Colligative Properties in Solutions

COLLIGATIVE PROPERTIES
 
-  Depends on the collective effect of the number of solute
particles but not on the nature of the solute.
 
1.  Boiling point elevation
  
T
b
  =  k
b
  
m
 
2.  Freezing point depression
  
T
f
  =  -k
f
 
m
 
3.  Vapor pressure lowering
  
Raoult’s law P
a
  =  
A
A
 
4.  Osmotic Pressure
  
  =  MRT  =    
n
   RT
                                                   V
 
Colligative Properties
Colligative Properties
 Those properties of a solvent (i.e. vapor pressure lowering,
freezing point depression, boiling point elevation, osmotic
pressure) that depend on the total concentration of solute
particles present.
NOTE
: 
i
 = van’t Hoff factor, which is determined experimentally
and represents the degree of dissociation of the solute in the
solvent.
Table of Molal Boiling Point Elevation/Freezing Point Depression
Constants for Various Solvents
Solvent
 
             
Normal BP (
C)
 
    
K
b
 (
C/
m
)
 
Normal FP (
C)
 
     
K
f
 (
C/
m
)
H
2
O
 
                      100.0
 
        0.52                       0.0
 
                     1.86
 
Benzene, C
6
H
6
 
         80.1
 
        2.53
 
         5.5
 
                     5.12
 
Ethanol, C
2
H
5
OH       78.4
 
        1.22
 
    -114.6
 
                     1.99
 
CCl
4
 
                       76.8
 
        5.02
 
      -22.3                     29.8
 
Chloroform, CHCl
3
    61.2                     3.63
 
      -63.5
 
                     4.68
 
 
Colligative Properties
1.
Boiling Point Elevation – The increase in
boiling point of a solution relative to that
of the pure solvent is directly proportional
to the number of solute particles per mole
of solvent molecules.  That is,
  
  
T
b
 = 
i 
K
b 
m
where 
T
b
 
= increase in boiling point relative
to that of the pure solvent, K
b
 is called the
molal boiling point elevation constant, and 
m
 =
molality of the solution.
 
BOILING POINT ELEVATION - indepth
Normal boiling point of a pure liquid or solution
is the temperature at which the vapor pressure
is at 1 atm.  A dissolved solute will reduce the
vapor pressure; the temperature of the solution
must be increased in order to induce boiling, the
boiling point is therefore higher than pure
solvant. 
  
T
T
b
b
 = 
 = 
i
i
K
K
b
b
  m
  m
NOTE:
The vapor pressure curve of a dilute solution lies below that of the
pure solvent therefore the 
P is the decrease of vapor pressure at
T
b 
(boiling point).
  
T
b
 is the change in temperature necessary to
hold the vapor pressure at 1 atm (
T
b
 is increase in boiling point
caused by addition of solute to pure solvant).  The following slide
gives the mathematical derivation.
AT Low [concentration]:
  
-  
P
1
  =  slope
               
    
   
T
b
 
 
T
b
  =  
- 
P
1
  =  
x
1
P
1
 
 =  
1
        
n
2
                             S            S        S   n
1
  +  n
2
constant S = property of pure solvant (independent of solute)
AT [Very dilute]:  n
1
>>n
2
T
b
  =  
1 n
2
  =  
1
   
m
2
/MM
2
           solute =  m
2
                   
S n
1  
     S   m
1
/MM
1
          solvent = m
1
K
b
  =  Boiling point elevation constant  =  
  
m
1
 
        
      
 1000 g/kg  * S
T
b
  =  K
b       
 
m
2
/MM
2
   
 
=  K
b
m
 
       m
1
/1000 g/kg
                                                   
m
  =  
moles solute/
 kg solvent
 
 
Colligative Properties
Colligative Properties
2.  Freezing Point Depression – Like the boiling
point elevation, the decrease in freezing point of a
solution relative to that of the pure solvent is
directly proportional to the molality of the solute.
That is,
                               
