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The Chemical Potential

of Liquids

Ideal Solutions: Raoult’s Law

Ideal- dilute Solutions: Henry’s Law

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Intermolecular forces in a

solution…once again

B

B

1

2

3

(1) Solvent molecules, A-A(2)Solute molecules, B-B(3)Solvent and solute molecules, A-B

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The Chemical Potential of Ideal Solutions

Letµ A* = the chemical potential of pure substance Aµ A = the chemical potential of substance A in solutionµ A = the standard chemical potential of substance A

When phases are at equilibrium, the chemical potential of a substance

as a vapor is equal to the chemical potential of a substance as aliquid.

As a pure substance,

ln A A A

RT p Liquid phase

In solution,

ln A A A RT p

ln A A A A

p RT

p

Vapor phase

When two or more phases arein equilibrium the chemicalpotential of a substance (and, ina mixture, a component) is thesame in each phase and is the

same at all points in eachphase .

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Raoult’s Law

French chemist FrançoisRaoult experimented onmixtures of closely relatedliquids (methylbenzeneand benzene).

* A A A p x p

The ratio of the partial vapor pressure of eachcomponent to its vapor pressure as a pure liquid,

p A /p* A, is approximately equal to the mole fractionof A in the liquid mixture, x A .

The vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in

the solution .

The law is only valid for Ideal Solutions!!!

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Raoult’s Law & Vapor Pressure of Solutions

Vapor pressure of solutions containing non-volatilesolutes,

P soln is the observed vapor pressure of the solution, X solvent is the mole fraction of the solvent, andP osolvent is the vapor pressure of the pure solvent.

The presence of the non-volatile solute simply dilutes the solvent.

If a pure solute which has zero vapor pressure (it will not evaporate) is dissolvedin a solvent, the vapor pressure of the final solution will be lower than that of thepure solvent.

Once the components in the solutin have reached equilibrium, the totalvapor pressure p of the solution is:

*soln solvent solvent p x p

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Raoult’s Law & the Chemical Potential

• For an ideal solution, then

ln A A A RT x

•This equation can be used to define an ideal solution (sothat it implies Raoult’s law rather than stem from it)!•The equation above provides a better definition of anideal solution since it does not assume that the vapor isan ideal gas.

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Raoult’s Law & Ideal Solutions

Components with similar structures form ideal solutions!

Methylbenzene

Benzene

Total

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Molecular Basis of Raoult’s Law

B

l o c

k e

d

Solute prevents the escape of solvent moleculesinto the vapor phase, but do not hinder their

return.

Pure solventSolution with a

non-volatilesolute

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Molecular Basis of Raoult’s Law

B l o c

k e

d

The rate at which A molecules leave the surface isproportional to the number of them at the surface, whichin turn is proportional to the mole fraction of A:

rate of vaporization = Akx

The rate at which A molecules condense is proportionalto their concentration in the gas phase, which in turn isproportional to their partial pressure:

rate of condensation = ' Ak p

At equilibrium, = ' A Akx k p

For a pure liquid, x A is 1.*

' A

k p

k

Analogous to*

A A A p x p

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The Validity of Raoult’s Law

Ideal mixing occurred which results in the formation of an idealsolution.

Both liquid and vapor behave ideally.

The molecules of the solute and the solvent are almost identicalchemically so that interactions between solute-to-solvent can beneglected.

Cohesive and adhesive forces are uniform between two liquids sothat chemical interactions between liquids are equal to the bonding

within liquids. If the deviations from ideality are not too strong, Raoult's law willstill be valid in a narrow concentration range when approaching x =1 for the majority phase (the solvent ). Will the solute still obeyRaoult’s law???

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Dilute-Ideal Solution

• A solution which followsHenry’s law and Raoult’s

law• Low solute concentration• Solute and solvent are

very similar

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Henry’s Law

B B B p x K

For real solutions at low concentrations, the constant of proportionality is not the vapor pressure of the puresubstance.

Let B the solute . K B is an empirical constant (with

the dimension of pressure) chosen so that theplot of the vapor pressure of B against its molefraction is tangent to the experimental curve at x B= 0.

William Henry, an Englishchemist, who is a close friendof John Dalton formulated this relationship.

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Henry’s Law

Similarly, Henry’s law reveals the pressureeffects on the solubilities of gases.

P kC P is the partial pressure of the gaseous solute above the solution, C is theconcentration of the dissolved gas, and k is the constant of proportionality

characteristic of a particular solution(depends on the solute and the solvent) andwhich depends on the temperature.

At a constant temperature, the amount of a given gas dissolved ina given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

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Henry’s Law

(a) A gaseous solute in equilibrium with a solution.(b) The piston is pushed in, which increases the pressure of the gas and the number of gas molecules

per unit volume.

(c) The greater the gas concentration in the solution causes an increase in the rate of escape. A newequilibrium is reached.

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Molecular Basis of Henry’s Law

In a dilute solution, the solvent molecules (the green spheres) are in an environment that differsfrom that of the pure solvent. The solute particles, however, are in an environment totally unlike solvent. Thus, the solvent behaves like a slightly modified liquid but the solute behaves entirely dipure state unless the solvent and solute molecules happento be very similar.

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Illustration of Henry’s Law

Carbonation in abottle of soda

Lake Nyos, Cameroon: A tragedyKilled 2,000 people on August 21, 1986

due to suffocation of CO 2

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Determination of Henry’s Constant

p A*

p C*

K AKC

Raoult’s law

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Henry’s law constants for gases in water at 298K

Gas Henry’s constant ,K B [ Torr]

Henry’s constant,k [kPa.kgmol -1 ]

CO 2

H 2

N 2

O 2

1.25 x 10 6

5.34 x 10 7

6.51 x 10 7

3.30 x 10 7

3.01 x 10 3

1.28 x 10 3

1.56 x 10 3

7.92 x 10 3

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The Validity of Henry’s Law

Henry's Law is a limiting law that only appliesfor sufficiently dilute solutions.

The range of concentrations in which it appliesbecomes narrower the more the systemdiverges from ideal behavior.

Only applies simply for solutions where thesolvent does not react chemically with the gasbeing dissolved.

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Real (Non-ideal) Solutions

Composed of particles for A-A, A-B, and B-Binteractions are all different

There is enthalpy change when liquids mix.

There may also be additional contribution to theentropy arising from the way in which themolecules of one type might cluster togetherinstead of mingling freely with the others.

E mix mix ideal S S S

The excess enthalpy and volume are both equal to the observed enthalpy andvolume of mixing. W H Y ? ? ?

What is aREGULAR SOLUTION

?

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Non-Ideal Solutions

B B x K p

*

A A p x p

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Non-Ideal Solutions

Match the letter corresponding to the figure in question. Identify which of the figures above exemplifies:i.Positive deviation from Raoult’s lawii.Negative deviation from Raoult’s lawiii.An ideal solution

(A) (C)(B)