1215Unit2_ColligativeProperties4

8/9/2019 1215Unit2_ColligativeProperties4

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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



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.



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



#aoult$s %a! " +&ample,

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



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! " +&ample,

Nonvolatile Solute



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! " +&ample, T!o

Volatile Components



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


Volatile Components




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-


Volatile Components

( :.:-2 mol

( 7.14- mol

( 7.4-81




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


Volatile Components

( 7.297



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


Volatile Components



<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.



<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.



<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



<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




+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




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.



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.




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



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




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




<oiling Point +levation and reezing

Point epression

Adding a

nonvolatile

solute to asolvent

raises its

boiling point

and lo!ersits freezing

point.



<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.



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.



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)



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 " +&ample



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







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



( -.874*C





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





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.



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.



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



3ypertonic Solutions

Osmotic pressure plays an important role in living

systems. or e&ample' 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.



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.



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 ?

1215Unit2_ColligativeProperties4

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