SOLUTION & COLLIGATIVE PROPERTIES
OSMOTIC PRESSURE :
(i) = gh Where, = density of soln., h = equilibrium height.
(ii) Vont – Hoff Formula (For calculation of O.P.)
= CST
n
= CRT = RT (just like ideal gas equation)
V
C = total conc. of all types of particles.
= C1 + C2 + C3 + .................
(n1 n 2 n3 .........)
=
V
Note : If V1 mL of C1 conc. + V2 mL of C2 conc. are mixed.
C1V1 C 2 V2 1V1 2 V2
= V V RT ; =
1 2 RT
Type of solutions :
(a) Isotonic solution – Two solutions having same O.P.
1 = 2 (at same temp.)
(b) Hyper tonic– If 1 > 2. Ist solution is hypertonic solution w.r.t. 2nd
solution.
(c) Hypotonic – IInd solution is hypotonic w.r.t. Ist solution.
Abnormal Colligative Properties : (In case of association or dissociation)
VANT HOFF CORRECTION FACTOR (i) :
exp/ observed / actual / abnormal value of colligativ e property
i
Theoritica l value of colligativ e property
exp . / observed no. of particles / conc. observed molality
= Theoritica l no. of particles = Theoritical molality
theoretical molar mass ( formula mass )
= exp erimental / observed molar mass (apparent molar mass )
i>1 dissociation.
i<1 association.
exp .
i=
theor
= iCRT
= (i1C1 + i2C2 + i3C3.....) RT
Relation between i & (degree of dissociation) :
i = 1 + ( n – 1) Where, n = x + y.
Relation b/w degree of association & i.
1
i = 1 + 1
n
RELATIVE LOWERING OF VAPOUR PRESSURE (RLVP) :
Vapour pressure : P Soln. < P
Lowering in VP = P – PS = P
P
Relative lowering in vapour pressure RLVP =
P
Raoult's law : (For non – volatile solutes)
Experimentally relative lowering in V.P = mole fraction of the non volatile
solute in solutions.
P - Ps n
RLVP = = XSolute =
P nN
P - Ps n
Ps = N
P - Ps M
Ps = ( molality ) × 1000 (M = molar mass of solvent)
If solute gets associated or dissociated
P - Ps i.n
Ps =
N
P - Ps M
Ps = i × (molality) ×
1000
According to Raoult’s law
(i) p1 = p10 X1. where X1 is the mole fraction of the solvent (liquid).
p10 p1
(ii) An alternate form = X 2.
p10
Elevation in Boiling Point :
Tb = i × Kbm
2 2
RTb RTb M
Kb = or Kb =
1000 L vap 1000 H vap
H vap
Lvap = M
Depression in Freezing Point :
Tf = i × Kf . m.
2 2
RTf RTf M
Kf = molal depression constant = = .
1000 L fusion 1000 Hfusion
Raoult’s Law for Binary (Ideal) mixture of Volatile liquids :
PA = XAPAº PB = XBPBº
if PA > PB
º º
A is more volatile than B
B.P. of A < B.P. of B
According to Dalton's law
PT = PA + PB = XAPA0 + XBPB0
xA' = mole fraction of A in vapour above the liquid / solution.
xB' = mole fraction of B
PA = XAPAº = XA' PT
PB = XB' PT = XBPBº
1 xA ' xB '
PT = PA º + PB º .
Graphical Representation :
PT PA º
PB,º PA
PB,
XA= 0 XA= 1
XB= 1 XB= 0
A more volatile than B (PAº > PBº)
Ideal solutions (mixtures) :
Mixtures which follow Raoul'ts law at all temperature.
A ------ A A -------- B,
B ----- B
Hmix = 0 : Vmix = 0 :
Smix = + ve as for process to proceed : Gmix = – ve
eg. (1 ) Benzene + Toluene.
(2) Hexane + heptane.
(3) C2H5Br + C2H5.
Non-deal solutions : Which do not obey Raoult's law.
(a) Positive deviation : –
(i) PT,exp > ( XAPºA + XBPBº )
A A
(ii) B B > A ---- B
Force of attraction
(iii) Hmix = +ve energy absorbed
(iv) Vmix = +ve ( 1L + 1L > 2L )
(v) Smix = +ve
(vi) Gmix = –ve
eg. H2O + CH3OH.
H2O + C2H5OH
C2H5OH + hexane
C2H5OH + cyclohexane.
CHCl3 + CCl4 dipole dipole interaction becomes weak.
P0A > P0B
XA = 0 XA = 1
XB = 1 XB = 0
(b) Negative deviation
(i) PT exp < XAPAº + XBPºB
A A
(ii) B B < A ------ B.
strength of force of altraction.
(iii) Hmix = –ve (iv) Vmix = –ve ( 1L + 1L < 2L )
(v) Smix = +ve (vi) Gmix = –ve
eg. H2O + HCOOH
H2O + CH3COOH
H2O + HNO3
CH3 Cl
CHCl3 + CH3OCH3 C=O H C Cl
CH3 Cl
P
P0A > P0B
xB = 1 X A= 1
XA = 0 XB = 0
Immiscible Liquids :
(i) Ptotal = PA + PB
(ii) PA = PA0 XA = PA0 [Since, XA = 1].
0 0
(iii) PB = P XB = P
B B
[Since, XB = 1].
PA0 nA PA0 W A MB
(iv) Ptotal = P + P 0 0
(v) = n (vi)
A B
PB0 B PB0 M A WB
n A RT nBRT
PA0 = ; PB0 =
V V
TA TB
Tsoln.
B.P. of solution is less than the individual B.P.’s of both the liquids.
Henry Law :
This law deals with dissolution of gas in liquid i.e. mass of any gas dissolved
in any solvent per unit volume is proportional to pressure of gas in equilibrium
with liquid.
mp
m = kp
weight of gas
m Volume of liquid
