Gas, ideal solubility

FinoteUo A, Bara JE, Narayan S et al (2008) Ideal gas solubilities and solubility selectivities in a binary mixture of room-temperature ionic liquids. J Phys Chem B 112 2335-2339... 

Characterization of the solvent power of supercritical fluids is often quantified by the enhancement factor. The enhancement factor is the ratio of the actual solubility to the ideal gas solubility at the same temperature... 

The first term A is for ideal gas solubility, the second term B accounts for the non-ideality, while the third term C (Poynting correction) accounts for the pressure effects. The product of the second and third terms is often referred as the Enhancement Factor (over the ideal). In the absence of data, the sublimation pressure may be approximated through extrapolation of the vapor pressure information. 

To understand the role of solute-solvent interac tions on solubilities and selectivities, it is instructive to define an enhancement factor, E, as the ac tual solubility, y9, divided by the solubility in an ideal gas, so that E = where P is the vapor pressure. This factor is a normahzed... 

Also of importance is the effect of temperature on the gas solubility. From this information it is possible to determine the enthalpy and entropy change experienced by the gas when it changes from the ideal gas state (/z and ) to the mixed liquid state ( andT,). 

The simplest method to measure gas solubilities is what we will call the stoichiometric technique. It can be done either at constant pressure or with a constant volume of gas. For the constant pressure technique, a given mass of IL is brought into contact with the gas at a fixed pressure. The liquid is stirred vigorously to enhance mass transfer and to allow approach to equilibrium. The total volume of gas delivered to the system (minus the vapor space) is used to determine the solubility. If the experiments are performed at pressures sufficiently high that the ideal gas law does not apply, then accurate equations of state can be employed to convert the volume of gas into moles. For the constant volume technique, a loiown volume of gas is brought into contact with the stirred ionic liquid sample. Once equilibrium is reached, the pressure is noted, and the solubility is determined as before. The effect of temperature (and thus enthalpies and entropies) can be determined by repetition of the experiment at multiple temperatures. 

Fig. 10. The mole fraction of carbon dioxide in saturated solutions in air at — 110°C (above the lower critical end point). The full line is the experimental curve of Webster and the dashed curves are 1, an ideal gas mixture 2, an ideal gas mixture with Poynting s correction and 3, the solubility calculated from Eq. 8 and the principle of corresponding states.

Flo. 3. Vapor-phase solubility of n-decane in nitrogen at 50°C. (a) Ideal gas, (b) virial equation, (c) Lewis rule, (0) experimental. 

An application of Eq. (19) is shown in Fig. 4, which gives the solubility of solid naphthalene in compressed ethylene at three temperatures slightly above the critical temperature of ethylene. The curves were calculated from the equilibrium relation given in Eq. (12). Also shown are the experimental solubility data of Diepen and Scheffer (D4, D5) and calculated results based on the ideal-gas assumption (ordinate scale is logarithmic and it is evident that very large errors are incurred when corrections for gas-phase nonideality are neglected. 

Fig. 4. Vapor-phase solubility of naphthalene in ethylene. Data points from G. A. M. Diepen and F. E. C. Scheffer, J. Am. Chem. Soc. 70, 4085 (1948) vapor-phase fugacities from (---) Redlich-Kwong equation (-) Ideal gas law.

Cohesive energy density is the energy of isothermal vaporization per unit volume to the ideal-gas state. It is the square of the Hildebrand solubility parameter. 

Weiss, R. F. (1974). Carbon dioxide in water and seawater the solubility of a non-ideal gas. Marine Chem. 2,203-215. 

Before calculating the pressures, we must visualize the reaction vessel. The container s total volume is 5.00 L, but 0.150 L is occupied by the aqueous solution. This leaves 4.85 L for the gas mixture. The partial pressure of hydrogen is calculated using the ideal gas equation and assuming that no H2 remains in solution this is a good assumption because hydrogen gas is not very soluble in water ... 

Solid-Fluid Equilibria The solubility of the solid is very sensitive to pressure and temperature in compressible regions, where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature often exhibit fairly simple linear behavior (Fig. 20-19). To understand the role of solute-solvent interactions on sofubilities and selectivities, it is instructive to define an enhancement factor E as the actual solubihty divided by the solubility in an ideal gas, so that E = ysP/Pf, where P is the vapor pressure. The solubilities in CO2 are governed primarily by vapor pressures, a property of the solid... 

Q = saturation solubility of drug (macroparticles) y = interfacial tension between drug particles and the solubilizing fluids M = Molecular weight of the drug r = radius of the microscopic drug particle R = ideal gas constant... 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

Solubility in water and vapor pressure are both saturation properties, i.e., they are measurements of the maximum capacity that a solvent phase has for dissolved chemical. Vapor pressure P (Pa) can be viewed as a solubility in air, the corresponding concentration C (mol/m3) being P/RT where R is the ideal gas constant (8.314 J/mol.K) and T is absolute temperature (K). Although most chemicals are present in the environment at concentrations well below saturation, these concentrations are useful for estimating air-water partition coefficients as ratios of saturation values. It is usually assumed... 

It is instructive to compare the thermochemical values with those obtained by the same authors when they assumed the ideal gas model (i.c.,/co = pco) and neglected the CO solubility change with temperature ArH%12 = 45.5 kJ mol-1 and ATS 72 = 267 J K-1 mol-1. 

What main conclusions can we draw from the three examples discussed here First, although van t Hoff plots should involve Km rather than Kc data, the use of the latter may afford sensible and possibly accurate thermochemical values (always under the assumption of ideal solutions ), particularly if the density term of equation 14.5 is considered in the calculation of the reaction entropy. Second, due to the lack of gas solubility data, the second law method is much... 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

Table 5.3 Solute and solvent solubility isotope effects for (benzene-water) solutions at 306.2 K obtained from IE s on Henry s Law coefficients, Ki and Kn- [Isotope effects on free energies of transfer, ideal gas to solution in the limit of infinite dilution] (Dutta-Choudhury, M., Miljevic, N.

It should be noted that estimating Hemy s law constant assumes the gas obeys the ideal gas law and the aqueous solution behaves as an ideally dilute solution. The solubility and vapor pressure data inputted into the equations are valid only for the pure compound and must be in the same standard state at the same temperature. 

While this technique can be used for gas solubility in volatile liquids, where the vapor pressure of the liquid is determined prior to the introduction of the gas, it is uniquely suited for fhe measurement of gas solubilities in ILs because the gas phase remains pure. This is the technique used by Costa Gomez and coworkers [8-10] to measure the solubility of various gases in ILs and a schematic of the apparatus is shown in Figure 8.3. These apparatuses are frequently made entirely from glass and, therefore, are limited to low-pressure operation. Nonetheless, this makes them ideal for determining Henry s law constants. 

The fugacity coefficient of the solid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity in brackets in equation 2, is defined as the real solubility divided by the solubility in an ideal gas. The solubility in an ideal gas is simply the vapor pressure of the solid over the pressure. Enhancement factors of 104 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 1010. Solubility data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting in a fairly linear relationship (52). 

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