Important Solutions Formulas for JEE and NEET

 Page 1


  
SOLUTION & COLLIGATIVE PROPERTIES
OSMOTIC PRESSURE :
(i) ? = ?gh Where, ? = density of soln.,  h = equilibrium height.
(ii) Vont ? Hoff Formula (For calculation of O.P.)
? = CST
? = CRT = 
V
n
 RT (just like ideal gas equation)
? C = total conc. of all types of particles.
       = C
1
 + C
2
 + C
3
 + .................
       = 
V
.........) n n n (
3 2 1
? ? ?
Note : If V
1
 mL of C
1
 conc. + V
2
 mL of C
2
 conc. are mixed.
? = 
?
?
?
?
?
?
?
?
?
?
2 1
2 2 1 1
V V
V C V C
RT ; ? = 
?
?
?
?
?
? ? ? ?
RT
V V
2 2 1 1
Type of solutions :
(a) Isotonic solution ? Two solutions having same O.P.
?
1
 = ?
2
 (at same temp.)
(b) Hyper tonic? 
 
If ?
1
 > ?
2
. ?  I
st
 solution is hypertonic solution w.r.t. 2
nd
solution.
(c) Hypotonic ? II
nd
 solution is hypotonic w.r.t. I
st
 solution.
Abnormal Colligative Properties : (In case of association or dissociation)
VANT HOFF CORRECTION FACTOR (i) :
property e colligativ of value l Theoritica
property e colligativ of value abnormal / actual / observed exp/
i?
= 
particles of . no l Theoritica
. conc / particles of . no observed / . exp
 =  
molality l Theoritica
molality observed
= 
) mass molar apparent ( mass molar observed / erimental exp
) mass formula ( mass molar l theoretica
? i > 1 ? dissociation.
i < 1 ? association.
? i = 
theor
. exp
?
?
? ? = iCRT
? = (i
1
C
1
 + i
2
C
2
 + i
3
C
3
.....) RT
Page 2


  
SOLUTION & COLLIGATIVE PROPERTIES
OSMOTIC PRESSURE :
(i) ? = ?gh Where, ? = density of soln.,  h = equilibrium height.
(ii) Vont ? Hoff Formula (For calculation of O.P.)
? = CST
? = CRT = 
V
n
 RT (just like ideal gas equation)
? C = total conc. of all types of particles.
       = C
1
 + C
2
 + C
3
 + .................
       = 
V
.........) n n n (
3 2 1
? ? ?
Note : If V
1
 mL of C
1
 conc. + V
2
 mL of C
2
 conc. are mixed.
? = 
?
?
?
?
?
?
?
?
?
?
2 1
2 2 1 1
V V
V C V C
RT ; ? = 
?
?
?
?
?
? ? ? ?
RT
V V
2 2 1 1
Type of solutions :
(a) Isotonic solution ? Two solutions having same O.P.
?
1
 = ?
2
 (at same temp.)
(b) Hyper tonic? 
 
If ?
1
 > ?
2
. ?  I
st
 solution is hypertonic solution w.r.t. 2
nd
solution.
(c) Hypotonic ? II
nd
 solution is hypotonic w.r.t. I
st
 solution.
Abnormal Colligative Properties : (In case of association or dissociation)
VANT HOFF CORRECTION FACTOR (i) :
property e colligativ of value l Theoritica
property e colligativ of value abnormal / actual / observed exp/
i?
= 
particles of . no l Theoritica
. conc / particles of . no observed / . exp
 =  
molality l Theoritica
molality observed
= 
) mass molar apparent ( mass molar observed / erimental exp
) mass formula ( mass molar l theoretica
? i > 1 ? dissociation.
i < 1 ? association.
? i = 
theor
. exp
?
?
? ? = iCRT
? = (i
1
C
1
 + i
2
C
2
 + i
3
C
3
.....) RT
  
