CHAPTER 9 IDEAL AND REAL SOLUTIONS - …chen.chemistry.ucsc.edu/Chapter-9.pdf2/26/2016 1 CHAPTER 9 IDEAL AND REAL SOLUTIONS • Raoult’slaw: ideal solution • Henry’s law: real

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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

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• Independent site binding

Multiple Binding Sites

N binding

sites

Scatchard equationScatchard plot