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Colligative Properties of Solutions
are properties of solutions that depend solelyon the number of particles of solute and NOT
on their chemical identity.
•
vapor pressure• boiling point
• freezing point
• osmotic pressure
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Vapor Pressure of a Solution
A solute that is nonvolatile isone that has no measurable
vapor pressure.
e !ill study the effects ofnonvolatile solutes on the
properties of solutions.
The presence of a nonvolatile
solute causes the vaporpressure of the solution to be
lo!er than the vapor pressure
of the pure solvent.
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Vapor Pressure of a Solution "
#aoult$s %a!The e&tent to !hich the vapor pressure of asolvent is lo!ered by a nonvolatile solute is
given' for an ideal solution' by #aoult$s %a!.
#aoult$s %a!
Psolvent over solution ( )solventP*solvent
)solvent is the mole fraction of the solvent.
P*solvent is the vapor pressure of the pure
solvent at the solution temperature.
Vapor pressure of
the solution
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#aoult$s %a! " +&le,
Nonvolatile Solutehat is the vapor pressure at -*C /roomtemperature0 of a solution made by adding
--1 g /2 cup0 sugar /C2-3--O220 to 224. m% /5
cup0 of !ater6
P!ater over sugar soln ( )!ater P*!ater
mol !ater ( 224. m% & 7.88979 g & 2 mol m% 24.72 g
mol sugar ( --1 g & 2 mol :;-.:7 g
)!ater ( 1.8 ( 7.874
9.-28-
( 1.8 mol
( 7.117 mol
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hat is the vapor pressure at -*C /room
temperature0 of a solution made by adding --1 g
/2 cup0 sugar /C2-3--O220 to 5 cup of !ater6
P!ater over sugar solution ( )!ater P*!ater
P!ater over sugar solution ( /7.8740 /-:.91 torr0
Adding sugar to the water lowered its vapor pressure.
Adding more sugar would lower it still more.
( -2.8 torr
fromAppendi& <
#aoult$s %a! " +&le,
Nonvolatile Solute
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hat is the vapor pressure at -*C of 47=proofalcohol /;7> alcohol by volume06
Alcohol, C-3O3' ?? ( ;1.79 g'
v.p./-*C0 ( ;.14 torr' density /-*C0 ( 7.941 g@m%
ater, ?? ( 24.72 g' v.p./-*C0 ( -:.91 torr'
density /-*C0 ( 7.889 g@m%
Apply Raoult’s Law to each volatile component.By convention, the liquid component present in
larger volume is the “solvent.”
#aoult$s %a! " +&le, T!o
Volatile Components
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hat is the vapor pressure at -*C of 47=proofalcohol /;7> alcohol by volume06
#aoult$s %a! for the !ater,
P!ater over !ater@alcohol solution ( )!ater P*!ater
ind )!ater , e need a volume for the solution'don$t !e6 Any volume will do! 277 m% is
convenient' though.
277 m% " ;7 m% alcohol ( 17 m% !ater
#aoult$s %a! " +&le, T!o
Volatile Components
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P!ater over !ater@alcohol solution ( )!ater P*!ater
ind )!ater ,
17 m% !ater & 7.889 g & 2 molm% 24.72 g
;7 m% alcohol & 7.941 g & 2 mol
m% ;1.79 g
)!ater ( :.:-2
:.:-2B7.14-
#aoult$s %a! " +&le, T!o
Volatile Components
( :.:-2 mol
( 7.14- mol
( 7.4-81
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P!ater over !ater@alcohol solution ( )!ater P*!ater
P!ater over !@alc soln ( 7.4-81 /-:.91 torr0 ( 28.92 torr
Palcohol over !ater@alc solution ( )alcoholP*alcohol
)alcohol ( 7.14-
;.77:Palcohol over !@alc soln ( 7.297 /;.14 torr0 ( 8.:- torr
#aoult$s %a! " +&le, T!o
Volatile Components
( 7.297
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P!ater over !ater@alcohol solution ( 28.92 torr
Palcohol over !ater@alcohol solution ( 8.:- torr
No! use alton$s %a! of Partial Pressures to findthe total vapor pressure of the solution,
Ptot ( 28.92 B 8.:- ( -8.7 torr
#aoult$s %a! " +&le, T!o
Volatile Components
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<oiling Point of a Solution
•
or !ater in an open container' the boilingpoint is the temperature at !hich the vapor
pressure of !ater eDuals the prevailing
atmospheric pressure.
• Our sugar solution at -*C has a lo!er vaporpressure than !ater at -*C.
