8.3 Colligative Notes

8/18/2019 8.3 Colligative Notes

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Objective :

At the end of this lesson students should be able to:

(a) Define colligative properties.

(b) Describe the colligative properties of a solution:

i. lowering of vapour pressure

ii. boiling point elevation

iii. freezing point depression

iv. osmotic pressure

(c) Perform calculations on colligative properties of

a nonelectrol!te solution containing nonvolatile

solutes.

".# $ %olligative Properties


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colligative properties

&'O*D+

boiling point elevation

freezing point depression

vapor pressure lowering

osmotic pressure


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%O,,-A/-0' P*OP'*/-'+

Properties depend onl! on the number of

solute particles in the solution and not their chemical identit!

Colligative means

1collective2

/here are 3 colligative properties4


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%O,,-A/-0' P*OP'*/-'+ O5 6O60O,A/l,'

6O6','%/*O,/'+ +O,7/-O6+

0apor Pressure ,owering

8oiling Point 'levation

5reezing point Depression

Osmotic Pressure

T b 9 K b m

T f 9 K f m

9 MRT

P 9 X soluteP solvento

P solution 9 X solvent P solvent o

or


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6O60O,A/-,' +O,7/'+

;ave negligible vapor pressure

'


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0APO* P*'++7*' ,O'*-6 ( P )

0apor pressure of a solution of a nonvolatile is alwa!s lower than the vapor pressure of

pure solvent


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Pure solvent +olution 9 +olvent > +olute

Present of solute molecules hinder the escape of

solvent molecules at or near the surface into vapor

6umber of solvent molecules in the vapor reduced

0apor pressure of the solution lower than that of

pure solvent


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According to *aoult?s ,aw@ the vapor pressure

of a solution containing a nonvolatile solute

is eual to the vapor pressure of pure solvent times the mole fraction of solvent


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Another method of calculation:

P solvent 9 X solvent P solvent o

X solvent > X solute 9 B /hus@ X solvent 9 B $ X solute

P solvent 9 X solvent P solvent o

P solvent 9 (B $ X solute) P solvent o

P solvent 9 P solvent $ ( X solute P solvent)o o

P solvent $ P solvent 9 ( X solute P solvent)o o

P 9 X solute P solvent

o

According to *aoult?s ,aw :


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%arbon tetrachloride (%%l3) has a vapor pressureof BCC torr at #o%. /his solvent can dissolves

candle wa@ which is essentiall! nonvolatile.

=olecular formula of candle wa 9 %;3E

hat is the vapor pressure at #o% of a solutionprepared b! dissolving BC.C g of wa in

3C.C g of %%l3F

EXAMPLE


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=ole of wa 9

(solute) (%;3E)

BC.C g

#BC gGmol9 C.C## mol wa

=ole of %%l3 9

(solvent)

3C.C g

BH3 gGmol9 C.EC mol %%l3

=ol of %%l3

/otal mol (wa > %%l3)

C.EC mol

(C.C## > C.EC) mol

9 C.""I

9

X %%l3

9

Ans: EXAMPLE


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+olvent 9 %%l3


9 C.""I BCC torr

9 "".I torr

P solution X P o

%%l3 %%l39

X %%l3 9 C.""I

According to *aoult?s ,aw:

Ans: EXAMPLE


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8O-,-6 PO-6/ ','0A/-O6 ( T b)

A solution boils at

higher temperature than

the pure solvent

T b (boiling point) is the temperature when

P solution 9 P atmosphere

;igher temperature needed to raise the

vapor pressure of the solution (P solution)

to eual the eternal pressure (P atmosphere)

P solution

J P solvent

o


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/OP-% " : P;A+' 'K7-8,-8*-A


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T b is proportional to the concentration of

of solute particles:

T b m

T b 9 K bm

K b: molal boiling point elevation constant

7nit: o%Gm o% &g mol $B

m: the solution molalit!

7nit: molal

9 T b(solution) $ T b(pure solvent) T b L C

***K b solution is given


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C.CB moles of sucrose dissolved in BCC g water.hat is the boiling point of the aueous solution

at B atmF K b for water is C.HBo%Gm.

EXAMPLE


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=olalit! of

sucrose solution

=ol of sucrose

&g of water

9 C.CB mol C.B &g

9 C.B m

T b 9 K bm

9 C.HB o%Gm C.B m 9 C.CHB o%

9

6onvolatile solute 9 sucrose +olvent 9 water

Ans: EXAMPLE

T b(solution) 9 T b(pure water) > T b

9 (BCC > C.CHB) o% 9 BCC.CHB o%


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5*''M-6 PO-6/ D'P*'++-O6 ( T f )

/he addition of solute reduce number of

solvent molecules that can enter the solid

phase

/he d!namic euilibrium disrupted and can

be re$established onl! at lower temperature


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/OP-% " : P;A+' 'K7-8,-8*-A


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T f is proportional to the concentration of

of solute particles:

T f m

T f 9 K f m

K f

: molal freezing point depression constant

7nit: o%Gm o% &g mol $B

m: the solution molalit!

7nit: molal

9 T f(pure solvent) $ T f(solution) T f L C

***K f solution is given


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hat is the freezing point of a solution

containing 3N" g of eth!lene gl!col

(antifreeze) in #C g of waterF /he molar

mass of eth!lene gl!col is E.CB g.

K f of water 9 B."Eo%Gm

EXAMPLE


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=ol of eth!lene gl!col 9=ass

=olar mass

9

3N" g

E.CB gGmol

9 N.NC" mol eth!lene gl!col

=olalit! of solution 9 =ol of eth!lene gl!col &g of water

9N.NC" mol

#.C &g9 .3CN m

+olute: eth!lene gl!col+olvent: water

Ans: EXAMPLE


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T f 9 K f m

9 B."E o%Gm .3CN m

9 3.3" o%

T f(solution) 9 T f(pure water) $ T f

9 (C.CC $ 3.3") o%

9 $ 3.3" o%

Ans: EXAMPLE


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Applies onl! to aueous solution

O+=O+-+

/wo solutions of different concentrations are

separated b! a semipermeable membrane

/he membrane allows water (solvent)@ butnot solute@ to pass through


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dilutemore

concentrated

/he net flow of water :

from dilute to more concentrated solution

increases the volume of the solution

decreases its concentration


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/OP-% " : P;A+' 'K7-8,-8*-A


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/he applied pressure reuired to stop osmosis

O+=O/-% P*'++7*' ( )

Prevent volumes changes

π M (molarit! of solution)

π mol of solute

volume of solution

π 9 MRT

R : gas constant

T : absolute temperature (in &)


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A ver! diluted solution@ C.CCBC M sugar in water@is separated from pure water b! an osmotic

membrane.

hat osmotic pressure in torr develop Ho%F

EXAMPLE


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π 9 MRT

T 9 (N# > H) &

9 C.CCBC mol, $B C.C"CE , atm mol $B& $B I" &

9 C.C3H atmNEC torr

B atm

9 B".E torr

9 I" &

π

+olute: sugar +olvent: water

Ans: EXAMPLE

/he effect of a nonvolatile solute on


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/he effect of a nonvolatile solute on

the phase diagram for water.

hen a non volatile solute is added to pure solvent@ the

mole fraction decreases. Addition of a solute at constant /and P lowers the solvent chemical potential.

8.3 Colligative Notes

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