lecture 6. nonelectrolyte solutons

Lecture 6. NONELECTROLYTE SOLUTONS

NONELECTROLYTE SOLUTIONS

SOLUTIONS – single phase homogeneous mixture of SOLUTIONS – single phase homogeneous mixture of two or more componentstwo or more components

NONELECTROLYTES – do not contain ionic species. NONELECTROLYTES – do not contain ionic species.

CONCENTRATION UNITS

components all ofmoles of no.

i component ofmoles of .no)(x fraction mole

%100Xsolution of wt.

solute of wt

%100Xsolute of wt.solvent of wt.

solute of wt. weight by percent

i

CONCENTRATION UNITS

kg in solvent of wt.

solute ofmoles of no. (m) olalityM

solution of L

solute ofmoles of no. (M) olarityM

PARTIAL MOLAR VOLUME

Imagine a huge volume of pure water at 25 °C. If we Imagine a huge volume of pure water at 25 °C. If we add 1 mol Hadd 1 mol H22O, the volume increases 18 cmO, the volume increases 18 cm33 (or 18 (or 18

mL).mL).

So, 18 cmSo, 18 cm33 mol mol-1-1 is the molar volume of pure water. is the molar volume of pure water.

• Now imagine a huge volume of pure ethanol and add 1 Now imagine a huge volume of pure ethanol and add 1 mol of pure Hmol of pure H22O it. How much does the total volume O it. How much does the total volume

increase by?increase by?

PARTIAL MOLAR VOLUME

• When 1 mol HWhen 1 mol H22O is added to a large volume of pure O is added to a large volume of pure ethanol, the total volume only increases by ~ 14 cmethanol, the total volume only increases by ~ 14 cm33..

• The packing of water in pure water ethanol (i.e. the The packing of water in pure water ethanol (i.e. the result of H-bonding interactions), results in only an result of H-bonding interactions), results in only an increase of 14 cmincrease of 14 cm33..

PARTIAL MOLAR VOLUME

• The quantity 14 cmThe quantity 14 cm33 mol mol-1-1 is the is the partial molar volumepartial molar volume of water in pure ethanol.of water in pure ethanol.

• The partial molar volumes of the components of a The partial molar volumes of the components of a mixture varies with composition as the molecular mixture varies with composition as the molecular interactions varies as the composition changes from interactions varies as the composition changes from pure A to pure B.pure A to pure B.

PARTIAL MOLAR VOLUME

'n,T,pJn

VV

B

n,T,pBA

n,T,pA

dnn

Vdn

n

VdV

AB

When a mixture is changed by When a mixture is changed by dndnAA of A and of A and dndnBB of B, then the total volume changes by: of B, then the total volume changes by:

PARTIAL MOLAR VOLUME

PARTIAL MOLAR VOLUME

BBAA nV nVV

:by givenis ncompositio particular

a at system the of volume the B), (A, system component two a for

• How to measure partial molar volumes?How to measure partial molar volumes?

• Measure dependence of the volume on composition.Measure dependence of the volume on composition.

• Fit a function to data and determine the slope by Fit a function to data and determine the slope by differentiation.differentiation.

PARTIAL MOLAR VOLUME

• Molar volumes are always positive, but partial molar Molar volumes are always positive, but partial molar quantities need not be. The limiting partial molar quantities need not be. The limiting partial molar volume of MgSOvolume of MgSO44 in water is -1.4 cm in water is -1.4 cm33molmol-1-1, which , which

means that the addition of 1 mol of MgSOmeans that the addition of 1 mol of MgSO44 to a large to a large

volume of water results in a decrease in volume of 1.4 volume of water results in a decrease in volume of 1.4 cmcm33..

PARTIAL MOLAR VOLUME

• The concept of partial molar quantities can be extended to any The concept of partial molar quantities can be extended to any extensive state function.extensive state function.

• For a substance in a mixture, the chemical potential, For a substance in a mixture, the chemical potential, is defined is defined as the partial molar Gibbs energy.as the partial molar Gibbs energy.