• his means the temperature at which the
sugar solution oils will e higher "#$%.&'()than the temperature at which water oils
"#$$.$'().
This is called boiling point elevation.
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<oiling Point +levation
The relationship bet!een boiling pointelevation and the number of particles of
solute in the solution is given by
ETb ( Fbm
!here ETb ( Tbp/solution0 = Tbp/pure solvent0
Fb is the molal boiling=point=elevation constant
and is for the solvent.
m is the molality of particles from the solute.
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<oiling Point +levation
No! you can calculate the boiling point of oursugar solution yourself /Fb of !ater is 7.2*C@m0,
ETb ( Fbm
The molality of solute particles in our sugar solution isthe same as the molality of the sugar itself.
m ( mol sugar ( 7.117 mol sugarGg !ater 7.2242 Gg !ater
ETb ( /7.2*C@m0 /.41m0
ETb ( Tbp/solution0 = Tbp/pure solvent0 ( -.4*C
Tbp/solution0 ( 277.77*C B -.4*C ( 27-.4*C
( .41 m
( -.4*C
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<oiling Point +levation = +lectrolytes
+lectrolytes dissolve in !ater to formions. +ach ion is a solute particle.
ETb ( Fbm
Hf !e made our solution up !ith 7.117 mol of NaClinstead of sugar' the boiling point elevation !ould
be different from that of sugar.
m ( 7.117 mol salt ( 2.:- mol ions
7.2242 Gg !ater 7.2242 Gg !ater
( 22.24 m
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<oiling Point +levation = +lectrolytes
+lectrolytes dissolve in !ater to formions. +ach ion is a solute particle.
ETb ( Fbm and m ( 22.24
ETb ( /7.2*C@m0 /22.24 m0
ETb ( Tbp/solution0 = Tbp/pure solvent0 ( .9*C
Tbp/solution0 ( 277.77*C B .9*C ( 27.9*C
( .9*C
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<oiling Point +levation = +lectrolytes
ETb ( Fbm
Hf !e made our solution up !ith 7.117
mol CaCl- instead of sugar or salt' the
boiling point elevation !ould be even
more' because CaCl- dissolves in !ater
to release : ions per mol.
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reezing Point epression
The addition of a nonvolatile solute
to a solution lo!ers the freezing
point of the solution relative to that
of the pure solvent.
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reezing Point epression
The relationship bet!een freezing pointdepression and the number of particles of
solute in the solution is given by
ETf ( Ff m
!here ETf ( Tfp/pure solvent0 = Tfp/solution0
Ff is the molal freezing=point=depression
constant and is for the solvent.
m is the molality of particles from the solute.
note the
differenceII
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e !ill no! calculate the freezing point of oursugar solution /Ff of !ater is 2.41*C@m0,
ETf ( Ff m
m ( mol sugar ( 7.117 mol sugarGg !ater 7.2242 Gg !ater
ETf ( /2.41*C@m0 /.41m0
ETf
( Tfp
/pure solvent0 = Tfp
/solution0 ( 27.;*C
Tfp/solution0 ( 7.77*C " 27.;*C ( =27.;*C
( .41 m
( 27.;*C
reezing Point epression
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e !ill no! calculate the freezing point of oursalt solution,
ETf ( Ff m
m ( mol ions ( 2.:- mol ionsGg !ater 7.2242 Gg !ater
ETf ( /2.41*C@m0 /22.29m0
ETf ( Tfp/pure solvent0 = Tfp/solution0 ( -7.4*C
Tfp/solution0 ( 7.77*C " -7.4*C ( = -7.4*C
*+ we had used (a(l % , +p"solution) would e even
lower. hat’s why (a(l % is sometimes used to salt
icy sidewals.
( 22.29 m
( -7.4*C
reezing Point epression
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<oiling Point +levation and reezing
Point epression
Adding a
nonvolatile
solute to asolvent
raises its
boiling point
and lo!ersits freezing
point.
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<oiling Point +levation and reezing
Point epression
Another
!ay to looG
at things,
Adding a
nonvolatile
solute to a
solvent
e&pands its
liDuid
range.
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inding the ?olar ?ass of a Solute from
<oiling Point +levation or reezing Point
epression ?easurement
Jsing either ETb ( Fbm or ETf ( Ff m
• Hf you Gno! the mass of solute that is not an
electrolyte and the mass of solvent used to
maGe a solution' and
•
you can measure the freezing pointdepression or boiling point elevation of the
solution'
• you can calculate the molar mass of the
solute.