Relation between i & ? (degree of dissociation) :
i = 1 + ( n ? 1) ? Where, n = x + y.
Relation b/w degree of association ? & i.
i = 1 + 
?
?
?
?
?
?
?1
n
1
?
RELATIVE LOWERING OF VAPOUR PRESSURE (RLVP) :
Vapour pressure :  P
 Soln.
  <  P
Lowering in VP  =  P ? P
S
    = ?P
Relative lowering in vapour pressure      RLVP  = 
P
P ?
Raoult's law : (For non ? volatile solutes)
Experimentally relative lowering in V.P = mole fraction of the non volatile
solute in solutions.
RLVP    =   
P
P - P
s
  = X
Solute
 = 
N n
n
?
   
s
s
P
P - P
 = 
N
n
   
s
s
P
P - P
 = ( molality ) × 
1000
M
     (M = molar mass of solvent)
If solute gets associated or dissociated
s
s
P
P - P
  = 
N
i.n
s
s
P
P - P
 = i × (molality) × 
1000
M
? According to Raoult?s law
(i) p
1
 = p
1
0
 X
1
. where X
1
 is the mole fraction of the solvent (liquid).
(ii) An alternate form ?  
0
1
1
0
1
p
p p ?
 = X
2
.
Page 3


  
SOLUTION & COLLIGATIVE PROPERTIES
OSMOTIC PRESSURE :
(i) ? = ?gh Where, ? = density of soln.,  h = equilibrium height.
(ii) Vont ? Hoff Formula (For calculation of O.P.)
? = CST
? = CRT = 
V
n
 RT (just like ideal gas equation)
? C = total conc. of all types of particles.
       = C
1
 + C
2
 + C
3
 + .................
       = 
V
.........) n n n (
3 2 1
? ? ?
Note : If V
1
 mL of C
1
 conc. + V
2
 mL of C
2
 conc. are mixed.
? = 
?
?
?
?
?
?
?
?
?
?
2 1
2 2 1 1
V V
V C V C
RT ; ? = 
?
?
?
?
?
? ? ? ?
RT
V V
2 2 1 1
Type of solutions :
(a) Isotonic solution ? Two solutions having same O.P.
?
1
 = ?
2
 (at same temp.)
(b) Hyper tonic? 
 
If ?
1
 > ?
2
. ?  I
st
 solution is hypertonic solution w.r.t. 2
nd
solution.
(c) Hypotonic ? II
nd
 solution is hypotonic w.r.t. I
st
 solution.
Abnormal Colligative Properties : (In case of association or dissociation)
VANT HOFF CORRECTION FACTOR (i) :
property e colligativ of value l Theoritica
property e colligativ of value abnormal / actual / observed exp/
i?
= 
particles of . no l Theoritica
. conc / particles of . no observed / . exp
 =  
molality l Theoritica
molality observed
= 
) mass molar apparent ( mass molar observed / erimental exp
) mass formula ( mass molar l theoretica
? i > 1 ? dissociation.
i < 1 ? association.
? i = 
theor
. exp
?
?
? ? = iCRT
? = (i
1
C
1
 + i
2
C
2
 + i
3
C
3
.....) RT
  
Relation between i & ? (degree of dissociation) :
i = 1 + ( n ? 1) ? Where, n = x + y.
Relation b/w degree of association ? & i.
i = 1 + 
?
?
?
?
?
?
?1
n
1
?
RELATIVE LOWERING OF VAPOUR PRESSURE (RLVP) :
Vapour pressure :  P
 Soln.
  <  P
Lowering in VP  =  P ? P
S
    = ?P
Relative lowering in vapour pressure      RLVP  = 
P
P ?
Raoult's law : (For non ? volatile solutes)
Experimentally relative lowering in V.P = mole fraction of the non volatile
solute in solutions.
RLVP    =   
P
P - P
s
  = X
Solute
 = 
N n
n
?
   
s
s
P
P - P
 = 
N
n
   
s
s
P
P - P
 = ( molality ) × 
1000
M
     (M = molar mass of solvent)
If solute gets associated or dissociated
s
s
P
P - P
  = 
N
i.n
s
s
P
P - P
 = i × (molality) × 
1000
M
? According to Raoult?s law
(i) p
1
 = p
1
0
 X
1
. where X
1
 is the mole fraction of the solvent (liquid).
(ii) An alternate form ?  
0
1
1
0
1
p
p p ?
 = X
2
.
  
