Thermodynamics

two sides of a water–air interface are also different even when air is saturated(Fig. 16–22). Therefore, when specifying mole fractions in two-phasemixtures, we need to clearly specify the intended phase.In most practical applications, the two phases of a mixture are not inphase equilibrium since the establishment of phase equilibrium requires thediffusion of species from higher concentration regions to lower concentrationregions, which may take a long time. However, phase equilibriumalways exists at the interface of two phases of a species. In the case ofair–water interface, the mole fraction of water vapor in the air is easilydetermined from saturation data, as shown in Example 16–8.The situation is similar at solid–liquid interfaces. Again, at a given temperature,only a certain amount of solid can be dissolved in a liquid, and thesolubility of the solid in the liquid is determined from the requirement thatthermodynamic equilibrium exists between the solid and the solution at theinterface. The solubility represents the maximum amount of solid that canbe dissolved in a liquid at a specified temperature and is widely available inchemistry handbooks. In Table 16–1 we present sample solubility data forsodium chloride (NaCl) and calcium bicarbonate [Ca(HO 3 ) 2 ] at various temperatures.For example, the solubility of salt (NaCl) in water at 310 K is36.5 kg per 100 kg of water. Therefore, the mass fraction of salt in the saturatedbrine is simplymf salt,liquid side m saltm 36.5 kgChapter 16 | 811xAiry H2 O,gas sideJump in y H2 O,liquid side 1concentrationWaterConcentrationprofileFIGURE 16–22Unlike temperature, the mole fractionof species on the two sides of aliquid–gas (or solid–gas orsolid–liquid) interface are usually notthe same.1100 36.52 kg 0.267 1or 26.7 percent2whereas the mass fraction of salt in the pure solid salt is mf 1.0.Many processes involve the absorption of a gas into a liquid. Most gases areweakly soluble in liquids (such as air in water), and for such dilute solutionsthe mole fractions of a species i in the gas and liquid phases at the interfaceare observed to be proportional to each other. That is, y i,gas side y i,liquid side orP i,gas side Py i,liquid side since y i P i /P for ideal-gas mixtures. This is known asthe Henry’s law and is expressed asy i,liquid side P i,gas sideH(16–22)where H is the Henry’s constant, which is the product of the total pressureof the gas mixture and the proportionality constant. For a given species, it isa function of temperature only and is practically independent of pressure forpressures under about 5 atm. Values of the Henry’s constant for a number ofaqueous solutions are given in Table 16–2 for various temperatures. Fromthis table and the equation above we make the following observations:1. The concentration of a gas dissolved in a liquid is inversely proportionalto Henry’s constant. Therefore, the larger the Henry’s constant, thesmaller the concentration of dissolved gases in the liquid.2. The Henry’s constant increases (and thus the fraction of a dissolved gas inthe liquid decreases) with increasing temperature. Therefore, the dissolvedgases in a liquid can be driven off by heating the liquid (Fig. 16–23).3. The concentration of a gas dissolved in a liquid is proportional to thepartial pressure of the gas. Therefore, the amount of gas dissolved in aliquid can be increased by increasing the pressure of the gas. This can beused to advantage in the carbonation of soft drinks with CO 2 gas.TABLE 16–1Solubility of two inorganiccompounds in water at varioustemperatures, in kg (in 100 kg ofwater)(from Handbook of Chemistry, McGraw-Hill,1961)SoluteCalciumTempera- Salt bicarbonateture, K NaCl Ca(HCO 3 ) 2273.15 35.7 16.15280 35.8 16.30290 35.9 16.53300 36.2 16.75310 36.5 16.98320 36.9 17.20330 37.2 17.43340 37.6 17.65350 38.2 17.88360 38.8 18.10370 39.5 18.33373.15 39.8 18.40