T
f
 = 
i
K
f
  m
where 
T
f
 
 = decrease in freezing point relative to
that of the pure solvent, K
f
 is called the molal
freezing point depression constant, and 
m
 =
molality of the solution.
Lecture Questions:
1.  When 5.5 g of biphenyl (C
12
H
10
) is dissolved
in 100g of benzene, the boiling point increases
by 0.903ºC.  Calculate K
b
 for benzene.
(Biphenyl M.M. = 154.2 g/mol)
2.  When 0.494g of K
3
Fe(CN)
6
 is dissolved in
100.0 g of H
2
O, the freezing point is found to be
-0.093 
o
C.  How many ions are present for each
formula unit of K
3
Fe(CN)
6
 dissolved?
3.
 
Vapor Pressure Lowering (similar to
mole fraction calculation from gas laws
unit)
 
P
solvent 
= 
solvent 
P
pure
 
 known as 
Raoult’s Law
where P
pure
 = vapor pressure of the pure
solvent, 
solvent
 = mole fraction of the
solvent, and P is the vapor pressure of the
solvent in the solution.
RAOULT’S LAW
P
P
A
A
 =  X
 =  X
A
A
P
P
A
A
º
º
A  =  solvent
B  =  solute
P
A
  =  vapor pressure of A in the solution
X
A
  =  mole fraction of A
P
A
º  =  vapor pressure of pure solvent
P
A
 must be non zero and the solute must be nonvolatile and
temperature is constant.  Raoult’s law is for ideal solutions
                      P
A
      ideal              P
A
º
                                 +          -
                             0      X
A
          1
positive deviation =  non ideal solutions
negative deviation =  vapor pressure is lowered
The solute attracts
the solvent molecules
reducing the solvents
escape into the vapor phase.
4.  
Osmotic Pressure 
Osmotic Pressure 
– The net movement of
solvent molecules from a less concentrated
solution into a more concentrated one is
known as 
osmosis
.  The pressure required to
prevent osmosis is known as the osmotic
pressure (defined by the variable 
) and can
be calculated as:
= 
i
 MRT
where M = Molarity, R = 0.08206 L atm K
-1
mol
-1
, and T = Temperature (K).
OSMOSIS
Osmosis is the phenomenon of solvent flow through a
semipermeable membrane to equalize the solute
concentration on both sides of the membrane.
Osmotic pressure is a colligative property of a solution
equal to the pressure that, when applied to the
solution just stops the flow of solute.
1.  Solvent flows in and out of the membrane but the solute
does not.
2.  The volume of the solution inside the membrane increases,
stretching the membrane, until equilibrium is reached.
3.  The pressure on the solution side of the membrane is greater
than atmospheric pressure on the surface of the pure solvent.
4.  The different between these two pressures is osmotic
pressure.
Lecture Questions:
1.  At 25ºC, the vapor pressure of C
6
H
6
 is 0.1252
atm. When 10.00 g of an unknown volatile substance
is dissolved in 100.0 g of benzene, the vapor
pressure of the solution, at 25ºC, is 0.1199 atm.
Calculate the molar mass of the solute.
2.
What is the osmotic pressure at 25º C of an
isotonic saline solution that contains 0.900 g NaCl in
100 mL of aqueous solution?  Assume 
i
 is ideal.
3. At 25ºC, the freezing point of a NaCl aqueous
solution is -0.406ºC.  Calculate the osmotic
pressure this solution has on a semi-permeable
membrane if the concentration of the solution is
equivalent to the molality.
Workshop on boiling point elevation:
1.  When a 11.2 G sample of sulfur was dissolved in 40.0 g
of CS
2
, the boiling point elevation of CS
2
 is 2.63ºC.  What
is the molecular weight of sulfur in the solution?
What is the formula of molecular sulfur?
2.  Lanthanum (III) chloride, LaCl
3
, like many soluble salts,
completely dissociates into ions in dilute aqueous solutions.
                      H
2
O
      LaCl
3(s)
    