PARTIAL MOLAR GIBBS ENERGIES

n,P,Tii n

GμG

• Using the same arguments for the derivation of partial molar volumes,Using the same arguments for the derivation of partial molar volumes,

• Assumption: Constant pressure and temperatureAssumption: Constant pressure and temperature

BBAA μnμnG

PARTIAL MOLAR GIBBS ENERGIES

• So we’ve seen how Gibbs energy of a mixture depends So we’ve seen how Gibbs energy of a mixture depends on composition.on composition.

• We know at constant temperature and pressure We know at constant temperature and pressure systems tend towards lower Gibbs energy.systems tend towards lower Gibbs energy.

• When we combine two ideal gases they mix When we combine two ideal gases they mix spontaneously, so it must correspond to a decrease in spontaneously, so it must correspond to a decrease in G.G.

THERMODYNAMICS OF MIXING

THERMODYNAMICS OF MIXING

• The total pressure is the sum of all the partial pressure.The total pressure is the sum of all the partial pressure.

p j x j p

pA pB (xA xB )pp

DALTON’S LAW

Gm Gm RT ln

p

p

RT lnp

p

RT ln p

lyrespective B, A, components offractions mole are x ,x

moles of number total n

)xlnxxlnx(nRTG

BA

BBAAmix

THERMODYNAMICS OF MIXING

Thermodynamics of mixingThermodynamics of mixing

RT ln p

Gi nA A RT ln p nB B

RT ln p G f nA A

RT ln pA nB B RT ln pB

mixGnART lnpAp

nBRT lnpBp

Thermodynamics of mixingThermodynamics of mixing

mixGnART lnpAp

nBRT lnpBp

pAp

xApAp

xB

mixGnART ln xA nBRT ln xBxAn nA xBn nBmixGnRT(xA ln xA xB ln xB )

mixG 0

THERMODYNAMICS OF MIXING

• A container is divided into two A container is divided into two equal compartments. One equal compartments. One contains 3.0 mol Hcontains 3.0 mol H22(g) at 25 (g) at 25

°C; the other contains 1.0 mol °C; the other contains 1.0 mol NN22(g) at 25 °C. Calculate the (g) at 25 °C. Calculate the

Gibbs energy of mixing when Gibbs energy of mixing when the partition is removed.the partition is removed.

SAMPLE PROBLEM:

Gibbs energy of mixingGibbs energy of mixing

mixGnRT(xA ln xA xB ln xB )

mixG3.0(RT ln3

4) 1.0(RT ln

1

4)

mixG 2.14 kJ 3.43 kJ

mixG 5.6 kJ

p

p

ENTHALPY, ENTROPY OF MIXING

)xlnxxlnx(nRS

ST

G

0H solutions, ideal for

STHG

BBBAmix

mixmix

mixmixmix

Other mixing functionsOther mixing functions

T) and p (constant 0H

STHG

)xlnxxlnx(nRS

)xlnxxlnx(nRTG

BBAAmix

BBAAmix

• To discuss theTo discuss the equilibrium properties of equilibrium properties of liquid mixtures we need to know how the liquid mixtures we need to know how the Gibbs energy of a liquid varies with Gibbs energy of a liquid varies with composition.composition.

• We use the fact that, at equilibrium, the We use the fact that, at equilibrium, the chemical potential of a substance present chemical potential of a substance present as a vapor must be equal to its chemical as a vapor must be equal to its chemical potential in the liquid.potential in the liquid.

IDEAL SOLUTIONS

A* A

RT ln pA* *denotes pure substance

• Chemical potential of vapor equals the chemical Chemical potential of vapor equals the chemical potential of the liquid at equilibrium.potential of the liquid at equilibrium.

If another substance is added to the pure liquid, the If another substance is added to the pure liquid, the chemical potential of A will change.chemical potential of A will change.

bar 1 p at potential chemical standard theis

plnRT

A

AAA

IDEAL SOLUTIONS

Ideal SolutionsIdeal Solutions

A* A

RT ln pA*

A A

* RT ln pA*

A A RT ln pA

A A* RT ln pA

* RT ln pA

A A* RT ln

pApA

*

pA xA pA*

RAOULT’S LAW

The vapor pressure of a component of a solution is equal to the product of its mole fraction and the vapor pressure of the pure liquid.

