Partially Miscible Liquids

3. Partially Miscible Liquids

a. Liquid and Gas Mixtures Many liquids are miscible within a certain range of concentrations. The solubility of liquids with one another generally increases with the temperature. The corresponding pres- sure–temperature relationships are a combination of the corresponding relationships for misci- ble and immiscible liquids. Figure 9 illustrates the T-X k(l) -X k diagram for a partially miscible

liquid. In the context of Figure 9 assume that methanol and water are partially miscible. Let

X 1(l) denote the methanol mole fraction and X 2,l the water mole fraction in the liquid. Suppose X 1(l) denote the methanol mole fraction and X 2,l the water mole fraction in the liquid. Suppose

to X 2(l) = 0.8 say at temperatures less than 40ºC, but at 60ºC it is immiscible for values of X 2(l) < 0.7. Region I is a miscible liquid mixture but rich in species 2, while region II is a miscible

liquid mixture but rich in species 1. The boundary DQG represents the variation of miscibility with temperature in the region richer in X 2,l . The region above line CED is similar to the im-

miscible case we have just discussed. Consider the vapor mixture at a 90% water vapor concentration (point K). As we cool the vapor from state K to M, first a liquid drop appears containing both species that has a com- position corresponding to point R, while the vapor has a composition corresponding to point M as discussed for miscible liquids. As the temperature is decreased to point N, the last liquid will have composition at N (at the bubble line) while the vapor is at state T. If temperature is further decreased, a liquid mixture fixed at a composition N forms.

If we start at point S, then we obtain the first drop at point T with drop composition corresponding to N, which is in the miscible region. As we cool further to point U, the liquid composition is at D (miscible limit at 60ºC) while the vapor is at E. However there is still wa- ter and methanol vapor left in the mixture. Condensation will occur at a constant vapor com- position with the liquid-I composition at D (rich in species 2) and liquid-II composition C (rich in species 1). If the temperature drops below 60ºC, there are two separate liquid phases I (composition rich in species 2 along DQG) and II (composition lean in species 2 along FLC). However, the fraction of species 2 in liquid–II will increase since the solubility of species 2 increases (DQG) while the fraction of species 2 in liquid–II will decrease (FLC).

b. Liquid and Solid Mixtures When a solid (a solute, such as salt) is dissolved in a liquid (a solvent, e.g., water), the dissolved solid can be considered as a liquid in the liquid solution. It is pertinent to know the maximum amount of solute that can be dissolved in a solvent. We will denote the salt in solid phase as s(s) and that in the liquid as s( l). At the equilibrium state of a saturated liquid solution with a solid salt,

ˆf s(l) =X sl f s(l)( T,P) = f s(s) (T,P), where (21)

f s(s)( T,P) = f s(s) (T,P sub ) POY s(s) , and (22) POY s(s)

(23) The P sub denotes the saturation pressure for the sublimation of a salt at a specified temperature.

= exp [v sub

s(s) (P–P )/RT].

Since f sub s(s) (T,P) = f s(g) (T,P ),

f s(s) (T,P) = f s(g) (T, P sub ) POY s(s) . (24) If the vapor phase behaves as an ideal gas,

f s(s) (T,P) = P sub POY s(s) . (25) Similarly,

f s(l)( T,P) = φ s(l)( T,P) P. (26) Employing Eqs. (21) and (26)

X s(l) φ s(l)( T,P) P = P sub (T) POY s(s) , and (27)