2/26/2016 CHAPTER 9 IDEAL AND REAL SOLUTIONS • Raoult’s law: ideal solution • Henry’s law: real solution • Activity: correlation with chemical potential and chemical equilibrium Ideal Solution • Raoult’s law: The partial pressure (Pi) of each component in a solution is directly proportional to the vapor pressure of the corresponding pure substance (Pi*) and that the proportionality constant is the mole fraction (xi) of the component in the liquid • Ideal solution • any liquid that obeys Raoult’s law • In a binary liquid, A-A, A-B, and B-B interactions are equally strong 1 2/26/2016 Chemical Potential of a Component in the Gas and Solution Phases • If the liquid and vapor phases of a solution are in equilibrium • For a pure liquid, Ideal Solution • ∆ ∑ Similar to ideal gas mixing • ∆ ∑ 2 2/26/2016 Example 9.2 • An ideal solution is made from 5 mole of benzene and 3.25 mole of toluene. (a) Calculate Gmixing and Smixing at 298 K and 1 bar. (b) Is mixing a spontaneous process? ∆ ∆ Ideal Solution Model for Binary Solutions • Both components obey Rault’s law • Mole fractions in the vapor phase (yi) Benzene + DCE 3 2/26/2016 Ideal Solution Mole fraction in the vapor phase Variation of Total Pressure with x and y 4 2/26/2016 Average Composition (z) • , , , , ,, • In the liquid phase, • In the vapor phase, za x b yb x c yc Phase Rule • In a binary solution, F = C – p + 2 = 4 – p, as C = 2 5 2/26/2016 Example 9.3 • An ideal solution of 5 mole of benzene and 3.25 mole of toluene is placed in a piston and cylinder assembly. At 298 K, the vapor pressure of the pure substances are 96.4 torr for benzene and 28.9 torr for toluene. • a. The pressure above this solution is reduced from 760 torr. At what pressure does the vapor phase first appear? • b. What is the composition of the vapor at this point? Lever Rule • To calculate the relative amount of material in each of the two phases in a coexistence region 6 2/26/2016 Fractional Distillation (T – z diagram) Gibbs-Duhem Equation • The chemical potentials of the two components in a binary solution is not independent const T and P 7 2/26/2016 Colligative Properties • Freezing point depression (with nonvolatile solute) • Boiling point elevation Freezing Point Depression 8 2/26/2016 Boiling Point Elevation 9 2/26/2016 Osmotic Pressure () van’t Semipermeable Hoff membrane equation Implication of Osmotic Pressure Sea water contains 1.1 M NaCl, which means that it will require a pressure of at least 27 bar to reverse osmosis and obtain pure water. 10 2/26/2016 Real Solution • Deviation from Raoult’s law • Real solution: A-A, B-B and A-B interactions are distinctly different Real Solution • Vmixing and Hmixing can be positive or negative ∆ , , • Partial molar quantity (any extensive variable, U, H, S, A, G, etc) • partial molar volume 11 2/26/2016 Gibbs-Duhem Equation • Applicable to both real and ideal solutions Ideal Dilute Solution • In a real solution, just like in an ideal solution, but * • Activity • Activity coefficient: quantify the degree to which the solution is nonideal (similar to fugacity plays in real gas) 12 2/26/2016 Ideal dilute solution Henry’s Law • solvent follows Raoult’s law • solute is described by Henry’s law Raoult’s law Henry’s law constant 13 2/26/2016 Activity and Activity Coefficient • Raoult’s law standard state • Henry’s law standard state Colligative Properties of Ideal Dilute Solution • A useful way to determine the activity coefficient • Example 9.11: in 500 g of water, 24 g of a nonvolatile solute of MW 241 g/mol is dissolved. The observed freezing point depression is 0.359 °C. Calculate the activity coefficient of the solute. 14 2/26/2016 Chemical Equilibrium in Solution Henry’s law standard state for each component Binding Equilibrium (Adsorption) • Assuming a single binding site for the molecule, the average number of bound molecules per species 15 2/26/2016 Multiple Binding Sites • Independent site binding N binding sites Scatchard equation Scatchard plot 16.