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inding the ?olar ?ass of a Solute from
<oiling Point +levation or reezing Point
epression ?easurementETf ( Ff m - + mol solute
g solvent
- + " mass solute ) " molar mass o+ solute )"g solvent)
Rearranging the equation gives/
molar mass o+ solute - + "mass solute)
ETf "g solvent)
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A solution of 7.1; g of adrenaline in :1.7 g of CCl;
has a b.p. of 99.7:*C. a0 hat is the molar mass
of adrenaline6 b0 hat is the f.p. of the solution6
CCl;, b.p. /917 torr0 ( 91.;*C Fb ( .7-*C@m m.p. /917 torr0 ( =--.:*C Ff ( -8.4*C@m
ETb ( Fbm
ETb ( 99.7: " 91.; ( 7.;8*C
m - ETb @ Fb ( 7.;8*C ( 7.7891 m
.7-*C@m
?olar ?ass from <oiling Point
+levation ata " +&le
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A solution of 7.1; g of adrenaline in :1.7 g of CCl; has ab.p. of 99.7:*C. a0 hat is the molar mass of adrenaline6
b0 hat is the f.p. of the solution6
CCl;, b.p. /917 torr0 ( 91.;*C Fb ( .7-*C@m
m.p. /917 torr0 ( =--.:*C Ff ( -8.4*C@m
?olar mass of adrenaline ( /.7-*C@m0 /7.1; g0
7.;8*C /7.7:17 Gg0
( 24- g@mol
/really 2470
?olar ?ass from <oiling Point
+levation ata " +&le
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A solution of 7.1; g of adrenaline in :1.7 g of CCl; has ab.p. of 99.7:*C. a0 hat is the molar mass of adrenaline6
b0 hat is the f.p. of the solution6
CCl;
, b.p. /917 torr0 ( 91.;*C Fb
( .7-*C@m
m.p. /917 torr0 ( =--.:*C Ff ( -8.4*C@m
ETf ( Ff m
ETf ( -8.4*C /7.7891 m0m
?olar ?ass from <oiling Point
+levation ata " +&le
( -.874*C
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A solution of 7.1; g of adrenaline in :1.7 g of CCl; has ab.p. of 99.7:*C. a0 hat is the molar mass of adrenaline6
b0 hat is the f.p. of the solution6
ETf ( -8.4*C /7.7891 m0 ( -.874*C
m
ETf (Tf /CCl;0 = Tf /soln0 ( -.874*C
Tf /soln0 ( Tf /CCl;0 = -.874 ( =--.: = -.874 ( =-.-*C
?olar ?ass from <oiling Point
+levation ata " +&le
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Osmotic Pressure
•
The last colligative property !e!ill study is osmotic pressure.
• Ht is based on the tendency of
solvent molecules to move
to!ard an area of lesserconcentration.
• This movement causes osmotic
pressure !hen the areas of
differing solvent concentrationare separated by a
semipermeable membrane.
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Osmotic Pressure
Osmotic pressure is
the pressure that
must be applied to
the solution in orderto Kust stop the
movement of solvent
molecules into the
solution.
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Osmotic Pressure
The eDuation relatingosmotic pressure /L0 to
concentration is very
similar to the ideal gas
la!
L ( ?#T
? ( molarity particles in
the solution
# ( gas constant
T ( temperature in F
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3ypertonic Solutions
Osmotic pressure plays an important role in living
systems. or e&le' the membranes of red blood
cells are semipermeable.
0hen we eat too
much salt, the highconcentration o+
salt in our plasma
maes it
hypertonic relative
to the inside o+ thered lood cell and
causes water to
di++use out o+ the
red lood cells.A red blood cell in a
hypertonic solution shrinGs.
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3ypotonic Solutions
0hen we perspireheavily and then
drin a lot o+ water
"not gatorade), the
low concentration
o+ salt in our
plasma maes it
hypotonic relative
to the inside o+ the
red lood cell andcauses water to
di++use into the red
lood cells.
A red blood cell in a
hypotonic solution e&pands
and may burst.
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Hsotonic Solutions
hen !e lose a lot of fluids and have to replace them'
the ideal situation is to receive fluids that are neitherhypertonic nor hypotonic. luids that have the same
osmotic pressure are said to be isotonic.
he osmotic pressure o+ lood is 1.1 atm at 21'(. 0hat
concentration o+ saline solution "3a(l in sterile water) isisotonic with lood at human ody temperature4
5sing 6 - 7 8R,
6 - molarity o+ solute particles - 1.1 atm .
$.$&%$9 L:atm "2#$. )mol:
6olarity o+ 3a(l +or isotonic saline - $.#; 6
*n mass percent, an isotonic saline solution is $.<= 3a(l.
( 7.:7 ?