LECTURE 6 NON ELECTROLYTE SOLUTION€¦ · LECTURE 6 NON ELECTROLYTE SOLUTION Ch 45.5 Applied Phy Chem First Sem 2014-15 Ch 45.5 Exam I September 1/3 (Multiple Choice/Problem Solving)

8/6/14

1

LECTURE 6 NON ELECTROLYTE SOLUTION

Ch 45.5 Applied Phy Chem First Sem 2014-15

Ch 45.5 Exam II

September 1/3 (Multiple Choice/Problem Solving) Coverage:

Second/Third Laws of Thermodynamics Nonelectrolyte Solution Electrolyte Solutions Phase Equilibria

EXAM III October 6 and 7 Chemical Equilibria, Electrochemistry

8/6/14

2

NONELECTROLYTE SOLUTIONS

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

=

+=

8/6/14

3

CONCENTRATION UNITS

kg in solvent of wt.solute ofmoles of no. (m) olalityM

solution of Lsolute ofmoles of no. (M) olarityM

=

=

PARTIAL MOLAR VOLUME

Imagine a huge volume of pure water at 25 °C. If we add 1 mol H2O, the volume increases 18 cm3 (or 18 mL). So, 18 cm3 mol-1 is the molar volume of pure water.

8/6/14

4

Now imagine a huge volume of pure ethanol and add 1 mol of pure H2O it. How much does the total volume increase by?


•  When 1 mol H2O is added to a large volume of pure ethanol, the total volume only increases by ~ 14 mL.

•  The packing of water in pure water ethanol (i.e. the result of H-bonding

interactions), results in only an increase of 14 mL.


8/6/14

5

•  The quantity 14 cm3 mol-1 is the partial molar volume of water in pure ethanol.

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


8/6/14

6

'n,T,pJnVV ⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ=

Bn,T,pB

An,T,pA

dnnVdn

nVdV

AB

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+⎟⎟

⎠

⎞⎜⎜⎝

⎛

∂

∂=

n  When a mixture is changed by dnA of A and dnB of B, then the total volume changes by:


8/6/14

7


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? •  Measure dependence of the volume on composition. •  Fit a function to data and determine the slope by

differentiation.


8/6/14

8

•  Molar volumes are always positive, but partial molar quantities need not be. The limiting partial molar volume of MgSO4 in water is -1.4 cm3mol-1, which means that the addition of 1 mol of MgSO4 to a large volume of water results in a decrease in volume of 1.4 cm3.


8/6/14

9

What is the total volume of a mixture of 50.0 g ethanol and 50.0 g of water at 25oC? The partial molar volumes of the 2 substances in mixtures of this compositions are 56.0 ml/mole and 18.0 ml per mole respectively. (Answer: 110 ml) (0.84)

SAMPLE PROBLEM 5.01

Answer: 110 ml) A commercial rubbing alcohol is 82.5% in ethyl alcohol and 17.5% water. Partial molar volumes of water at this composition is 16.8 ml/mole and 57.4 ml/mole for ethanol. What is the density of the rubbing alcohol? (What is the density0.84)

SAMPLE PROBLEM 5.02

8/6/14

10

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

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

PARTIAL MOLAR GIBBS ENERGIES

n,P,Tii n

GµG ⎟⎠

⎞⎜⎝

⎛Δ

Δ==

8/6/14

11

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

•  Assumption: Constant pressure and temperature

BBAA µnµnG +=

PARTIAL MOLAR GIBBS ENERGIES

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

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

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

THERMODYNAMICS OF MIXING

8/6/14

12


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

€

p j = x j ppA + pB +L = (xA + xB +L )p = p

DALTON’S LAW

8/6/14

13

€

Gm =Gmθ + RT ln p

pθ

µ = µθ + RT ln ppθ

µ = µθ + RT ln p

lyrespective B, A, components offractions mole are x ,xmoles of number total n

)xlnxxlnx(nRTG

BA

BBAAmix

=

+=Δ



€

µ = µθ + RT ln p

Gi = nA µAθ + RT ln p( )+ nB µB

θ + RT ln p( )Gf = nA µA

θ + RT ln pA( )+ nB µBθ + RT ln pB( )

ΔmixG = nART lnpAp

+ nBRT lnpBp

8/6/14

14

€

ΔmixG = nART lnpAp

+ nBRT lnpBp

pAp

= xApAp

= xB

ΔmixG = nART ln xA + nBRT ln xBxAn = nA xBn = nBΔmixG = nRT(xA ln xA + xB ln xB )ΔmixG < 0



8/6/14

15

•  A container is divided into two equal compartments. One contains 3.0 mol H2(g) at 25 °C; the other contains 1.0 mol N2(g) at 25 °C. Calculate the Gibbs energy of mixing when the partition is removed.

