Ideal solubility of a gas

Since it is unlikely that the latent heat of vaporization of the liquefied gas can be determined at normal temperatures and pressures, it is more convenient for practical purposes to regard — as the heat of solution per mole of gas. If this may be taken as independent of temperature, equation (34.27) can be integrated so as to yield an expression for the variation of the solubility of the gas with temperature. On the other hand, if the solubilities at two or more temperatures are known, the heat of solution can be calculated. It may be noted that since the heat of vaporization A/fv is always positive, the ideal solubility of a gas, at a given pressure, should decrease with increasing temperature. The relatively few cases in which this rule fails, e.g., certain aqueous solutions of hydrogen halides, are to be attributed to marked deviations from ideal behavior (cf. 35a). 

The ideal solubility of a gas is the solubility calculated on the assumption that the dissolved gas obeys Raoult s law for partial pressure / b = abPb- " e ideal solubility, expressed as a mole fraction, is then given as a function of partial pressure by... 

This wild extrapolation Pr= 10.5 ) is independent of which solvent the O2 was dissolved in. The quantity calculated is called the ideal solubility of a gas. Table 9.2 and Figure 9.8 makes clear that the solubility is highest in solvents with the lowest values of the solubility parameter. The lowest solubility parameters known are for perfluor-ocarbons of which perfluoro- -hexane has the lowest value shown on that table and figure. The reported solubility, oxygen in perfluoro-n-hexane X 10. If instead of Compar-... 

The solubility of a gas is unaffected by the presence of other gases unless the total pressure of gas (i.e. dissolving gas added to other gases) is above about 1 atm (101 kPa) pressure. Above this pressure, all gases show significant deviations from Henry s law because the gas mixture behaves non-ideally. 

If Henr s law is valid, then the curve between solubility of a gas and equilibrivim presswe of the gets at a constant temperature should be a straight line as shown in figure (1). Henry s law has been found to hold good in many cases especially at low pressures and where the gas and solution behave ideally. 

Henry s law The concentration (C) of a gas in solution is proportional to the partial pressure (p) of that gas in equilibrium with the solution, i.e. p = kC, where i is a proportionality constant. The relationship is similar in form to that for RAOULT s LAW, which deals with ideal solutions. A consequence of Henry s law is that the volume solubility of a gas is independent of pressure. The law is named for the British physician and chemist William Henry (1755-1836), who formulated it in 1801. 

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

Suppose that a pure gas dissolves in some hquid solvent to produce an ideal solution. Show that the solubility of this gas must fit the following relationships ... 

The aqueous solubility of a gaseous compound is commonly reported for 1 bar (or 1 atm = 1.013 bar) partial pressure of the pure compound. One of the few exceptions is the solubility of 02 which is generally given for equilibrium with the gas at 0.21 bar, since this value is appropriate for the earth s atmosphere at sea level. As discussed in Chapter 3, the partial pressure of a compound in the gas phase (ideal gas) at equilibrium above a liquid solution is identical to the fugacity of the compound in the solution (see Fig. 3.9d). Therefore equating fugacity expressions for a compound in both the gas phase and an equilibrated aqueous solution phase, we have ... 

The calculated ideal solubilities of the gases in n-heptane are very close to the experimental ones, but the ideal solubilities of the gases in water are too large, giving y > 1. For y > 1, there is a great difference in intermolecular forces between gas and solvent. 

Sjoberg, E.L. A fundamental equation for calcite dissolution kinetics. Geochim. Cosmochim. Acta 40, 441-447 (1976). Weiss, R.F. Carbon dioxide in water and sea water the solubility of a non-ideal gas. Mar. Chem. 2, 203-215 (1974). Lyman, J. Buffer mechanism of sea water. Ph. D. Thesis,... 

As already mentioned, the Krichevsky equation (eq 1) is valid when the binary mixtures 1—2 and 2—3 (gas solute/pure solvents) and the ternary mixture 1—2—3 are ideal. However, these conditions are often far from reality. Let us consider, for example, the solubility of a hydrocarbon in a water—alcohol solvent (for instance, water—methanol, water—ethanol, etc.). The activity coefficient of propane in water at infinite dilution is 4 X 10 , whereas the activity coefficients of alcohols and water in aqueous solutions of simple alcohols seldom exceed 10. It is therefore clear that the main contribution to the nonideality of the ternary gas-binary solvent mixture comes from the nonidealities of the gas solute in the individual solvents, which are neglected in the Krichevsky equation. 