Elevation in Boiling Point :
?T
b
 = i × K
b
m
K
b
 = 
vap
2
b
L 1000
RT
?
or K
b
 =  
vap
2
b
H 1000
M RT
? ?
L
vap
 =  
?
?
?
?
?
?
?
??
M
H
vap
Depression in Freezing Point :
? ?T
f
= i × K
f 
. m.
K
f 
 = molal depression constant = 
fusion
2
f
L 1000
RT
?
 = 
fusion
2
f
H 1000
M RT
? ?
.
Raoult?s Law for Binary (Ideal) mixture of Volatile liquids :
P
A
  = X
A
P
A
º ? P
B
 = X
B
P
B
º
if  P
A
º
 > P
B
º
? A is more volatile than B
? B.P. of A < B.P. of B
? According to Dalton's law
P
T
 = P
A
 + P
B
 = X
A
P
A
0
 + X
B
P
B
0
x
A
' = mole fraction of A in vapour above the liquid / solution.
x
B
' = mole fraction of B
P
A
 = X
A
P
A
º 
 =  X
A
' P
T
P
B
 = X
B
' P
T
 = X
B
P
B
º
T
P
1
= 
º P
' x
A
A
 + 
º P
' x
B
B
.
Graphical Representation :
P º
A
P
T
P
A
P
B,
P º
B,
X = 0
X = 1
A
B
X = 1
X = 0
A
B
A more volatile than B  (P
A
º > P
B
º)
Page 4


  
SOLUTION & COLLIGATIVE PROPERTIES
OSMOTIC PRESSURE :
(i) ? = ?gh Where, ? = density of soln.,  h = equilibrium height.
(ii) Vont ? Hoff Formula (For calculation of O.P.)
? = CST
? = CRT = 
V
n
 RT (just like ideal gas equation)
? C = total conc. of all types of particles.
       = C
1
 + C
2
 + C
3
 + .................
       = 
V
.........) n n n (
3 2 1
? ? ?
Note : If V
1
 mL of C
1
 conc. + V
2
 mL of C
2
 conc. are mixed.
? = 
?
?
?
?
?
?
?
?
?
?
2 1
2 2 1 1
V V
V C V C
RT ; ? = 
?
?
?
?
?
? ? ? ?
RT
V V
2 2 1 1
Type of solutions :
(a) Isotonic solution ? Two solutions having same O.P.
?
1
 = ?
2
 (at same temp.)
(b) Hyper tonic? 
 
If ?
1
 > ?
2
. ?  I
st
 solution is hypertonic solution w.r.t. 2
nd
solution.
(c) Hypotonic ? II
nd
 solution is hypotonic w.r.t. I
st
 solution.
Abnormal Colligative Properties : (In case of association or dissociation)
VANT HOFF CORRECTION FACTOR (i) :
property e colligativ of value l Theoritica
property e colligativ of value abnormal / actual / observed exp/
i?
= 
particles of . no l Theoritica
. conc / particles of . no observed / . exp
 =  
molality l Theoritica
molality observed
= 
) mass molar apparent ( mass molar observed / erimental exp
) mass formula ( mass molar l theoretica
? i > 1 ? dissociation.
i < 1 ? association.
? i = 
theor
. exp
?
?
? ? = iCRT
? = (i
1
C
1
 + i
2
C
2
 + i
3
C
3
.....) RT
  
