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Lecture 7.pdf-Simple mixtures Chapter 5 Sections A

Lecture_7.pdf-Simple mixtures Chapter 5 Sections A

Lecture 7.pdf-Simple mixtures Chapt...

Lecture_7.pdf-Simple mixtures Chapter 5 Sections A

##### Page 12

Chemical potential (

μ

) wider

significance

Chemical potential does more than show how G varies with composition

Similarly, chemical potential shows how H and A may change

##### Page 13

Thermodynamics of mixing

Perfect gases

•

Gibbs energy of a mixture depends on its

composition :

–

G = n

A

μ

A

+ n

B

μ

B

(for 2 components)

•

At constant T & p, systems tend towards lower

Gibbs energy

•

Mixing : spontaneous change of composition

–

Example : 2 gases, introduced into the same

container, will spontaneously mix; this

##### Page 14

PHYSICAL CHEMISTRY: THERMODYNAMICS, STRUCTURE, AND CHANGE 10E | PETER ATKINS | JULIO DE PAULA

©2014

W. H. FREEMAN AND COMPANY

CHAPTER 5:

FIGURE 5A.6

##### Page 15

Thermodynamics of mixing

Perfect gases - 2

Two perfect gases (A & B) at same T & p

Initially (before mixing), they each have their “pure” values

of chemical potential:

μ

= G

m

=

μ

ϴ

+RT ln (p/p

ϴ

)

(where

μ

ϴ

is the standard chemical potential of the pure gas

at 1 bar)

Convention : replace p/p

ϴ

by p (since p

ϴ

is = 1 bar)

Then :

μ

=

μ

ϴ

+ RT ln p for each gas

Thus in the initial state (before mixing) , for the

system:

G

i

= n

A

μ

A

+ n

B

μ

B

=

##### Page 16

Thermodynamics of mixing

Perfect gases - 3

Before mixing , for the

system:

G

i

= n

A

(

μ

ϴ

A

+ RT ln p) + n

B

(

μ

ϴ

B

+RT ln p)

After mixing, the partial pressures of the gases are p

A

and p

B

, with p

A

+

p

B

= p

After mixing, for the system :

G

f

= n

A

(

μ

ϴ

A

+ RT ln p

A

) + n

B

(

μ

ϴ

B

+RT ln p

B

)

The difference G

f

–

G

i

=

∆

mix

G is given by :

∆

mix

G = n

A

RT ln (p

A

/p) + n

B

R

T ln (p

B

/p)

Which may be rewritten as :

∆

mix

G =

Recall :

##### Page 17

Thermodynamics of mixing

Perfect gases - 4

∆

mix

G = nRT(x

A

ln x

A

+ x

B

ln x

B

)

Because mole fractions are always < 1,

the ln values in the equation are

always negative.

Thus

∆

mix

G <0 for all compositions, i.e.

perfect gases mix spontaneously in all

proportions

##### Page 18

Thermodynamics of mixing

Perfect gases - 5

Entropy

Since

It follows that:

∆

mix

S= - nR(x

A

lnx

A

+ x

B

lnx

B

)

##### Page 19

Thermodynamics of mixing

Perfect gases - 6

Enthalpy

Since

∆

G =

∆

H -T

∆

S

⇨

∆

H =

∆

G + T

∆

S

And

∆

mix

G = nRT(x

A

ln x

A

+ x

B

ln x

B

)

∆

mix

S= - nR(x

A

lnx

A

+ x

B

lnx

B

)

∆

mix

H = nRT(x

A

ln x

A

+ x

B

ln x

B

) +T [- nR(x

A

lnx

A

+ x

B

lnx

B

)]

##### Page 20

Chemical potentials of liquids

•

To discuss the equilibrium properties

of liquid mixtures, we need to know

how

G varies with composition.

•

Recall : at equilibrium, the chemical

potential of a substance in the liquid

phase is equal to its chemical

potential in the gas phase.

##### Page 21

μ

of liquids : ideal solutions

•

Using superscript

*

for quantities related to pure substances :

μ

A

* (l) for example

•

Vapor pressure of a pure liquid is p

A

*

•

Recall, for a perfect gas

μ

=

μ

ϴ

+RT ln (p/p

ϴ

)

•

Since, at equilibrium,

μ

A

(l) =

μ

A

(g), we can write

If another substance (solute) is also present in the liquid, its

μ

A

*

is changed to

μ

A

and its vapour pressure is changed to pA. The

vapour and solvent are still in equilibrium, so :

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