SAMPLE PROBLEM 5.03

GIBBS ENERGY OF MIXING

€

ΔmixG = nRT(xA ln xA + xB ln xB )

ΔmixG = 3.0(RT ln 34

) +1.0(RT ln 14

)

ΔmixG = −2.14 kJ − 3.43 kJΔmixG = −5.6 kJ

p

p

8/6/14

16

ENTHALPY, ENTROPY OF MIXING

)xlnxxlnx(nRS

ST

G

0H solutions, ideal for

STHG

BBBAmix

mixmix

mixmixmix

+−=Δ

Δ−=Δ

=Δ

Δ−Δ=Δ

8/6/14

17

OTHER MIXING FUNCTIONS

T) and p (constant 0H

STHG

)xlnxxlnx(nRS)xlnxxlnx(nRTG

BBAAmix

BBAAmix

=Δ

Δ−Δ=Δ

+−=Δ

+=Δ

SAMPLE PROBLEM 5.03

Calculate the Gibbs Energy and entropy of mixing 1.6 moles of Argon at 1.0 atm with 2.6 moles of Nitrogen at 1.0 atm and 25oC. Assume ideal behavior.

8/6/14

18

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

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

IDEAL SOLUTIONS

€

µA* = µA

θ + RT ln pA* *denotes pure substance

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

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

bar 1 p at potential chemical standard theis plnRT

A

AAA

=µ

+µ=µθ

θ

IDEAL SOLUTIONS

8/6/14

19

IDEAL SOLUTIONS

€

µA* = µA

θ + RT ln pA*

µAθ = µA

* − RT ln pA*

µA = µAθ + RT ln pA

µA = µA* − RT ln pA

* + RT ln pA

µA = µA* + RT ln pA

pA*

€

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.

8/6/14

20

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.

SAMPLE PROBLEM 5.04

€

µA = µA* + RT ln pA

pA*

pA = xA pA*

µA = µA* + RT ln xA

IDEAL SOLUTIONS:

8/6/14

21

NON-IDEAL SOLUTIONS

IDEAL-DILUTE SOLUTIONS

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

8/6/14

22

HENRY’S LAW

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

€

pB = xBKB

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

HENRY’S LAW

8/6/14

23

•  Mixtures for which the solute obeys Henry’s Law and the solvent obeys Raoult’s Law are called ideal-dilute solutions.

IDEAL-DILUTE SOLUTIONS

PROPERTIES OF SOLUTIONS

•  We’ve looked at the thermodynamics of mixing ideal gases, and properties of ideal and ideal-dilute solutions, now we shall consider mixing ideal solutions, and more importantly the deviations from ideal behavior.

8/6/14

24

IDEAL SOLUTIONS

€

Gi = nAµA* + nBµB

*

µA = µA* + RT ln xA

Gf = nA{µA* + RT ln xA}+ nB{µB

* + RT lnxB}ΔmixG = nART lnxA + nBRT lnxBΔmixG = nRT{xA ln xA + xB ln xB}

€

ΔmixG = nRT{xA ln xA + xB ln xB}

ΔmixS = −nR{xA ln xA + xB ln xB}

ΔmixH = 0

IDEAL SOLUTIONS

8/6/14

25

€

ΔmixG = nRT{xART ln xA + xBRT ln xB}

∂G∂p⎛

⎝ ⎜

⎞

⎠ ⎟ T

=V

∂ΔmixG∂p

⎛

⎝ ⎜

⎞

⎠ ⎟ T

= ΔmixV = 0

IDEAL SOLUTIONS

•  Real solutions are composed of particles for which A-A, A-B and B-B interactions are all different.

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

•  ΔG=ΔH-TΔS •  So if ΔH is large and positive or ΔS is negative,

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

REAL SOLUTIONS

8/6/14

26

EXCESS FUNCTIONS

•  Thermodynamic properties of real solutions are expressed in terms of excess functions, XE.

•  An excess function is the difference between the observed thermodynamic function of mixing and the function for an ideal solution.

REAL SOLUTIONS

€

SE = ΔmixS −ΔmixSideal

GE = ΔmixG −ΔmixGideal

HE = ΔmixH −ΔmixHideal = ΔmixH

V E = ΔmixV −ΔmixVideal = ΔmixV

8/6/14

27

Real Solutions

Benzene/cyclohexane

Tetrachloroethene/cyclopentane

•  A colligative property is a property that depends only on the number of solute particles present, not their identity.

•  The properties we will look at are: lowering of vapor pressure; the elevation of boiling point, the depression of freezing point, and the osmotic pressure arising from the presence of a solute.

•  Only applicable to dilute solutions.

COLLIGATIVE PROPERTIES:

8/6/14

28

•  All the colligative properties stem from the reduction of the chemical potential of the liquid solvent as a result of the presence of solute.

A*AA xlnRT+µ=µ

COLLIGATIVE PROPERTIES:

As solute molecules are added to a solution, the solvent become less volatile (=decreased vapor pressure).

