Chemistry 232 Properties of Solutions
Feb 24, 2016
Chemistry 232
Properties of Solutions
Concentration Terms Dilute - not a lot of solute. Concentrated - a large amount of
solute. Concentration can be expressed
quantitatively is many ways:• Molarity• Molality• Percentage• Mole fraction
Molarity and Molality The molarity is the number of moles of
solute in 1 litre of solution.• M = moles of solute / V sol’n (litres)
The molality is the number of moles of solute in 1 kg of solvent.• M = moles of solute / kg solvent
Conversion between the two requires the solutions density.
Partial Molar Thermodynamic Properties
Define a partial molar thermodynamic property as
Euler’s Theorem
'n,P,TJJ n
YY
J
JJYnY
The Chemical Potential
We define the chemical potential of a substance as
'n,P,TJJ n
G
The Wider Significance of Shows how all
the extensive thermodynamic properties depend on system composition
'n,V,SJJ n
U
'n,P,SJJ n
H
'n,V,TJJ n
A
Thermodynamics of Mixing Spontaneous mixing of two or
more substances to form solutions
Gibbs energy of the solution must be less than G(pure components)
The Gibbs Energy of Mixing
J
JJmix XlnXnRTG
The Enthalpy and Entropy
lnmixJ J
JP
mix
G nR X XT
S
2
mixmix
P
GHT
T T
The Ideal SolutionTmixS/n
TmixG/n
TmixH/n0
kJ/mol
XA
The Volume and Internal Energy of Mixing
VPG
mixT
mix
VPHU mixmixmix
Ideal Solution Def’n For an ideal solution
0H;0V mixmix
0VPHU mixmixmix
Raoult’s Law
Consider the following system
Raoult’s Law #2
The chemical potential expressions
AO
AA
A*AA
plnRTvapvapXlnRTliqliq
Raoult’s Law: Depression of Vapour pressure
VP of solution relates to VP of pure solvent
PA = XAP*A
Solutions that obey Raoult’s law are called ideal solutions.
Raoult’s Law Example The total vapour
pressure and partial vapour pressures of an ideal binary mixture
Dependence of the vp on mole fractions of the components.
An Ideal Solution
Benzene and toluene behave almost ideally
Follow Raoult’s Law over the entire composition range.
Henry’s Law Henry’s law relates
the vapour pressure of the solute above an ideally dilute solution to composition.
The Ideal Dilute Solution
Ideal Dilute Solution• Solvent obeys
Raoult’s Law• Solute obeys
Henry’s Law
Henry’s Law #2 The chemical potential
expressions
JO(H)
is the Henry’s law standard state.
It is the chemical potential of J in the vapour when PJ = kJ.
( )' lnln
O HJ J J
OJ J J
sol n liq RT X
vap vap RT p
Henry’s Law #3 The Standard State
Chemical potential for Henry’s Law
When the system is in equilibrium
The chemical potential expressions reduce to Henry’s Law
J
oJ
oH,J
klnRTvap
vapn'sol JJ
JJJ XkP
Henry’s Law in terms of molalities The Standard State
Chemical potential for Henry’s Law
When the system is in equilibrium
The chemical potential expressions reduce to Henry’s Law in terms of molalities
oJoHJ
omJ mMRT ln,,
vapn'sol JJ
J
mJJ mkP
Chemical Potentials in terms of the Molality
The chemical potential expressions
o
JmJJ m
mRTnsol ln' ,
oJ,m = chemical potential of the solute in an
ideal 1 molal solution
The Gibbs-Duhem Equation The Gibbs-Duhem gives us an
interrelationship amongst all partial molar quantities in a mixture
J
JJdYn0
Colligative Properties
Colligative Properties All colligative properties
• Depend on the number and not the nature of the solute molecules
Due to reduction in chemical potential in solution vs. that of the pure solvent• Freezing point depression• Boiling Point Elevation• Osmotic Pressure
Boiling Point Elevation Examine the chemical potential
expressions involved
vapliq JJ
J*JJ XlnRTliqvap
G
XRTliqvap
vap
JJJ
ln*
Boiling Point Elevation #2 The boiling point elevation
B
vap
bb X
JHJRTT
2
*
BbJvap
Jbb mKm
JHMRTT
2
*
Freezing Point Depression Examine the chemical potential
expressions involved
sliq *JJ
J*JJ XlnRTliqliq
G
XlnRTliqs
fus
J*J
*J
Freezing Point Depression #2 Define the freezing point depression
B
fus
ff X
