Solutions

SHORT NOTES
Vapour Pressure ⇒ VT < (V1 + V2)
Pressure exerted by vapours over the liquid surface at equilibrium. ⇒ DHsolution < 0
T↑ ⇒ V.P.↑
Attractive Forces↑ ⇒ V.P. ↓ PAº
Raoult’s Law V.P.
(1) Volatile binary liquid mix: Ptotal
PBº
Volatile liq. A B PA
Mole fraction XA / YA XB / YB ⇒ liq/vapour
V.P. of pure liq. PAº PBº
PB
Binary liquid solution:
0 XA 1
PAº
1 XB 0
PBº
Fig.: A solution that shows -ve deviation from Raoult’s law
Table: Deviation from Raoult’s Law
O XA 1 Negative
Positive deviation (DH Zero deviation
By Raoult’s law ⇒ PT = XA + PA0 PB0 XB = PA + PB ...(i) = +ve)
deviation
(DH = 0)
By Dalton’s law ⇒ PA = YA PT ...(ii) (DH = – ve)
PB = YB PT ...(iii) acetone +
(i) ethanol + cyclohexane benzene + toluene
chloroform
Ideal and Non-Ideal Solutions
Ideal Solutions acetone + carbon benzene + n-hexane +
(ii)
Solution-A Solution-B disulphide chloroform n-heptane
A.......A B.......B
nitric acid + ehyl bromide +
F1 F2 (iii) acetone + benzene
chloroform ethyl iodide
V1 V2
acetone + chlorobenzene +
(iv) ethanol + acetone
aniline bromo benzene

water + nitric
A.......B (v) ethanol + water
acid
F
carbon tetrachloride + diethyl ether +
VT (vi)
chloroform chloroform
F1  F2  F
Ideal solution : ⇒ DHsolution = 0
VT= V1 + V2
Azeotropic mixtures: Some liquids on mixing in a particular
Non-Ideal Solutions
composition form azeotropes which are binary mixture having
(1) Solution showing +ve deviation :
F < F1 or F2 same composition in liquid and vapour phase and boil at a
VT > V1 + V2 constant temperature. Azeotropic mixture cannot be separated by
Q DHsolution > 0 fractional distillation.
Types of Azeotropic Mixtures
(i) Maximum boiling Azeotropic mixtures: The mixture of
two liquids whose boiling point are more than either of
the two pure components. They are formed by non-ideal
solutions showing negative deviation. For example, HNO3
(68%) + water (32%) mixture boils at 393.5 K.
(ii) Minimum boiling Azeotropic mixtures: The mixture
of two liquids whose boiling point is less than either
of the two pure components. They are formed by
Fig.: A solution that shows +ve deviation from Raoult’s law
non-ideal soluton showing positive deviation. For
(2) Solution showing -ve deviation: example, ethanol (95.5%) + water (4.5%) water boils at
⇒ F > F1 and F2 351.15 K.

1
Colligative Properties
Properties depends on relative no. of particles of non volatile
solute in solution.
No. of particle of Colligative
⇒
Non volatile solute Properties
(1) Relative lowering of V.P. :
PA0 - PA nB n (3) Depression in FP:
=i  i B [For dilute solution] DTf = Tf – Tf′ = i Kf × m
PAº nA + nB nA
RTf2
where nB = mole of Non-volatile solute. where Kf =
1000´ f
i = Van’t Hoff’s factor. Tf = F.P. of pure solvent
(2) Elevation in B.P. : Kf = molal depression constant
lf = latent heat of fusion per gm.
DTb = (Tb′ – Tb) = i. Kb × m.
(4) Osmotic pressure:
RTb2
where Kb = p ∝ (PA0 – PA) Pext = Posmotic = 
1000 × lv
p = iC. R.T.
where Tb = B.P. of pure solvent.
where p = osmotic pressure
l = Latent heat of vapourization (per gm) C = molarity (mole/lit) Solution Solvent
Kb = molal elevation constant Sol. (1) and Sol (2)
M = Molar mass If p1 = p2 Isotonic
 ∆H vap  soln (1) hypertonic
where lv =   If pl > p2
 M  soln (2) hypotonic

Table: Van’t Hoff factor for different cases of solutes undergoing Ionisation and Association

Solute Example Ionisation/association (x degree) y* Van’t Hoff factor Abnormal mol. wt. (m1′)
Non-
urea, glucose, sucrose etc. none 1 1 normal mol.wt.
electrolyte
Ternary  2A+ + B2- m1
K2SO4, BaCl2 A 2 B  3 (1 + 2x)
electrolyte 1-x 2x x (1 + 2x )

 A3+ + 3B- m1

Associated  A 2
2A  1  x 2− x 2m1
Solute
benzoic acid in benzene 1 −  =  
1-x x /2 2  2  2  (2 - x )

1 1 2m1
forming dimer  A 2
A   x 2− x
(1-x ) 2 x /2 2 1 −  =  (2 - x )
 2  2 

é m1 ù
1 é æ1 ö ù ê ú
any solute  A n
nA  ê1 + çç -1÷÷ x ú ê æ 1 ö÷ ú
1-x x /n n êë çè n ÷ø úû ê 1 + ççç -1÷÷ x ú
êë è n ø úû

ml
1
 A n 1 x
forming polymer An A  1− x + x
(1-x) n x /n n n 1− x +
n
one mole of solute giving y  yB
A  m1
General y [1 + (y –1)x]
mol of products 1-x xy [1 + (y -1)x]

* number of products from one mole of solute