8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

1/31

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

2/31

Simple Mixtures hapter Outline

Introduction to Simple MixturesThermodynamic description of mixtures

6.1 Partial molar quantities

6.2 Thermodynamics of mixing

6.3 The chemical potential of liquidsThe properties of solutions

6.4 Ideal solutions, simple mixtures, and

non-ideal solutions

6.5 Colligative properties

6.6 Activities of regular solutions

6.9 The activities of ions in solution

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

3/31

REVIEW OF BASIC CONCEPTS

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

4/31

Mixtures

All matter

Substance

Compound

Element

Mixture

Homogeneous

Heterogeneous

 A mixture of substances can vary in composition and properties from one sample 

to another.

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

5/31

What are Solutions?

•Solutions  are homogeneous

mixtures of substances

composed of at least one

solute and one solvent.

•Solutions   can be gases,

liquids, or solids.

Ideal and non-ideal solutions

Electrolytes and non-electrolytes

GENERAL TYPES

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

6/31

How is a solution formed?

Steps that lead to the formation of a liquid solution

“Like dissolves like.”

1. Breaking up the solute into

individual components(expanding the solute).

2. Overcoming intermolecular 

forces in the solvent to make

room for the solute

(expanding the solvent).3. Allowing the solute and

solvent to interact to form the

solution.

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

7/31

Enthalpy (Heat) of Solution

The enthalpy change associated with the formation of asolution

soln 1 2 3 H H H H 

Energy is absorbed!

Energy is released!

endothermic

exothermic

0 H   ???

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

8/31

Enthalpy (Heat) of Solution

(a) Process is exothermic if Step 3 releases more energy than that required in Step 1 & 2.

(b) Process is endothermic if Steps 1 & 2 require more energy than what is released in Step 3.

Pure

components

Separate solventmolecules ΔH1

Separate solute

molecules ΔH2

(Endothermic)

(Exothermic)

ΔHsoln = 0

ΔHsoln > 0

ΔHsoln

< 0

Allow solvent

and solute

molecules to mixΔH3

    E   n    t    h   a    l   p   y

 .    H

      

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

9/31

Intermolecular forces in a solution

1

B

B2

3

(1) Solvent molecules, A-A

(3)Solvent and solutemolecules, A-B

(2)Solute molecules, B-B

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

10/31

IMFs in Mixtures

Four possibilities for the relative strengths of IMFs:

1.IMFs are of the same type and of the same strength, solute and solvent

mix randomly ΔHsoln

= 0 : IDEAL SOLUTIONS.

2.IMFs between unlike molecules  exceed   

  IMFs between like molecules,  asolution forms, ΔH

soln

< 0 exothermic : NON-IDEAL SOLUTIONS

3.IMFs between solute and solvent molecules are   somewhat weaker     than

between molecules of the same kind, complete mixing may still occur,

ΔH

soln

> 0 endothermic : NON-IDEAL SOLUTIONS

4.IMFs between unlike molecules are   much weaker     than those between like

molecules, the components remain segregated   in a heterogeneous mixture:

NO SOLUTION FORMS.

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

11/31

Solubility of a Nonpolar Solute and a

Polar Solvent

H2   will be large & positive

because it takes considerable

energy to overcome thehydrogen bonding forces

among the water molecules to

expand.

Large amounts ofenergy would have to

be expended in order to

form an oil-water

solution!

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

12/31

Solubility of an Ionic Solute and a

Polar Solvent

1 786 / NaCl s Na g Cl g H kJ mol 

2 2 3

  = 783 /

hyd  H O l Na g Cl g Na aq Cl aq H H H 

kJ mol 

soln 3 / H kJ mol 

Why is NaCl soluble in

water???

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

13/31

Solubility of an Ionic Solute and a

Polar Solvent

(a)Orange & yellow spheres separated by apartition in a closed container. (b) The

spheres after the partition is removed and the

container has been shaken for some time.

(a) (b)Increase indegree of

disorder!

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

14/31

Possible ases for Solution Formation

Processes that require large amounts of energy tend not to occur!!!

Solvent/solute

combination

H1 H2 H3 Hsol’n Outcome

Polar solvent,

polar solute

Large Large Large,

negative

Small Solution forms

Polar solvent,non polar solute

Small Large Small Large,positive

No solution forms

Nonpolar

solvent,

nonpolar solute

Small Small Small Small Solution forms

Nonpolar

solvent, polar

solute

Large Small Small Large,

positive

No solution forms

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

15/31

Factors Affecting Solubility 

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

16/31

Try this….1. Predict whether or not a

solution will form in

each of the following

mixtures:

a Ethyl alcohol and water

b Octanol and water

c Hexane and octane

2. Benzoic acid is much more

soluble in aqueous NaOH

solution than it is in pure

water. Can you suggest a

reason for this?

