Formula for Physical Chemistry | Physical Chemistry PDF Download

 Page 1


  
Planck's Quantum Theory :
Energy of one photon = h?  =
?
hc
Photoelectric Effect :
h? = h?
0
 + 
2
1
m
e
?
2
Bohr?s Model for Hydrogen like atoms :
1. mvr = n 
? 2
h
(Quantization of angular momentum)
2. E
n
 = ? 
2
1
n
E
 z
2
 = ?2.178 × 10
?18
 
2
2
n
z
 J/atom  =   ?13.6 
2
2
n
z
eV
E
1
 = 
2
4 2
n
me 2? ?
3. r
n
 = 
Z
n
2
 × 
m e 4
h
2 2
2
?
 = 
Z
n 529 . 0
2
?
 Å
4. v = 
nh
ze 2
2
?
 = 
n
z 10 18 . 2
6
? ?
 m/s
De?Broglie wavelength :
? = 
p
h
mc
h
?
(for photon)
Wavelength of emitted photon :
?
1
 = ? = 
?
?
?
?
?
?
?
?
?
?
?
2
2
2
1
2
n
1
n
1
RZ
PHYSICAL CHEMISTRY
ATOMIC STRUCTURE
Page 2


  
Planck's Quantum Theory :
Energy of one photon = h?  =
?
hc
Photoelectric Effect :
h? = h?
0
 + 
2
1
m
e
?
2
Bohr?s Model for Hydrogen like atoms :
1. mvr = n 
? 2
h
(Quantization of angular momentum)
2. E
n
 = ? 
2
1
n
E
 z
2
 = ?2.178 × 10
?18
 
2
2
n
z
 J/atom  =   ?13.6 
2
2
n
z
eV
E
1
 = 
2
4 2
n
me 2? ?
3. r
n
 = 
Z
n
2
 × 
m e 4
h
2 2
2
?
 = 
Z
n 529 . 0
2
?
 Å
4. v = 
nh
ze 2
2
?
 = 
n
z 10 18 . 2
6
? ?
 m/s
De?Broglie wavelength :
? = 
p
h
mc
h
?
(for photon)
Wavelength of emitted photon :
?
1
 = ? = 
?
?
?
?
?
?
?
?
?
?
?
2
2
2
1
2
n
1
n
1
RZ
PHYSICAL CHEMISTRY
ATOMIC STRUCTURE
  
No. of photons emitted by a sample of H atom :
2
) 1 n ( n ? ? ?
Heisenberg?s uncertainty principle :
?x.?p > 
? 4
h
or m ?x.?v ? 
? 4
h
or ?x.?v ? 
m 4
h
?
Quantum Numbers :
* Principal quantum number (n) = 1, 2, 3, 4 .... to ?.
* Orbital angular momentum of electron in any orbit  = 
? 2
nh
.
* Azimuthal quantum number (?) = 0, 1, ..... to (n ? 1).
* Number of orbitals in a subshell = 2? + 1
* Maximum number of electrons in particular subshell = 2
 
× (2? + 1)
* Orbital angular momentum L = 
? 2
h
 ) 1 ( ? ? ? = ? ) 1 ( ? ? ?
?
?
?
?
?
?
?
?
2
h
?
STOICHIOMETRY
? Relative atomic mass (R.A.M) = 
atom carbon one of mass
12
1
element an of atom one of Mass
?
= Total Number of nucleons
? Y-map
Mole
× 22.4 lt
? 22.4 lt
Volume at STP
? N
A
× N
A
Number
× mol. wt.
× At. wt.
?
? At. wt.
 mol. wt.
Mass
Page 3


  
Planck's Quantum Theory :
Energy of one photon = h?  =
?
hc
Photoelectric Effect :
h? = h?
0
 + 
2
1
m
e
?
2
Bohr?s Model for Hydrogen like atoms :
1. mvr = n 
? 2
h
(Quantization of angular momentum)
2. E
n
 = ? 
2
1
n
E
 z
2
 = ?2.178 × 10
?18
 
2
2
n
z
 J/atom  =   ?13.6 
2
2
n
z
eV
E
1
 = 
2
4 2
n
me 2? ?
3. r
n
 = 
Z
n
2
 × 
m e 4
h
2 2
2
?
 = 
Z
n 529 . 0
2
?
 Å
4. v = 
nh
ze 2
2
?
 = 
n
z 10 18 . 2
6
? ?
 m/s
De?Broglie wavelength :
? = 
p
h
mc
h
?
(for photon)
Wavelength of emitted photon :
?
1
 = ? = 
?
?
?
?
?
?
?
?
?
?
?
2
2
2
1
2
n
1
n
1
RZ
PHYSICAL CHEMISTRY
ATOMIC STRUCTURE
  