       La
3+
 
(aq)
  +  3 Cl
-
 
(aq)
Suppose 0.2453 g of LaCl
3
 will dissolve in 10.00 g of H
2
O,
what will be the boiling point of the solution at 1 atm?
Workshop on Colligative Properties
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COLLOIDS
COLLOIDS
Colloidal Suspensions are heterogeneous
mixtures. A dispersion of particles of one
substance throughout another substance or
solution.
Tyndall Effect
Tyndall Effect
The scattering of light by colloidal-size
particles usually around 1 x 10
3
 pm to 2 x 10
5
pm (picometers).  Some common materials
which exhibit the Tyndall effect would be
soluble starch in water or fog.
Continous
 
Dispersed
  
Name
  
Example
    Phase                  Phase
Gas
  
Liquid
   
Aerosol
  
Fog, mist
Gas
  
Solid
   
Aerosol
  
Smoke
Liquid
  
Gas
   
Foam
  
Whipped Cream
Liquid
  
Liquid
   
Emulsion
 
Mayonnaise
       
(oil dispersed
       
in water
Liquid
  
Solid
   
Sol
  
AgCl(s) dispersed
       
in H
2
O
Solid
  
Gas
   
Foam
  
Pumice, plastic
       
foams
Solid
  
Liquid
   
Gel
  
Jelly, Opal
       
(mineral with
       
liquid inclusions
)
Solid
  
Solid
   
Solid sol
  
Ruby glass
       
(glass with
       
dispersed metal)
Types of COLLOIDS
Hydrophillic Colloid
 
A colloid in which there is a strong
attraction between the dispersed phase and
the continuous phase (water)
Hydrophobic Colloid
 
A colloid in which there is a lack of
attraction between the dispersed phase and
the continuous phase (water)
Coagulation
 
The process by which the dispersed phase
of a colloid is made up to aggregate and
thereby separate from the continuous phase
ASSOCIATION COLLOID
Micelle
 
A colloidal-size particle formed in water by the
 
association of molecules or Ions that each have a
 
hydrophobic and hydrophillic end.
Sodium Lauryl Sulfate: CH
3
(CH
2
)
11
OSO
3
- 
Na
+
sterate ion: CH
3
(CH
2
)
16
COO
-
 Na
+
Slide Note
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Colligative properties in solutions depend on the total concentration of solute particles present, impacting properties such as boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Boiling point elevation is directly proportional to the number of solute particles, while freezing point depression decreases the freezing point compared to the pure solvent. These properties play a crucial role in various applications in chemistry and biology.

  • Colligative properties
  • Solutions
  • Boiling point elevation
  • Freezing point depression
  • Osmotic pressure

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  1. COLLIGATIVE PROPERTIES - Depends on the collective effect of the number of solute particles but not on the nature of the solute. 1. Boiling point elevation Tb = kbm 2. Freezing point depression Tf = -kfm 3. Vapor pressure lowering Raoult s law Pa = AP A 4. Osmotic Pressure = MRT = n RT V

  2. Colligative Properties Those properties of a solvent (i.e. vapor pressure lowering, freezing point depression, boiling point elevation, osmotic pressure) that depend on the total concentration of solute particles present. NOTE: i = van t Hoff factor, which is determined experimentally and represents the degree of dissociation of the solute in the solvent. Table of Molal Boiling Point Elevation/Freezing Point Depression Constants for Various Solvents Solvent Normal BP ( C) Kb ( C/m) H2O 100.0 Benzene, C6H6 80.1 Ethanol, C2H5OH 78.4 CCl4 76.8 Chloroform, CHCl3 61.2 3.63 Normal FP ( C) Kf ( C/m) 0.52 0.0 1.86 2.53 5.5 5.12 1.22 -114.6 1.99 5.02 -22.3 29.8 -63.5 4.68

  3. Colligative Properties 1. Boiling Point Elevation The increase in boiling point of a solution relative to that of the pure solvent is directly proportional to the number of solute particles per mole of solvent molecules. That is, Tb = i Kb m where Tb= increase in boiling point relative to that of the pure solvent, Kb is called the molal boiling point elevation constant, and m = molality of the solution.

