Equilibrium Solubility of Gases in Liquids

The rate at which a gaseous constituent of a mixture will dissolve in an absorbent liquid depends upon the departure from equilibrium which exists, and 

If a quantity of a single gas and a relatively nonvolatile liquid are brought to equilibrium in the manner described in Chap. 5, the resulting concentration of dissolved gas in the liquid is said to be the gas solubility at the prevailing temperature and pressure. At fixed temperature, the solubility concentration will increase with pressure in the manner, for example, of curve A, Fig. 8.1, which shows the solubility of ammonia in water at 30 C. 

Different gases and liquids yield separate solubility curves, which must ordinarily be determined experimentally for each system. If the equilibrium pressure of a gas at a given liquid concentration is high, as in the case of curve B (Fig. 8.1), the gas is said to be relatively insoluble in the liquid, while if it is low, as for curve C, the solubility is said to be high. But these are relative matters 

When the liquid phase can be considered ideal, we can compute the equilibrium partial pressure of a gas from the solution without resort to experimental determination. 

There are four significant characteristics of ideal solutions, all interrelated  

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Many definitions are used to express the solubility of gases in liquids, but usually the equilibrium law is defined as ... 

The resistance to mass transfer according to (1.221) and (1.223) is made up of the individual resistances of the gas and liquid phases. Both equations show how the resistance is distributed among the phases. This can be used to decide whether one of the resistances in comparison to the others can be neglected, so that it is only necessary to investigate mass transfer in one of the phases. Overall mass transfer coefficients can only be developed from the mass transfer coefficients if the phase equilibrium can be described by a linear function of the type shown in eq. (1.217). This is normally only relevant to processes of absorption of gases by liquids, because the solubility of gases in liquids is generally low and can be described by Henry s law (1.217). So called ideal liquid mixtures can also be described by the linear expression, known as Raoult s law. However these seldom appear in practice. As a result of all this, the calculation of overall mass transfer coefficients in mass transfer play a far smaller role than their equivalent overall heat transfer coefficients in the study of heat transfer. 

The solubility of gases in liquids is often treated as an equilibrium process. Take the dissolution of carbonyl sulphide (OCS) as an example ... 

Equilibrium data are presented in a variety Of ways. Frequently, the solubilities of gases in liquids in which they are sparingly soluble are given in terras of Henry s Law constant H. Henry s Law states simply that lbe solubility of a gas in a liquid is directly proportional to its partial pressure in the gas phase that... 

The study of vapor-liquid equilibria (Sec 10.1) of the solubility of gases in liquids (Sec. 11.1), and of the solubility of solids in liquids (Sec. 12.1), all involve nonsimple, mixtures. To see why this occurs, consider the criterion for vapor-liquid equilibrium ... 

Equation (14.28) states that the solubility Xj of a volatile constituent is proportional to the partial pressure of that constituent in the gaseous phase in equilibrium with the liquid. Equation (14.28) is used to correlate the data on solubility of gases in liquids. If the solvent and gas do not react chemically, the solubility of gases in liquids is usually small and the condition of diluteness is fulfilled. Here we have another example of the physical significance of the partial pressure. 

The solubility of gases in ice can be described by the same principles governing solubility of gases in liquids. Solubility of gases in liquids or ice occurs to establish equilibrium, where the affinities of the gas to reside in the gaseous, liquid, and solid state are balanced. The solubility process can be described by two principle mechanisms ... 

Cukor and Prausnitz (16, 27) developed two apparatuses for rapid and accurate measurement of the solubility of gases in liquids at pressures in the vicinity of 1 atm over the temperature range 25-200 °C. Equilibrium compositions were determined from the total gas pressure and from a material balance. Their apparatuses with a careful operation, yielded solubilities of about 1 % accuracy. They reported values of solubility expressed in mole fraction (x2) of methane in n-hexadecane at 1 atm partial pressure and some experimental values of Henry s constant for methane, ethane and hydrogen in n-hexadecane, bicyclohexyl and diphenylme-thane for temperature range 25-200 C. 

The solubility of gases in liquids generally follows Henry s law, which states that, at equilibrium, the partial pressure of a gas lying above a solution is proportional to the concentration of the gas in the solution (see Table 3-5) ... 

The sorption coefficient (K) in Equation (2.84) is the term linking the concentration of a component in the fluid phase with its concentration in the membrane polymer phase. Because sorption is an equilibrium term, conventional thermodynamics can be used to calculate solubilities of gases in polymers to within a factor of two or three. However, diffusion coefficients (D) are kinetic terms that reflect the effect of the surrounding environment on the molecular motion of permeating components. Calculation of diffusion coefficients in liquids and gases is possible, but calculation of diffusion coefficients in polymers is much more difficult. In the long term, the best hope for accurate predictions of diffusion in polymers is the molecular dynamics calculations described in an earlier section. However, this technique is still under development and is currently limited to calculations of the diffusion of small gas molecules in amorphous polymers the... 

Yaws and coworkers have presented many compilations and correlations of solubility data, for example, hydrocarbons in water. Methods are available for estimating the solubility of gases in organic liquids. " And special compendia include those in the Solubility Data Series, Seidell and coworkers, " ° and Back." Extensive reviews have been provided by Markham and Kobe, Long and McDevit, Battino and Clever, Wilhelm and Battino, and Wilhelm et al., among others. Often data usually associated with vapor-liquid equilibrium in distillation can be used. Finally, various handbooks contain some useful solubility data. 

Carbonated drinks are bottled under high CO2 pressure, permitting the gas to dissolve into aqueous solution. When the bottle is opened, the partial pressure of CO2 in the gas phase rapidly decreases to the value in the atmosphere, and the gas bubbles out of solution. When the bottle is closed again, CO2 gas pressure builds until a saturated solution at equilibrium is again obtained. The solubility of gases in a liquid also increases in the bloodstream of deep-sea divers when they experience high pressures. 

Equation 7.3 is the more complete Gibbs phase rule. For a single component, it becomes equation 6.19. Note that it is applicable only to systems at equilibrium. Also note that although there can be only one gas phase, due to the mutual solubility of gases in each other, there can be multiple liquid phases (that is, immiscible liquids) and multiple solid phases (that is, independent, nonalloyed solids in the same system). 

The equilibrium solubility of common inorganic gases in petroleum liquids can now be estimated by nomograph. The relationship is based on an earlier correlation established by the U.S. National Aeronautics and Space Administration and the subject of a standard method approved by the American Society of Testing and Materials. 

Henry s Law. This is an empirical formulation that describes equilibrium solubilities of noncondensable gases in a liquid when Raoult s law fails. It states that the mole fraction of a gas (solute i) dissolved in a liquid (solvent) is proportional to the partial pressure of the gas above the liquid surface at given temperature. That is,... 

The principles of equilibrium have wide applicability and great utility. For example, they aid us in understanding and controlling the solubility of solids and gases in liquids. We shall consider, first, the solubility of a molecular solid in a liq-... 

The atmosphere is not completely inert. N2 and 02 have some solubility in most solutions. We will see in Chapter 8 that dissolving gases in liquids lowers the vapor pressure of the liquid. Also, in a system open to the atmosphere, complete equilibrium will not be established because material will continually he transported to the ambient environment. In practice, however, a small opening will be sufficient to maintain the pressure of the atmosphere while allowing neglect of the loss of gaseous material by diffusion or convection. 

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