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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
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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 • ∆ ∑
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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
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Ideal Solution
Mole fraction in the vapor phase
Variation of Total Pressure with x and y
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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
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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
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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
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Colligative Properties
• Freezing point depression (with nonvolatile solute) • Boiling point elevation
Freezing Point Depression
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Boiling Point Elevation
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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.
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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
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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)
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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
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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.
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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
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Multiple Binding Sites
• Independent site binding N binding sites
Scatchard equation Scatchard plot
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