Solute-solvent interactions

contribute to this effect.

VAPOR PRESSURE LOWERING:

8/6/14

29

Therefore, the vapor pressure of a solution is lower than that of the pure solvent.

VAPOR PRESSURE LOWERING:

PA = xAP°A where

•  XA is the mole fraction of compound A •  P°A is the normal vapor pressure of A at that temperature

NOTE: This is one of those times when you want to make sure you have the vapor pressure of the solvent.

VAPOR PRESSURE LOWERING: RAOULT’S LAW

8/6/14

30

Glycerin (C3H8O3) is a nonvolatile nonelectrolyte with a density of 1.26 g/mL at 25oC. Calculate the vapor pressure at 25oC of a solution made by adding 50.0 mL of glycerin to 500.0 mL of water. The vapor pressure of pure water at 25°C is 23.8 torr.

PRACTICE EXERCISE

The vapor pressure of pure water at 110oC is 1070 torr. A solution of ethylene glycol and water has a vapor pressure of 1.00 atm at 110°C. Assuming that Raoult’s law is obeyed, what is the mole fraction of ethylene glycol in the solution?

SAMPLE PROBLEM:

8/6/14

31

•  How do we figure out where the new boiling point is when a solute is present?

•  Look for the temperature at which at 1 atm, the vapor of pure solvent vapor has the same chemical potential as the solvent in the solution.

BOILING POINT ELEVATION:

•  Let’s denote solvent A and solute B. •  Equilibrium is established when:

€

µA (g) = µA* (g)+ RT lnxA = µA

* (l)+ RT lnxA

€

ΔT =KxB K =RT*2

Δ vapH


8/6/14

32

n  ΔT makes no reference to the identity of the solute, only to its mole fraction.

n  So the elevation of boiling point is a colligative property.

€

ΔT =KxB K =RT*2

Δ vapH


8/6/14

33

molality m constant; point boiling K mKT:purposes practical For

KxT

bb

B

===Δ

=Δ


8/6/14

34

•  Let’s denote solvent A and solute B. •  Equilibrium is established when:

€

µA (s) = µA* (l)+ RT lnxA

n  Same calculation as before (Justification 5.1)

€

ΔT = ʹ′ K xB ʹ′ K =RT*2

Δ fusH

FREEZING POINT DEPRESSION:

molality m constant; point freezing K mKT:purposes practical For

xKT

ff

B

===Δ

ʹ′=Δ

FREEZING POINT DEPRESSION:

8/6/14

35

What will be the freezing point and boiling point of an aqueous solution containing 55.0 g of glycerol, C3H5(OH)3, and 250 g of water? Kb(H2O) = 0.51oC/m and Kf = 1.86o C/m.

SAMPLE PROBLEM:

8/6/14

36

A solution is prepared from 25.0 g of benzene, C6H6, and 2.50 g of an unknown compound. The freezing point of this solution is 4.3oC. The normal freezing point of benzene is 5.5 oC and the freezing point depression constant for benzene is –5.12 oC/m . Determine the molar mass of the compound.

SAMPLE PROBLEM:

Cryoscopy

€

ΔT =K fb K f = freezing point constant; b = molality

b =n

1 kg solvent=

m M1 kg solvent

8/6/14

37

Solubility •  Although solubility is not strictly a colligative

property (because solubility varies with the identity of the solute), it may be estimated using the same techniques.

•  When a solid solute is left in contact with a solvent, it dissolves until the solution is saturated with the dissolved solute.

8/6/14

38

Solubility

•  See Justification 5.2

€

µB (s) = µB* (l)+ RT lnxB

€

lnxB =Δ fusHR

1Tf−1T

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

•  Osmosis refers to the spontaneous passage of a pure solvent into a solution separated from it by a semi-permeable membrane.

•  In this case, the membrane is permeable to the solvent but not to the solute.

OSMOSIS:

8/6/14

39

•  The osmotic pressure, π, is the pressure that must be applied to the solution to stop the influx of solvent.

•  Examples of osmosis includes the transport of fluids across cell membranes and dialysis.

OSMOSIS:

8/6/14

40

OSMOSIS:

solute the ofmass molar theis Mg/L in solute the of ionconcentrat theis c

MRT

c

orsolution the of molarityis M

solution the of pressure osmotic theis MRT

2

2

22

=π

π

=π

An aspartic acid solution will produce an osmotic pressure of 1.80 atm measured against pure water at 18.5 °C. How many g of Aspartic Acid(C4H7NO4, M=133.1 g/mol) must be dissolved in a liter of water to produce an isotonic solution?

SAMPLE PROBLEM:

Documents

LECTURE 6 NON ELECTROLYTE SOLUTION€¦ · LECTURE 6 NON ELECTROLYTE SOLUTION Ch 45.5 Applied Phy Chem First Sem 2014-15 Ch 45.5 Exam I September 1/3 (Multiple Choice/Problem Solving)