Chapter 13

Properties of Solutions
Solution
Formed when one substance is uniformly
dispersed throughout another
Solutions form when solute-solvent
intermolecular forces are comparable to
those between the solute-solute and
solvent-solvent molecules
Enthalpy of solution can be either
Exothermic
MgSO4 + ( x + y )H 2O → Mg +2 ( H 2O )x + SO4−2 ( H 2O )y
∆H soln = −91.2kJ / mol
or
Endothermic
NH 4 NO3 + ( x + y )H 2O → NH 4+ ( H 2O )x + NO3− ( H 2O )y
∆H soln = +26.4kJ / mol
Both are spontaneous!
Spontaneity & Disorder
Processes in which the energy content of
the system decreases tend to occur
spontaneously
Exothermic processes tend to be
spontaneous
Endothermic processes can be
spontaneous if the
entropy change is positive
Entropy measures disorder
Criterion for spontaneity is
∆G < 0
∆G = ∆H − T ∆S
Solubility
Given that one material dissolves in
another what determines how much?
Solubility of NaCl
35.7 grams in 100 mL water
Enthalpy of Solution-Components
∆H soln = ∆H1 + ∆H 2 + ∆H 3
Solubility (continued)
Polar liquids tend to dissolve
in polar solvents
Non-polar liquids tend to be
insoluble in polar solvents
Non-polar liquids tend to be
soluble in non-polar solvents
Liquids that mix in all proportions
are miscible
Liquids that do not dissolve in one
another are immiscible
“like dissolves like”
Entropy of Mixing
∆S mix = − R( ηa ln xa + ηb ln xb )
Saturated Solution
Pressure & Temperature Effects
Pressure has no effect on the solubility of
liquids & solids
Pressure has a large effect on the
solubility of gases
Henry’s Law
The solubility of a gas is directly
proportional to the partial pressure of the
gas above the solution
S gas ( mol / L ) = kPgas ( atm )
k depends on the solvent as well as the
dissolved gas
k for N2 in water at 25 0C is
6.8 x 10-4 mol/L-atm
Solubility of ionic solids in water
increases
with increasing temperature
Colligative Properties
Depends on the concentration of the
solute but not on its identity
Vapor pressure lowering
Adding a non-volatile solute to a solvent
always lowers the vapor pressure of the
solution
Raoult’s law
PA = X P
0
A A
PA0 vapor pressure of pure A
X A mole fraction of A in solution
PA vapor pressure of A above solution
Example of Raoult’s Law
What is the vapor pressure of a solution
made by adding
50.0 mL of glycerin (non-volatile)
to
500.0 mL of water at 25 0C?
Density of glycerin (C3H8O3) 1.26g/mL
Vapor pressure of pure water at 25 0C
23.8 torr
Ideal Solution
A mixture of two or more
volatile components,
each of which obeys
Raoult’s law
PA = X
soln
A
P & PB = X
0
A
soln 0
B
B
P
Ptotal = PA + PB
XA + XB =1
Mole fraction of A and B in Vapor
X
vapor
A
PA
PB
vapor
=
& XB =
Ptotal
Ptotal
Solution of benzene (C6H6) and
toluene (C7H8) made by mixing
1.0 mol benzene and 2.0 mol toluene
X Bsoln = 1 / 3 & X Tsoln = 2 / 3
P = 75torr & P = 22torr
0
B
0
T
75torr
PB =
= 25torr
3
2
PT = 22torr = 14.7torr
3
Ptotal = PB + PT = 39.7torr
X
Vapor
B
PB
25.0torr
=
=
= 0.63
Ptotal 39.7torr
Boiling Point Elevation
Consequence of the lowering of the
vapor pressure of a solvent by the
addition of a non-volatile solute
∆Tb = K b m
m the molality
K b the molal boiling point elevation constant
Freezing Point Depression
Consequence of the lowering of the
vapor pressure of a solvent by the
addition of a non-volatile solute
∆T f = K f m
m the molality
K f the molal freezing-point depression constant
Boiling Point Elevation
&
Freezing Point Depression
What is the boiling-point and the
freezing-point of a 25% by mass aqueous
solution of ethylene glycol (C2H6O2)?
Osmosis
Net movement of a solvent through a
semipermeable membrane from a region
of low solute concentration to one of
high solute concentration
Osmotic Pressure
Osmotic pressure given by
π V = nRT
or
n
π =   RT = MRT
V 
What is the osmotic pressure of
a 0.0020 M aqueous solution of
sucrose (C12H22O11) at 200C?
hypotonic, isotonic & hypertonic
Solution A is hypotonic relative to B
if ΠA is greater than ΠB
Solution A is isotonic relative to B
if ΠA = ΠB
Solution A is hypertonic relative to B
if ΠA is less than ΠB
Reverse Osmosis
One can stop the flow of solvent into the
more concentrated solution by applying
pressure to the concentrated solution
equal to its Osmotic pressure
One can even drive the process in the
opposite direction by increasing the
pressure on the concentrated solution in
excess of the Osmotic pressure
Used to desalinate water
All colligative properties can be used
to determine the
molecular mass of a material
A solution contains 3.50mg of protein
dissolved in water so that the volume of
the solution is 5.00mL. The osmotic
pressure at 25 0C was measured to be
1.54 torr. What is the molecular weight
of the protein?
Example of Molality & Molarity
Solution contains equal masses of water
and glycerol (C3H8O3) and has a density
of 1.10g/mL. Calculate
molality of glycerol
mole fraction of glycerol
molarity of glycerol