Relation between i & ? (degree of dissociation) :
i = 1 + ( n ? 1) ? Where, n = x + y.
Relation b/w degree of association ? & i.
i = 1 + 
?
?
?
?
?
?
?1
n
1
?
RELATIVE LOWERING OF VAPOUR PRESSURE (RLVP) :
Vapour pressure :  P
 Soln.
  <  P
Lowering in VP  =  P ? P
S
    = ?P
Relative lowering in vapour pressure      RLVP  = 
P
P ?
Raoult's law : (For non ? volatile solutes)
Experimentally relative lowering in V.P = mole fraction of the non volatile
solute in solutions.
RLVP    =   
P
P - P
s
  = X
Solute
 = 
N n
n
?
   
s
s
P
P - P
 = 
N
n
   
s
s
P
P - P
 = ( molality ) × 
1000
M
     (M = molar mass of solvent)
If solute gets associated or dissociated
s
s
P
P - P
  = 
N
i.n
s
s
P
P - P
 = i × (molality) × 
1000
M
? According to Raoult?s law
(i) p
1
 = p
1
0
 X
1
. where X
1
 is the mole fraction of the solvent (liquid).
(ii) An alternate form ?  
0
1
1
0
1
p
p p ?
 = X
2
.
  
Elevation in Boiling Point :
?T
b
 = i × K
b
m
K
b
 = 
vap
2
b
L 1000
RT
?
or K
b
 =  
vap
2
b
H 1000
M RT
? ?
L
vap
 =  
?
?
?
?
?
?
?
??
M
H
vap
Depression in Freezing Point :
? ?T
f
= i × K
f 
. m.
K
f 
 = molal depression constant = 
fusion
2
f
L 1000
RT
?
 = 
fusion
2
f
H 1000
M RT
? ?
.
Raoult?s Law for Binary (Ideal) mixture of Volatile liquids :
P
A
  = X
A
P
A
º ? P
B
 = X
B
P
B
º
if  P
A
º
 > P
B
º
? A is more volatile than B
? B.P. of A < B.P. of B
? According to Dalton's law
P
T
 = P
A
 + P
B
 = X
A
P
A
0
 + X
B
P
B
0
x
A
' = mole fraction of A in vapour above the liquid / solution.
x
B
' = mole fraction of B
P
A
 = X
A
P
A
º 
 =  X
A
' P
T
P
B
 = X
B
' P
T
 = X
B
P
B
º
T
P
1
= 
º P
' x
A
A
 + 
º P
' x
B
B
.
Graphical Representation :
P º
A
P
T
P
A
P
B,
P º
B,
X = 0
X = 1
A
B
X = 1
X = 0
A
B
A more volatile than B  (P
A
º > P
B
º)
  
Ideal solutions (mixtures) :
Mixtures which follow Raoul'ts law at all temperature.
A ------ A ? A -------- B,
B ----- B
?H
mix
 = 0 : ?V
mix
 = 0 :
?S
mix 
= + ve as for process to proceed : ?G
mix 
= ? ve
eg. (1 ) Benzene + Toluene.
(2) Hexane + heptane.
(3) C
2
H
5
Br + C
2
H
5
?.
Non-?deal solutions : Which do not obey Raoult's law.
(a) Positive deviation : ?
(i) P
T,exp
 > ( X
A
Pº
A 
+ X
B
P
B
º )
(ii)
B B
A A
? ? ? ?
? ? ? ?
> A ---- B
  
?
Force of attraction
(iii) ?H
mix
 = +ve energy absorbed
(iv) ?V
mix
 = +ve ( 1L + 1L > 2L )
(v) ?S
mix
 = +ve
(vi) ?G
mix
 = ?ve
eg. H
2
O + CH
3
OH.
H
2
O + C
2
H
5
OH
C
2
H
5
OH + hexane
C
2
H
5
OH + cyclohexane.
CHCl
3
 + CCl
4
 ?  dipole dipole interaction becomes weak.
P
XA = 0
XB = 1
XA = 1
XB = 0
  P
0
A > P
0
B
(b) Negative deviation
(i) P
T
 exp < X
A
P
A
º + X
B
Pº
B
(ii)
B B
A A
? ? ? ?
? ? ? ?
< A ------ B.
strength of force of altraction.
Page 5


