2/26/2016 1 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 (P i ) of each component in a solution is directly proportional to the vapor pressure of the corresponding pure substance (P i *) and that the proportionality constant is the mole fraction (x i ) 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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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,
xbxc
ybyc
za
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?
• To calculate the relative amount of material in each of the two phases in a coexistence region
Lever Rule
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Fractional Distillation (T – z diagram)
• The chemical potentials of the two components in a binary solution is not independent
Gibbs-Duhem Equation
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’tHoff
equation
Semipermeable membrane
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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• Deviation from Raoult’s law
• Real solution: A-A, B-B and A-B interactions are distinctly different
Real Solution
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
• 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)
Ideal Dilute Solution
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Henry’s Law
Henry’s law
constant
Ideal dilute solution• solvent follows Raoult’s law• solute is described by Henry’s law
Raoult’slaw
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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 SolutionHenry’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