Multicomponent systemsDoba Jackson, Ph.D.

Huntingdon College

Problem 1: Acetone has a normal boiling point of 56.2*C and a molar enthalpy of vaporization of 31.97 kJ/mol. Calculate the equilibrium vapor pressure of acetone at 20.0*C.

Problem 2: The vapor pressure of bromine is 133 torr at 20.0*C and 48.1 torr at 0.00*C. Calculate the enthalpy of vaporization of bromine.

Chemical Potentials of Liquids and liquid mixturesP

= RTLnPA

A AA

**

P= RTLn

PA

A AA

Θ is pressure at 1 bar

* is pressure of pure A

Rauolt’s Law*

A A AP P*A

AA

P

P

*= RTLnA A A

Rauolt’s law states that the chemical potentialof the liquid is altered by the presence of a solute.The amount of the deviation is based on the molefraction of the solute.

Ideal Solutions

• Ideal solutions are solutions that obey Rauolt’s law throughout its composition range from pure A to pure B.

Rauolt’s Law is observed when two solutions have similar structures

Obey’s Rauolt’s Law Does not obey’s Rauolt’s Law

Dilute solutions typically do not obey Rauolt’s Law but follows Henry’s Law

P= RTLn

PA

A AA

**

P= RTLn

PA

A AA

Θ is pressure at 1 bar

* is pressure of pure A

Henry’s LawA A AP K AA

A

P

K

**

= RTLn A AA A

A

K

P

Henry’s law states that the chemical potentialof the liquid is altered by the presence of a solute.The amount of the deviation is based on the molefraction of the solute.

Vapor-Pressure Lowering of Solutions: Raoult’s Law

The vapor pressure of pure water at 25 °C is 23.76 mm Hg. What is the vapor pressure of a solution made from 1.00 mol glucose in 15.0 mol of water at 25 °C? Glucose is a nonvolatile solute.

Psoln = Psolv Xsolv

= 22.3 mm Hg1.00 mol + 15.0 mol

x23.76 mm Hg 15.0 mol=

Basis for Rauolt’s and Henry’s Law

*A A AP P

A A AP K

Rauolt’s Law

Henry’s Law

General model of solutions

Problem 5.24a

• It is found that the normal boiling point of a binary solution of A and B with XA=.6589 is 88*C. At this temperature the vapor pressures of pure A and B are 129.6 kPa and 51.60 kPa, respectively.

• (a) Is the solution Ideal?• (b) What is the composition of the vapor

above the solution mixture?

Temperature-composition diagrams

• Distillation- separation of mixtures by withdrawing the more volatile component

in the vapor phase.

• Theoretical plates- number of vaporization-condensation steps required to achieve a given composition.

Theoretical Plates

# of Theoretical Plates depend on several factors:

- Temperature- Distillation Apparatus- Composition

- Vaporization temp. difference- Azeotropes

-Amount of each phase can be determined by the lever rule

Types of Phase Diagrams• Vapor Pressure-Composition Diagrams

– Upper Liquid Phase (P=1)– Bi-Phase intermediate (P=2)– Lower Vapor Phase (P=1)

• Liquid-Composition Diagrams– Upper vapor Phase– Bi-Phase intermediate– Lower vapor Phase

Two miscible liquids

Two partially miscible liquids

Azeotropic composition

Liquid-only Phase diagrams

Upper consolute temp. (Tuc)-

Is the temperature at whichboth liquids are miscible.

Inside the circle, two phasesexist.

Each composition is givenby the lever rule.

Hexane-Nitrobenzene

Liquid-only Phase diagrams

Lower consolute temp. (Tlc)-

Is the temperature at whichboth liquids are miscible.

Inside the circle, two phasesexist.

Each composition is givenby the lever rule.

Water-Triethanolamine

Liquid-only Phase diagrams

Lower consolute temp. (Tlc)-

Is the temperature at whichboth liquids are miscible.

Inside the circle, two phasesexist.

Each composition is givenby the lever rule.

Water-Nicotine solution

Liquid-only Phase diagrams

A temperature-composition diagram in which boiling occurs before the

solution becomes miscible

Colligative Properties

• Colligative Properties- properties of solutions that depend only on the number of molecules present in a volume of solvent and not on the identity of the solute.

–Vapor Pressure lowering–Boiling Point Elevation–Freezing Point Depression–Osmosis

Osmosis

Osmosis: the spontaneous passage of a pure solvent intoa solution while separated by asemi-permeable membrane.

- Cell membrane transport - Dialysis - Blood Transfusions - Osmometry (M.W. determinations)

Osmotic Pressure (π): the pressure required to stop the influx of solvent.

Calculation of Osmotic Pressure

* P

A A mPG p p V dP

* P

A A mPp p V dP

Fundamental Equation;Assume const. Temperature

* = RTLnA A Ap p

Change in pressure is due to soluteconcentration in the solution.

RTLnP

m APV dP

RTLn 1m BV

Calculation of Osmotic Pressure

RTLn 1m BV 1 B BLn

RTm BV B

BT

n

n

RT Bm

T

nV

n

T mn V VRT BV n

RT Bn

V

RT M Bn M

V

Molar Concentration

Assume the solute concentration is small