  
SOLUTION & COLLIGATIVE PROPERTIES
OSMOTIC PRESSURE :
(i) ? = ?gh Where, ? = density of soln.,  h = equilibrium height.
(ii) Vont ? Hoff Formula (For calculation of O.P.)
? = CST
? = CRT = 
V
n
 RT (just like ideal gas equation)
? C = total conc. of all types of particles.
       = C
1
 + C
2
 + C
3
 + .................
       = 
V
.........) n n n (
3 2 1
? ? ?
Note : If V
1
 mL of C
1
 conc. + V
2
 mL of C
2
 conc. are mixed.
? = 
?
?
?
?
?
?
?
?
?
?
2 1
2 2 1 1
V V
V C V C
RT ; ? = 
?
?
?
?
?
? ? ? ?
RT
V V
2 2 1 1
Type of solutions :
(a) Isotonic solution ? Two solutions having same O.P.
?
1
 = ?
2
 (at same temp.)
(b) Hyper tonic? 
 
If ?
1
 > ?
2
. ?  I
st
 solution is hypertonic solution w.r.t. 2
nd
solution.
(c) Hypotonic ? II
nd
 solution is hypotonic w.r.t. I
st
 solution.
Abnormal Colligative Properties : (In case of association or dissociation)
VANT HOFF CORRECTION FACTOR (i) :
property e colligativ of value l Theoritica
property e colligativ of value abnormal / actual / observed exp/
i?
= 
particles of . no l Theoritica
. conc / particles of . no observed / . exp
 =  
molality l Theoritica
molality observed
= 
) mass molar apparent ( mass molar observed / erimental exp
) mass formula ( mass molar l theoretica
? i > 1 ? dissociation.
i < 1 ? association.
? i = 
theor
. exp
?
?
? ? = iCRT
? = (i
1
C
1
 + i
2
C
2
 + i
3
C
3
.....) RT
  
Relation between i & ? (degree of dissociation) :
i = 1 + ( n ? 1) ? Where, n = x + y.
Relation b/w degree of association ? & i.
i = 1 + 
?
?
?
?
?
?
?1
n
1
?
RELATIVE LOWERING OF VAPOUR PRESSURE (RLVP) :
Vapour pressure :  P
 Soln.
  <  P
Lowering in VP  =  P ? P
S
    = ?P
Relative lowering in vapour pressure      RLVP  = 
P
P ?
Raoult's law : (For non ? volatile solutes)
Experimentally relative lowering in V.P = mole fraction of the non volatile
solute in solutions.
RLVP    =   
P
P - P
s
  = X
Solute
 = 
N n
n
?
   
s
s
P
P - P
 = 
N
n
   
s
s
P
P - P
 = ( molality ) × 
1000
M
     (M = molar mass of solvent)
If solute gets associated or dissociated
s
s
P
P - P
  = 
N
i.n
s
s
P
P - P
 = i × (molality) × 
1000
M
? According to Raoult?s law
(i) p
1
 = p
1
0
 X
1
. where X
1
 is the mole fraction of the solvent (liquid).
(ii) An alternate form ?  
0
1
1
0
1
p
p p ?
 = X
2
.
  