  4. BOILING POINT ELEVATION - indepth Normal boiling point of a pure liquid or solution is the temperature at which the vapor pressure is at 1 atm. A dissolved solute will reduce the vapor pressure; the temperature of the solution must be increased in order to induce boiling, the boiling point is therefore higher than pure solvant. Tb = iKb m NOTE: The vapor pressure curve of a dilute solution lies below that of the pure solvent therefore the P is the decrease of vapor pressure at Tb (boiling point). Tb is the change in temperature necessary to hold the vapor pressure at 1 atm ( Tb is increase in boiling point caused by addition of solute to pure solvant). The following slide gives the mathematical derivation.

  5. - P1 = slope Tb AT Low [concentration]: Tb = - P1 = x1P1 = 1 n2 S S S n1 + n2 constant S = property of pure solvant (independent of solute) AT [Very dilute]: n1>>n2 Tb = 1 n2 = 1 m2/MM2 solute = m2 S n1 S m1/MM1 solvent = m1 Kb = Boiling point elevation constant = m1 1000 g/kg * S Tb = Kb m2/MM2 m1/1000 g/kg m = moles solute/ kg solvent = Kbm

  6. Colligative Properties 2. Freezing Point Depression Like the boiling point elevation, the decrease in freezing point of a solution relative to that of the pure solvent is directly proportional to the molality of the solute. That is, Tf = iKf m where Tf= decrease in freezing point relative to that of the pure solvent, Kf is called the molal freezing point depression constant, and m = molality of the solution.

  7. Lecture Questions: 1. When 5.5 g of biphenyl (C12H10) is dissolved in 100g of benzene, the boiling point increases by 0.903 C. Calculate Kb for benzene. (Biphenyl M.M. = 154.2 g/mol) 2. When 0.494g of K3Fe(CN)6 is dissolved in 100.0 g of H2O, the freezing point is found to be -0.093 oC. How many ions are present for each formula unit of K3Fe(CN)6 dissolved?

  8. 3. mole fraction calculation from gas laws unit) Vapor Pressure Lowering (similar to Psolvent = solvent Ppure known as Raoult s Law where Ppure = vapor pressure of the pure solvent, solvent = mole fraction of the solvent, and P is the vapor pressure of the solvent in the solution.

  9. RAOULTS LAW PA = XAPA A = solvent B = solute PA = vapor pressure of A in the solution XA = mole fraction of A PA = vapor pressure of pure solvent PA must be non zero and the solute must be nonvolatile and temperature is constant. Raoult s law is for ideal solutions PA ideal PA + - The solute attracts the solvent molecules reducing the solvents escape into the vapor phase. 0 XA 1 positive deviation = non ideal solutions negative deviation = vapor pressure is lowered

  10. 4. Osmotic Pressure The net movement of solvent molecules from a less concentrated solution into a more concentrated one is known as osmosis. The pressure required to prevent osmosis is known as the osmotic pressure (defined by the variable ) and can be calculated as: = i MRT where M = Molarity, R = 0.08206 L atm K-1 mol-1, and T = Temperature (K).

  11. OSMOSIS Osmosis is the phenomenon of solvent flow through a semipermeable membrane to equalize the solute concentration on both sides of the membrane. Osmotic pressure is a colligative property of a solution equal to the pressure that, when applied to the solution just stops the flow of solute. 1. Solvent flows in and out of the membrane but the solute does not. 2. The volume of the solution inside the membrane increases, stretching the membrane, until equilibrium is reached. 3. The pressure on the solution side of the membrane is greater than atmospheric pressure on the surface of the pure solvent. 4. The different between these two pressures is osmotic pressure.

  12. Lecture Questions: 1. At 25 C, the vapor pressure of C6H6 is 0.1252 atm. When 10.00 g of an unknown volatile substance is dissolved in 100.0 g of benzene, the vapor pressure of the solution, at 25 C, is 0.1199 atm. Calculate the molar mass of the solute. 2. What is the osmotic pressure at 25 C of an isotonic saline solution that contains 0.900 g NaCl in 100 mL of aqueous solution? Assume i is ideal. 3. At 25 C, the freezing point of a NaCl aqueous solution is -0.406 C. Calculate the osmotic pressure this solution has on a semi-permeable membrane if the concentration of the solution is equivalent to the molality.

