kd is 1000, at equilibrium, 1 part is in the water and 1000 parts are retained in the soil. If the water-soil contact time is sufficient, complete equilibrium will be established. After the first pore volume flush (theoretically), the concentration in the water will be 0.9 and that on the soil will be 999. With each succeeding flush, the 1000 1 ratio will remain the same. If the time of water-soil contact is not sufficient to establish equilibrium, the recovered water will contain a lesser concentration. A typical decline curve is shown on Figure 9.2. Note the asymptotic shape of the curve where the decline rate is significantly reduced. 

We can write the absorption equilibrium coefficients for A and B in terms of their partial pressures (PA and PB) and the concentration of open sites (Cs) ... 

F — Molar flow for / sfream Xj-j — Mole fraction of component in / sfreom Kj — Phose-equilibrium coefficient for the component The design variables are ... 

The corresponding equilibrium coefficient for reaction j in the mixture 3delds ... 

In addition, the method assumes a constant equilibrium coefficient for each com-... 

No experimentally determined value for the equilibrium coefficient for reaction... 

For reactions controlled by activation, solvation effects on the reagents and the transition state can affect the equilibrium coefficient for the formation of the transition state and therefore the reaction rate. Equilibria can also be affected by solvation effects on reagents and products. In a supercritical fluid, solvation effects can be controlled by density, and therefore at constant... 

Interfacial equilibrium coefficient for each component that represents the ratio of the bulk gas-phase mole fraction to the interfadal molar density in the liquid phase, multiplied by the inlet molar density of liquid benzene. 

In many cases (actually, the majority of them), a given reaction will be reversible, meaning that instead of reacting to completion, it will stop at a certain point and not go any farther. How far the reaction goes is dictated by the value of the equilibrium coefficient. Recall from general chemistry that the equilibrium coefficient for the reaction aJi + bB — cC + dD is defined as follows ... 

The intrinsic separation of lanthanide ions on sulfonic acid resins is minimal. They typically offer only a few parts-per-thousand separation factors (ratio of distribution ratios or extraction equilibrium coefficients) for adjacent lanthanide ions, as is shown in fig. 2 (Marcus 1983, Surls and Choppin 1957). Values reported for gadoliniiun numbers (ratio of distribution coefficients normalized to Gd) in 0.01 M HCIO4 vary almost linearly across the series while the 0.11 M HCIO4 data show better selectivity for the light lanthanides... 

The complexation equilibrium coefficients for the respective reactions (15-17) are rigorously a function of the ratio of the ionic activities of the species ... 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

IF BINARY SYSTEM CONTAINS NO ORGANIC ACIDS. THE SECOND VIRTAL coefficients ARE USED IN A VOLUME EXPLICIT EQUATION OF STATE TO CALCULATE THE FUGACITY COEFFICIENTS. FOR ORGANIC ACIDS FUGACITY COEFFICIENTS ARE PREDICTED FROM THE CHEMICAL THEORY FOR NQN-IOEALITY WITH EQUILIBRIUM CONSTANTS OBTAINED from METASTABLE. BOUND. ANO CHEMICAL CONTRIBUTIONS TO THE SECOND VIRIAL COEFFICIENTS. 

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). 

The equilibrium constant for this ion-exchange reaction, which is also called the selectivity coefficient, is... 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

Table 3. Equilibrium Segregation Coefficients for Impurities in Silicon...

Kl Xbm /cl x bm kc y yt When the equilibrium cui ve is a straight line, the terms in parentheses can be replaced by the slope m as before. In this case the overall mass-transfer coefficients for concentrated systems are related to each other by the equation... 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

The solubility coefficient S is used as a measure of water solubility. It is the ratio between the concentrations in water and air phases at equilibrium. Ethanol, a very soluble gas, has a solubility coefficient of 1 100 at, 37 C while the coefficient for nitrous oxide, a poorly soluble gas, is 0.1.5. 

The case with k = 0.4 s (open squares) is close to the situation where mass transfer resistance is negligible. These differences are due to mass transfer resistances as we can easily conclude by comparing the separation regions obtained for the cases with k = 0.4 and k = 1 s k If mass transfer resistance is important, the region of complete separation can be significantly reduced from the one obtained by the Equilibrium Theory. For example, for a mass transfer coefficient of k = 0.1 s there is no separation region where extract and raffinate are 99.5 % pure. 

Kj = equilibrium distribution coefficient for component, i Kf = equilibrium distribution coefficient for component to which relative volatilities are referred... 

Figure 8-129. Discharge coefficients for vapor flow, sieve trays. Used by permission, Smith, B. O., Design of Equilibrium Stage Processes, Chapter 15, by J. R. Fair, McGraw-Hill Book Co. (1963) data from I. Liebson, R. E. Kelley, and L. A. Bullington, Petroleum Refiner, V. 36 (2), Feb. (1957) p. 127 V. 36 (3), (1957) pg. 288, all rights reserved.

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