JHJRTT
2
*
BfJ
fus
ff mKm
JHJMRTT
2
*
Osmosis
Osmosis The movement of water through a
semi-permeable membrane from dilute side to concentrated side• the movement is such that the two sides
might end up with the same concentration Osmotic pressure: the pressure
required to prevent this movement
Osmosis – The Thermodynamic Formulation Equilibrium is established across
membrane under isothermal conditions
PP *JJ
J*JJJ XlnRTPX,P
- the osmotic pressure
The Final Equation
RTMRTVn
BB
The osmotic pressure is related to the solutions molarity as follows
Terminology Isotonic: having the same osmotic
pressure Hypertonic: having a higher osmotic
pressure Hypotonic: having a lower osmotic
pressure
Terminology #2 Hemolysis: the process that ruptures a
cell placed in a solution that is hypotonic to the cell’s fluid
Crenation: the opposite effect
The Partial Molar Volume In a multicomponent system
J
JJVnV
'n,P,TJJ n
VV
Volume Vs. Composition The partial molar volume of
a substance • slope of the variation of the
total sample volume plotted against composition.
PMV’s vary with solution composition
The PMV-Composition Plot
The partial molar volumes of water and ethanol at 25C.
Note the position of the maxima and minima!!
Experimental Determination of PMV’s
Obtain the densities of systems as a function of composition
Inverse of density – specific volume of solution
mLg1
gmLVs
2CmBmAmolmLV
Example with Methanol. Plot volumes vs. mole fraction of
component A or B Draw a tangent line to the plot of
volume vs. mole fraction. Where the tangent line intersects the
axis – partial molar volume of the components at that composition
The Solution Volume vs. Composition
The Mean Molar Volume
Define the mean mixing molar volume as• V*
J – the molar volume of the pure liquid
• Vm = V/nT
J
*JJmmix VxVV
The Mean Molar Volume Plot
-1.20
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.00 0.50 1.00
XMeOH
m
ixV m
/ (m
L/m
ol)
VA-VA* VB-VB
*
Infinite Dilution Partial Molar Properties
The value of a partial molar thermodynamic property in the limit of zero volume is its infinite dilution value• E.g., for the volumes
J0xJ VlimVJ
The Definition of the Activity
For any real system, the chemical potential for the solute (or solvent) is given by
Jo
J aRT ln
Activities of Pure Solids/Liquids The chemical potential is essentially
invariant with pressure for condensed phases
ooJ
p
PJ
ooJJ
P
dpVPPo
Pure Solids and Pure Liquids For a pure solid or a pure liquid at
standard to moderately high pressures
JaRT0 ln
or aJ = 1
Activities in Gaseous Systems The chemical potential of a real gas
is written in terms of its fugacity
Jo
J fRT ln
Define the Activity Coefficient The activity coefficient (J) relates the
activity to the concentration terms of interest.
In gaseous systems, we relate the fugacity (or activity) to the ideal pressure of the gas via
JJJ fP
Activities in Solutions Two conventions Convention I
• Raoult’s Law is applied to both solute and solvent
Convention II• Raoult’s Law is applied to the solvent;
Henry’s Law is applied to the solute
Convention I We substitute the activity of the
solute and solvent into our expressions for Raoult’s Law
*J
IJJ PaP
IJJ
IJ ax
Convention I (cont’d) Vapour pressure above real
solutions is related to its liquid phase mole fraction and the activity coefficient
*JJ
IJJ PxP
Note – as XJ 1J
I 1 and PJ PJid
Convention II The solvent is treated in the same
manner as for Convention I For the solute, substitute the solute
activity into our Henry’s Law expression
JIIJJ kaP
IIJJ
IIJ ax
Convention II (cont’d) Vapour pressure above real dilute
solutions is related to its liquid phase mole fraction and activity coefficient
JJIIJJ kxP
Note – as XJ 0J
II 1 and PJ PJid
Convention II - Molalities For the solute, we use the molality
as our concentration scale
mJJ
mJ am
mJ
moJJ aRT ln
Note – as mJ 0J
(m) 1 and aJ(m) mJ