Elevation in Boiling Point :
?T
b
 = i × K
b
m
K
b
 = 
vap
2
b
L 1000
RT
?
or K
b
 =  
vap
2
b
H 1000
M RT
? ?
L
vap
 =  
?
?
?
?
?
?
?
??
M
H
vap
Depression in Freezing Point :
? ?T
f
= i × K
f 
. m.
K
f 
 = molal depression constant = 
fusion
2
f
L 1000
RT
?
 = 
fusion
2
f
H 1000
M RT
? ?
.
Raoult?s Law for Binary (Ideal) mixture of Volatile liquids :
P
A
  = X
A
P
A
º ? P
B
 = X
B
P
B
º
if  P
A
º
 > P
B
º
? A is more volatile than B
? B.P. of A < B.P. of B
? According to Dalton's law
P
T
 = P
A
 + P
B
 = X
A
P
A
0
 + X
B
P
B
0
x
A
' = mole fraction of A in vapour above the liquid / solution.
x
B
' = mole fraction of B
P
A
 = X
A
P
A
º 
 =  X
A
' P
T
P
B
 = X
B
' P
T
 = X
B
P
B
º
T
P
1
= 
º P
' x
A
A
 + 
º P
' x
B
B
.
Graphical Representation :
P º
A
P
T
P
A
P
B,
P º
B,
X = 0
X = 1
A
B
X = 1
X = 0
A
B
A more volatile than B  (P
A
º > P
B
º)
  
Ideal solutions (mixtures) :
Mixtures which follow Raoul'ts law at all temperature.
A ------ A ? A -------- B,
B ----- B
?H
mix
 = 0 : ?V
mix
 = 0 :
?S
mix 
= + ve as for process to proceed : ?G
mix 
= ? ve
eg. (1 ) Benzene + Toluene.
(2) Hexane + heptane.
(3) C
2
H
5
Br + C
2
H
5
?.
Non-?deal solutions : Which do not obey Raoult's law.
(a) Positive deviation : ?
(i) P
T,exp
 > ( X
A
Pº
A 
+ X
B
P
B
º )
(ii)
B B
A A
? ? ? ?
? ? ? ?
> A ---- B
  
?
Force of attraction
(iii) ?H
mix
 = +ve energy absorbed
(iv) ?V
mix
 = +ve ( 1L + 1L > 2L )
(v) ?S
mix
 = +ve
(vi) ?G
mix
 = ?ve
eg. H
2
O + CH
3
OH.
H
2
O + C
2
H
5
OH
C
2
H
5
OH + hexane
C
2
H
5
OH + cyclohexane.
CHCl
3
 + CCl
4
 ?  dipole dipole interaction becomes weak.
P
XA = 0
XB = 1
XA = 1
XB = 0
  P
0
A > P
0
B
(b) Negative deviation
(i) P
T
 exp < X
A
P
A
º + X
B
Pº
B
(ii)
B B
A A
? ? ? ?
? ? ? ?
< A ------ B.
strength of force of altraction.
  
(iii) ?H
mix
 = ?ve (iv) ?V
mix
 = ?ve ( 1L + 1L < 2L )
(v) ?S
mix
 = +ve (vi) ?G
mix
 = ?ve
eg. H
2
O + HCOOH
H
2
O + CH
3
COOH
H
2
O + HNO
3
CHCl
3
 + CH
3
OCH
3
?
C = O         H
CH
3
CH
3
C
Cl
Cl
Cl
P
X
xB = 1
XA = 0 
A = 1
XB = 0 
P
0
A > P
0
B
Immiscible Liquids :
(i) P
total
 = P
A
 + P
B
(ii) P
A
 = P
A
0
 X
A
  = P
A
0
[Since, X
A
 = 1].
(iii) P
B
 = P
B
0
 X
B
 = P
B
0
[Since, X
B
 = 1].
(iv) P
total
 = P
A
0
 + P
B
0
(v) 
0
B
0
A
P
P
 = 
B
A
n
n
(vi) 
B A
B A
0
B
0
A
W M
M W
P
P
?
P
A
0
 = 
V
RT n
A
  ;   P
B
0
 =
V
RT n
B
T
A T
B
T
soln.
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.
m ? p
m = kp
m ? 
liquid of Volume
gas of weight