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

17/31

 Partial Molar Quantities 

 The Thermodynamics of Mixing 

 The Chemical Potentials of Liquids 

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

18/31

Partial Molar Properties

Partial pressure

Partial molar volumePartial molar Gibbs energy (Chemicalpotential )

The thermodynamic contribution of a substance (per 

mole) to an overall property of a mixture

Partial olar Quantities

NOTE: Partial molar properties are intensive properties!

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

19/31

The Partial Molar Volume

The contribution (per mole) of substance, J, to the overall volume, V J , of a solution at constant temperature, pressure, and amount of solution

components (Silbey & Alberty, 2001)

  FINITION

1000 mL H2O 1 mol H2O 1018 mL H2O

1014 mL EtOH-H2O sol’n1000 mL EtOH 1 mol H2O

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

20/31

The Partial Molar Volume

The partial molar volume can also

be regarded as the change in

volume per mole of A added to a

large volume of the mixture.

, , '(the amount of all other substances present are constant)

 J 

 J   p T n

V V 

n

a b Amount of A, n A

   V  o   l  u  m

  e ,

      V

V(a)

V(b)

The partial molar volume of a substance is

the slope of the variation of the total volume

of the sample plotted against the

composition.

 A A B BV n V n V  NOTE:

The partial molar volume is a function of  

composition!

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

21/31

The Partial Molar Volume

•   The partial molar volume varies

with composition since the

environment of each type of molecule changes with each

change in composition.

The partial molar volumes of water

and ethanol at 25oC.

1014 mL EtOH-H2O sol’n1000 mL EtOH 1 mol H2O

Does the partial molar volume always have a positive value

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

22/31

Partial Molar Gibbs Energy Chemical Potential

•   For a substance in a mixture, the chemical potential is defined

as being the partial molar Gibbs energy 

, , '(the amount of all other substances present are constant)

 J 

 J    p T n

G

n

•   The slope of a plot of Gibbs energy

against the amount of the component 

J  , with the pressure and temperature

(and the amounts of other substances)held constant 

 A A B BG n n

Total Gibbs energy of the binary mixture @ constant T & p

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

23/31

Partial Molar Gibbs Energy Chemical Potential

• When composition, T , & p vary 

... A A B BdG Vdp SdT dn dn

 Fundamental equation of chemical thermodynamics

At constant pressure and temperature,

... A A B BdG dn dn

,maxedG dw

Non-expansion work takes place due to the changing composition of the

systems!

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

24/31

 The Chemical Potential:On A Wider Scope 

•  The chemical potential also shows how the internal

energy varies with composition.

Recall,

TS  pV U G   GTS  pV U 

So,

 An infinitesimal change in U f or a system of variable composition

dGSdT TdS Vdp pdV dU ... B B A A   nnTdS  pdV dU 

 At constant volume and entropy

...

 B B A A

  nndU 

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

25/31

 The Chemical Potential:On A Wider Scope 

•   The chemical potential also shows how the extensive

thermodynamic properties   – H, U, A, and G   –   vary

with composition.

',,   n pS  J 

 J n

 H 

',,   nV S  J 

 J n

U 

',,   nT V  J 

 J n

 A

',,   nT  p J 

 J n

G

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

26/31

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

27/31

The Gibbs-Duhem Equation

i

 j

i

i

 j

i

ii   dnd ndG11

i

 j

i

idnSdT VdpdG1

SdT Vdpd n j

i

ii

1

 At constant p and T 

01

 j

i

iid n

For a binary system

 A

 B

 A B   d 

n

nd  The partial molar property of another substance can

be determined from the property of the other.

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

28/31

To ponder on…

1 Distinguish ideal solutions

from non-ideal solutions with

respect to chemical

potential?

2 Interpret

Raoult’s and

Henry’s laws using the

underlying principle ofchemical potential?

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

29/31

Remember,

The Gibbs energy of the mixture depends on itscomposition.

At constant T and p systems tend towards lower

Gibbs energy.

Spontaneous mixing results inspontaneous change in

composition!

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

30/31

Other Thermodynamic Mixing Functions

Entropy of mixing

 ) xln x xln x( nRT 

GS 

 B B A An ,n , p

mix

mix B A

Enthalpy of mixing

S T  H G

0 H mix   At constant T and pThere are nointeractions between

the molecules

forming the gaseous

mixture!The driving force for mixing is the increasing

entropy of the system as the molecules mingle.

The entropy of the surroundings remain

unchanged.

8/19/2019 ChE 323 lecture 6_1 ed_02_12_14

31/31

Thermodynamic Functions of Perfect Gases

Perfect gases mix spontaneously in all proportions since entropy increases

for all compositions and temperatures.

There is no heat transfer to the surroundings when perfect gases mix thus

the entropy of the surroundings remain unchanged.