SAMPLE PROBLEM:

Liquids A and B form an ideal solution. At 45oC, the vapor pressure of pure A and pure B are 66 torr and 88 torr, respectively. Calculate the composition of the vapor in equilibrium with a solution containing 36 mole percent A at this temperature.

A A* RT ln

pApA

*

pA xA pA*

A A* RT ln xA

IDEAL SOLUTIONS:

Non-Ideal SolutionsNon-Ideal Solutions

Ideal-dilute solutionsIdeal-dilute solutions

• Even if there are strong Even if there are strong deviations from ideal deviations from ideal behaviour, Raoult’s law is behaviour, Raoult’s law is obeyed increasingly closely obeyed increasingly closely for the component in excess for the component in excess as it approaches purity.as it approaches purity.

Henry’s lawHenry’s law

• For real solutions at low For real solutions at low concentrations, although the concentrations, although the vapor pressure of the solute vapor pressure of the solute is proportional to its mole is proportional to its mole fraction, the constant of fraction, the constant of proportionality is not the proportionality is not the vapor pressure of the pure vapor pressure of the pure substance.substance.

Henry’s LawHenry’s Law

pB xBKB• Even if there are strong deviations from Even if there are strong deviations from

ideal behaviour, Raoult’s law is obeyed ideal behaviour, Raoult’s law is obeyed increasingly closely for the component in increasingly closely for the component in excess as it approaches purity.excess as it approaches purity.

Ideal-dilute solutionsIdeal-dilute solutions• Mixtures for which the solute obeys Henry’s Mixtures for which the solute obeys Henry’s

Law and the solvent obeys Raoult’s Law Law and the solvent obeys Raoult’s Law are called ideal-dilute solutions.are called ideal-dilute solutions.

Properties of SolutionsProperties of Solutions• We’ve looked at the thermodynamics of We’ve looked at the thermodynamics of

mixing ideal gases, and properties of ideal mixing ideal gases, and properties of ideal and ideal-dilute solutions, now we shall and ideal-dilute solutions, now we shall consider mixing ideal solutions, and more consider mixing ideal solutions, and more importantly the deviations from ideal importantly the deviations from ideal behavior.behavior.

Ideal SolutionsIdeal Solutions

Gi nAA* nBB

*

A A* RT ln xA

G f nA{A* RT ln xA} nB{B

* RT ln xB}

mixGnART ln xA nBRT ln xBmixGnRT{xA ln xA xB ln xB}

Ideal SolutionsIdeal Solutions

mixGnRT{xA ln xA xB ln xB}

mixS nR{xA ln xA xB ln xB}

mixH 0

Ideal SolutionsIdeal Solutions

mixGnRT{xART ln xA xBRT ln xB}

Gp

T

V

mixG

p

T

mixV 0

Real SolutionsReal Solutions• Real solutions are composed of particles for Real solutions are composed of particles for

which A-A, A-B and B-B interactions are all which A-A, A-B and B-B interactions are all different. different.

• There may be enthalpy and volume changes There may be enthalpy and volume changes when liquids mix.when liquids mix.

G=G=H-TH-TSS• So if So if H is large and positive or H is large and positive or S is negative, S is negative,

then then G may be positive and the liquids may be G may be positive and the liquids may be immiscible.immiscible.

Excess FunctionsExcess Functions• Thermodynamic properties of real solutions are Thermodynamic properties of real solutions are

expressed in terms of excess functions, Xexpressed in terms of excess functions, XEE..• An excess function is the difference between the An excess function is the difference between the

observed thermodynamic function of mixing and observed thermodynamic function of mixing and the function for an ideal solution.the function for an ideal solution.

Real SolutionsReal Solutions

SE mixS mixSideal

GE mixG mixGideal

H E mixH mixHideal mixH

V E mixV mixVideal mixV

Real SolutionsReal Solutions

Benzene/cyclohexaneBenzene/cyclohexane Tetrachloroethene/Tetrachloroethene/cyclopentanecyclopentane