Phase Equilibria ) ( ) ( g l A A ) ( 2 ) ( 2 g l O H O H ) ( ) ( l s A A ) ( ) ( g s A A Melting-Freezing Evaporation- Condensation Sublimation- Condensation ) ( ) ( II solid I solid A A Phase transition m p m m m S T dp V dT S d dG dp n V dT n S n G d Vdp SdT dG
Phase Equilibria. Evaporation-Condensation. Melting-Freezing. Sublimation-Condensation. Phase transition. S g >> S l > S s. The most stable phase is that with lowest chemical potential. Pressure Effect. - PowerPoint PPT Presentation
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Phase Equilibria
)()( gl AA )(2)(2 gl OHOH
)()( ls AA )()( gs AA Melting-Freezing
Evaporation-Condensation
Sublimation-Condensation
)()( IIsolidIsolid AA Phase transition
mp
mmm
ST
dpVdTSddG
dpnVdT
nS
nGd
VdpSdTdG
gasm
p
gas
liquidm
p
liquid
solidm
p
solid
ST
ST
ST
diagramTinslope
Sm
Sg >> Sl > Ss
The most stable phase is that with lowest chemical potential.
Benzene has a normal boiling point of 353.25 K. If benzene is to be boiled at 30oC, to what value must the pressure be lowered. Hvap=30.76 kJ/mol
Determine the change in the freezing point of ice upon pressure increase from 1 atm to 2 atm. Vm(water)=18.02 cm3/mol and Vm(ice)=19.63 cm3/mol at 273.15 K. Hfus=6.009 kJ/mol.
Phase RuleF: Number of degrees of freedomNumber of independent variables that can be changed without changing the number of phases
C: number of independent componentsP: number of coexisting phases
0 mixH Energy of interaction AA,BB = A-BIntramolecular forces AA,BB = A-B
0 mixV mixturemmixturempurempurem BVAVBVAV
mixturemLBmLAmL
200100100
Ideal solutions obey Raoults Law
oiii pxp
L
V
L
V
(pA)solvent > (pA)solution
oiii pxp
1
BA
AA nn
nx
BA pppsolution
BBAABATotal PXPXPPP
AAA PXP
BBB PXP
xbay
xpppp
pxpxpp
pxpxp
pxpxp
ppp
BoA
oB
oAsolution
oBB
oAB
oAsolution
oBB
oABsolution
oBB
oAAsolution
BAsolution
1
p-x phase diagramT=const.
A+BL
V
BoA
oB
oA
oBB
B
oBB
oAA
oAA
oB
LB
oA
LA
oB
LB
tot
BB
totBBtotAA
totVBBtot
VAA
BAgastotal
xppppxy
pxpxpx
pxpxpx
ppy
pyppyp
pxppxp
ppp
BoB
oA
oB
oA
oB
total
BoA
oB
oAtotal
BoB
oA
oB
oAB
B
ypppppp
xppppinsubstitute
yppppyx
solve for xB
L
V
T const.
Ex. Benzene and Toluene
• Consider a mixture of benzene, C6H6, and toluene, C7H8, containing 1.0 mol benzene and 2.0 mol toluene. At 20 °C, the vapor pressures of the pure substances are:P°benzene = 75 torrP°toluene = 22 torr
• Assuming the mixture obeys Raoult’s law, what is the total pressure above this solution?
23
T-x phase diagramp=const.
aB
cB
VcB
aB
L xxnxxn 'Lever Rule
totBA
totVL
nnn
nnn
Distillationp=const.
Colligative Properties
Colligative Properties
Kf and Kb
31
Ex. Boiling Point ElevationA 2.00 g sample of a large biomolecule was dissolved in 15.0 g of CCl4. The boiling point of this solution was determined to be 77.85 °C. Calculate the molar mass of the biomolecule. For CCl4, the Kb = 5.07 °C/m and BPCCl4 = 76.50 °C.
b
solventbsolute
solvent
solutebb
solvent
solutesolute
solutebb
KkgwtTn
kgwtnKT
kgwtnm
mKT
/
/
/
mCKkgkgwt
CCCTTT
obsolvent
oooob
/07.5015.0/
35.150.7685.77
molnsolute310026.4
molgmol
gnmMwt
solute
solutesolute /497
10026.42
3
Ex. Freezing Point DepressionEstimate the freezing point of a permanent type of antifreeze solution made up of 100.0 g ethylene glycol, C2H6O2, (MM = 62.07) and 100.0 g H2O (MM = 18.02).
33CCCTTT
TTT
Ckgwt
nKT
kgwtnmm
mKT
ooof
off
foff
o
EG
EGff
EG
EGEGsolute
soluteff
30300
3010.0
611.186.1/
/
molmolg
gMwt
mnEG
EGEG 611.1
/07.62100
Membranes and PermeabilityMembranes – Separators – Example: Cell walls– Keep mixtures organized and
separated
Permeability– Ability to pass substances through membrane
Semipermeable Membrane– Some substances pass, others don’t.– Selective
Osmosis and Osmotic Pressure
A. Initially, Soln B separated from pure water, A, by osmotic membrane (permeable to water). No osmosis occurred yet
B. After a while, volume of fluid in tube higher. Osmosis has occurred.
35
Flow of water molecules
Net flow
Column risesPressure increases
Increase of flow from right to leftFinally:
Equilibrium established
Flow of water molecules
Net flow = 0
Osmotic pressure (p): Pressure needed to stop the flow.
Equation for Osmotic Pressure
• Assumes dilute solutions
p = i M R T– p = osmotic pressure– i = number of ions per formula unit = 1 for molecules– M = molarity of solution
• Molality, m, would be better, but M simplifies• Especially for dilute solutions, where m M
– T = Kelvin Temperature– R = Ideal Gas constant
= 0.082057 L·atm·mol1K1
37
Eye drops must be at the same osmotic pressure as the human eye to prevent water from moving into or out of the eye. A commercial eye drop solution is 0.327 M in electrolyte particles. What is the osmotic pressure in the human eye at 25°C?
atmKmolKatmLM 00.829808206.0327.0
p
p = MRT T(K) = 25°C + 273.15
Using p to determine MMThe osmotic pressure of an aqueous solution of certain protein was measured to determine its molar mass. The solution contained 3.50 mg of protein in sufficient H2O to form 5.00 mL of solution. The measured osmotic pressure of this solution was 1.54 torr at 25 °C. Calculate the molar mass of the protein.