Problem The vapor pressure of liquid ethane at 25 C is 42 atm. Calculate the ideal solubility of ethane in a liquid solvent at the same temperature at a pressure of 1 atm., assuming the gas to behave ideally. 

One kmol/s of a gas consisting of 75 mol% methane and 25% n-pentane at 300 K and 1 atm is to be scrubbed with 2 kmol/s of a nonvolatile paraffin oil entering the absorber free of pentane at 308 K. Estimate the number of ideal trays for adiabatic absorption of 98.6% of the pentane. Neglect the solubility of methane in the oil, and assume operation to be at constant pressure. The pentane forms ideal solutions with the paraffin oil. The average molecular weight of the oil is 200 and the heat capacity is 1.884 kJ/kg-K. The heat capacity of methane over the range of temperatures to be encountered is 35.6 kJ/kmol-K for liquid pentane, is 177.5 kJ/kmol-K for pentane vapor, is 119.8 kJ/kmol-K. The latent heat of vaporization of n-pentane at 273 K is 27.82 MJ/kmol (Treybal, 1980). 

The solubility (y) of a material in an SCF is usually expressed in terms of the overall mole fraction of the solute in the SCF phase. The ability of SCFs to dissolve many substances arises from the highly nonideal behavior of pure SCFs. The solubility of a component as predicted by the ideal gas law, decreases asymptotically with increasing pressure because the solubility is simply the ratio of the vapor pressure (p ) to the total pressure (p). Under supercritical conditions, however, the solubility is enhanced by several orders of magnitude above that predicted by the ideal gas law. 

The simplest type of phase behavior to understand is the solubility of a solid solute, such as naphthalene, in a supercritical fluid. When the solute is a crystalline solid, the solid phase may be assumed to be pure and only the supercritical phase is a mixture. Imagine solid naphthalene in a closed vessel under one atmosphere of carbon dioxide at 40°C. The reduced temperature and reduced density of CO2 are 1.03 and 3.7x10 respectively. At this pressure, the gas phase is ideal and the naphthalene solubility is determined by its vapor pressure. As the container volume is decreased isothermally, the solubility initially decreases when the gas phase is still nearly ideal. As the pressure is increased further, however, the gas phase density becomes increasingly nonideal and approaches the mixture critical density (near the critical density of CO2 because the gas phase is still mostly CO2). The reduced density of CO2 increases rapidly near the critical region as shown in Figure 2. The solvent power of CO2 is related to the density which leads to a rapid solubility increase. A brief description of intermolecular interactions is helpful in understanding this behavior. 

The solubility of chlorine gas at 0°C and an air pressure of latm is about 4.6 m of gas per cubic metre of water. Assuming no subsequent reaction, estimate the concentration of dissolved gas (in moldm ) in a saturated solution under these conditions. (The molar volume of an ideal gas at 0 C and 1 atm pressure is 22.4 dm. )... 

Figure 9 illustrates the behavior and solubility of a solid in a compressed gas. At low pressure (e.g., < 1 MPa for CO2), the solubility of a solid in a gas follows ideal behavior and is inversely proportional to the pressure. As the pressure approaches the sublimation pressure of the solid, the mole fraction solubility tends toward 1 below the sublimation pressure the solid completely vaporizes. Beyond the ideal region, the solubility experiences a minimum before becoming proportional to the... 

The act or process by which a compound such as oxygen is molecularly mixed with a liquid (such as water) or a solid (such as a polymer) is called dissolution, and the result of the mixing is a solution. If a solution is very dilute, as is commonly found in packaging, it behaves as an ideal solution, and again the activity coefficient is approximately 1, so concentration can be substituted for activity in thermodynamic relationships. In order to describe the solubility of a compound present in a gas phase that is in contact with a solid phase, as may be the case of oxygen in air contacting a polymer, we need a relationship between the concentration in the liquid (or solid) phase and the concentration (or partial pressure) in the gas phase. In other words, we need an expression for the solubility of the substance at equilibrium, as a function of the partial pressure of the gas or vapor in the contacting gas phase. 

Suppose that an ideal solution of two components (i = 1,2) is in the presence of a noncondensable gas (subscript g). Neglecting the solubility of the gas in the liquid, the liquid contains only the liquid components while the gas contains the noncondensable gas well as vapors of the liquid components. The vapor/liquid equilibrium of the condensable components is described by Raoult s law ... 

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