chapter12 - Chapter 12 Phase Equilibria Involving Dissolved...

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Chapter 12 Phase Equilibria Involving Dissolved Solids in Liquids Crystallization is the formation of solid particles from within a homogeneous phase and it is one of the unit operations used to separate substances in pure solid form from a liquid mixture. Therefore, reliable data on the solubility of solids in liquid solvents are needed in designing crystallizers. This chapter f rst provides equations to estimate solid solubility in solvents. Then, how boiling and freezing points of liquids are a f ected by the presence of dissolved solids will be discussed. 12.1 EQUILIBRIUM BETWEEN A PURE SOLID AND A LIQUID MIXTURE Let substance i be present as a pure solid and also as a component in a liquid solution at constant temperature and pressure. The condition of equilibrium states that f S i ( T,P )= b f L i ( T,P,x i ) = f L i ( ) γ i ( i ) x i (12.1-1) Rearrangement of Eq. (12.1-1) gives ln ( γ i x i )=ln " f S i ( ) f L i ( ) # (12.1-2) The fugacities of pure solid and liquid are related to the molar Gibbs energies by Eq. (5.2-1), i.e., ln " f S i ( ) P # = e G S i ( ) e G IG i ( ) RT (12.1-3) ln " f L i ( ) P # = e G L i ( ) e G i ( ) RT (12.1-4) Thus, ln " f S i ( ) f L i ( ) # = e G S i ( ) e G L i ( ) RT = e G fus i ( ) RT = e H i ( ) T e S i ( ) RT (12.1-5) 365
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The use of Eq. (12.1-5) in Eq. (12.1-2) leads to ln ( γ i x i )= e H fus i ( T,P ) T e S i ( ) RT (12.1-6) Since the solution temperature, T , is usually much lower than the normal melting point temperature, T m , of pure solid, a pure substance does not exist in the liquid form at the solution temperature. Thus, extrapolation of the liquid-vapor pressure curve from the triple point temperature to the solid region is necessary until the temperature reaches the solution temperature as shown in Figure 12.1. vap solid P vap liquid subcooled P Pressure Temperature T t T VAPOR LIQUID SOLID Figure 12.1 Extrapolation of vapor-liquid pressure curve to the solution temperature, T . Systematic way of extrapolation can be carried out by devising a following path as shown in Figure 12.2. Step 1: Solid is heated at constant pressure from solution temperature, T ,tot r ip l epo in t temperature, T t . Step 2: Solid is melted to form a liquid ( e H i and e S i at T t are known). Step 3: Liquid is subcooled without solidi f cation from T t to T . Temperature t T T Solid Subcooled Liquid Phase Figure 12.2 Calculation path for e H i ( T ) and e S i ( T ) . For steps 1 and 3, the changes in enthalpy and entropy can be calculated from Eqs. (3.3-1) and (3.4-2), respectively. Since pressure remains constant, the changes in enthalpy and entropy for the overall process are expressed as e H i ( T Z T t T e C S P i dT + e H i ( T t )+ Z T T t e C L P i dT (12.1-7) 366
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e S fus i ( T )= Z T t T e C S P i T dT + e S i ( T t )+ Z T T t e C L P i T dT (12.1-8) At the triple point, solid and liquid phases of pure component i are in equilibrium with each other, i.e., e G i ( T t e H i ( T t ) T t e S i ( T t )=0 e S i ( T t e H i ( T t ) T t (12.1-9) The use of Eq. (12.1-9) in Eq. (12.1-8) leads to e S i ( T Z T t T e C S P i T dT + e H i ( T t ) T t + Z T T t e C L P i T dT (12.1-10) If heat capacities are independent of temperature, Eqs. (12.1-7) and (12.1-10) simplify to
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This note was uploaded on 04/06/2010 for the course CHE 327 taught by Professor Ozbelge during the Fall '10 term at Middle East Technical University.

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chapter12 - Chapter 12 Phase Equilibria Involving Dissolved...

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