  13. Workshop on boiling point elevation: 1. When a 11.2 G sample of sulfur was dissolved in 40.0 g of CS2, the boiling point elevation of CS2 is 2.63 C. What is the molecular weight of sulfur in the solution? What is the formula of molecular sulfur? 2. Lanthanum (III) chloride, LaCl3, like many soluble salts, completely dissociates into ions in dilute aqueous solutions. H2O LaCl3(s) La3+(aq) + 3 Cl-(aq) Suppose 0.2453 g of LaCl3 will dissolve in 10.00 g of H2O, what will be the boiling point of the solution at 1 atm?

  14. Workshop on Colligative Properties 1. Determine the vapor pressure of a solution of 92.1 g of glycerin, C3H5(OH)3, in 184.4 g of ethanol at 40 C. The vapor pressure of pure ethanol is 0.178 atm at 40 C, and glycerin is essentially nonvolatile. 2. Find the boiling point of a solution of 92.1 g of iodine in 800.0 g of chloroform. 3. Calculate the freezing point of a solution of 0.724 g of calcium chloride in 175 g of water, assuming complete dissociation by the solute. 4. Determine the osmotic pressure of a solution with a volume of 0.750 L that contains 5.0 g of methanol in water at 37 C. 5. List the following aqueous solutions in order of their expected freezing points: 0.050 m CaCl2, 0.15 m NaCl, 0.10 m HCl, 0.050 m HC2H3O2, and 0.10 m C12H22O11.

  15. Workshop continue: 6. A solution of 4.00 g of a nonelectrolyte dissolved in 55.0 g of benzene is found to freeze at 2.32 C. What is the molar mass of this compound? 7. 0.500 L of an aqueous solution that contains 10.0 g of hemoglobin has an osmotic pressure of 5.9 torr at 22 C. What is the molar mass of hemoglobin? 8. A solution of 35.7 g of a nonelectrolyte in 220.0 g of chloroform has a boiling point of 64.5 C. What is the molar mass of this compound? 9. An organic compound has a composition of 93.46% C and 6.54% H by mass. A solution of 0.090 g of this compound in 1.10 g of camphor melts at 158.4 C. The melting point of pure camphor is 178.4 C, and its freezing point depression constant is 37.7 C m-1. What is the molecular formula of the solute?

  16. COLLOIDS Colloidal Suspensions are heterogeneous mixtures. A dispersion of particles of one substance throughout another substance or solution. Tyndall Effect The scattering of light by colloidal-size particles usually around 1 x 103 pm to 2 x 105 pm (picometers). Some common materials which exhibit the Tyndall effect would be soluble starch in water or fog.

  17. Types of COLLOIDS Continous Phase Phase Dispersed Name Example Gas Gas Liquid Liquid Liquid Solid Solid Solid Liquid Solid Gas Liquid Solid Gas Liquid Solid Aerosol Aerosol Foam Emulsion Sol Foam Gel Solid sol Fog, mist Smoke Whipped Cream Mayonnaise (oil dispersed in water AgCl(s) dispersed in H2O Pumice, plastic foams Jelly, Opal (mineral with liquid inclusions) Ruby glass (glass with dispersed metal)

  18. Hydrophillic Colloid A colloid in which there is a strong attraction between the dispersed phase and the continuous phase (water) Hydrophobic Colloid A colloid in which there is a lack of attraction between the dispersed phase and the continuous phase (water) Coagulation The process by which the dispersed phase of a colloid is made up to aggregate and thereby separate from the continuous phase

  19. ASSOCIATION COLLOID Micelle A colloidal-size particle formed in water by the association of molecules or Ions that each have a hydrophobic and hydrophillic end. Sodium Lauryl Sulfate: CH3(CH2)11OSO3- Na+ sterate ion: CH3(CH2)16COO- Na+

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