No. of photons emitted by a sample of H atom :
2
) 1 n ( n ? ? ?
Heisenberg?s uncertainty principle :
?x.?p > 
? 4
h
or m ?x.?v ? 
? 4
h
or ?x.?v ? 
m 4
h
?
Quantum Numbers :
* Principal quantum number (n) = 1, 2, 3, 4 .... to ?.
* Orbital angular momentum of electron in any orbit  = 
? 2
nh
.
* Azimuthal quantum number (?) = 0, 1, ..... to (n ? 1).
* Number of orbitals in a subshell = 2? + 1
* Maximum number of electrons in particular subshell = 2
 
× (2? + 1)
* Orbital angular momentum L = 
? 2
h
 ) 1 ( ? ? ? = ? ) 1 ( ? ? ?
?
?
?
?
?
?
?
?
2
h
?
STOICHIOMETRY
? Relative atomic mass (R.A.M) = 
atom carbon one of mass
12
1
element an of atom one of Mass
?
= Total Number of nucleons
? Y-map
Mole
× 22.4 lt
? 22.4 lt
Volume at STP
? N
A
× N
A
Number
× mol. wt.
× At. wt.
?
? At. wt.
 mol. wt.
Mass
  
Density :
Specific gravity = 
C 4 at water of density
ce tan subs the of density
?
For gases :
Absolute density (mass/volume) = 
gas the of volume Molar
gas the of mass Molar
? ? =  
RT
PM
Vapour density      V.D.= 
2
H
gas
d
d
 = 
RT H
RT gas
2
PM
PM
 = 
2
H
gas
M
M
 = 
2
M
gas
M
gas
 = 2 V.D.
Mole-mole analysis :
Mass
??At. wt. / Mol. Wt.
Mole
Mole-mole 
relationship 
of equation
Mole
× 22.4 lt
Volume at STP
× mol. wt./At. wt.
Mass
Concentration terms :
Molarity (M) :
? Molarity (M) = 
inml
V ) solute of wt . Mol (
1000 w
?
?
Molality (m) :
Molality = 
1000
gram  in  solvent  of  mass
solute  of  moles  of  number
?
 = 1000 w
1
 / M
1
w
2
Mole fraction (x) :
? Mole fraction of solution (x
1
) = 
N n
n
?
? Mole fraction of solvent (x
2
) = 
N n
N
?
x
1
 + x
2
 = 1
Page 4


  
Planck's Quantum Theory :
Energy of one photon = h?  =
?
hc
Photoelectric Effect :
h? = h?
0
 + 
2
1
m
e
?
2
Bohr?s Model for Hydrogen like atoms :
1. mvr = n 
? 2
h
(Quantization of angular momentum)
2. E
n
 = ? 
2
1
n
E
 z
2
 = ?2.178 × 10
?18
 
2
2
n
z
 J/atom  =   ?13.6 
2
2
n
z
eV
E
1
 = 
2
4 2
n
me 2? ?
3. r
n
 = 
Z
n
2
 × 
m e 4
h
2 2
2
?
 = 
Z
n 529 . 0
2
?
 Å
4. v = 
nh
ze 2
2
?
 = 
n
z 10 18 . 2
6
? ?
 m/s
De?Broglie wavelength :
? = 
p
h
mc
h
?
(for photon)
Wavelength of emitted photon :
?
1
 = ? = 
?
?
?
?
?
?
?
?
?
?
?
2
2
2
1
2
n
1
n
1
RZ
PHYSICAL CHEMISTRY
ATOMIC STRUCTURE
  
No. of photons emitted by a sample of H atom :
2
) 1 n ( n ? ? ?
Heisenberg?s uncertainty principle :
?x.?p > 
? 4
h
or m ?x.?v ? 
? 4
h
or ?x.?v ? 
m 4
h
?
Quantum Numbers :
* Principal quantum number (n) = 1, 2, 3, 4 .... to ?.
* Orbital angular momentum of electron in any orbit  = 
? 2
nh
.
* Azimuthal quantum number (?) = 0, 1, ..... to (n ? 1).
* Number of orbitals in a subshell = 2? + 1
* Maximum number of electrons in particular subshell = 2
 
× (2? + 1)
* Orbital angular momentum L = 
? 2
h
 ) 1 ( ? ? ? = ? ) 1 ( ? ? ?
?
?
?
?
?
?
?
?
2
h
?
STOICHIOMETRY
? Relative atomic mass (R.A.M) = 
atom carbon one of mass
12
1
element an of atom one of Mass
?
= Total Number of nucleons
? Y-map
Mole
× 22.4 lt
? 22.4 lt
Volume at STP
? N
A
× N
A
Number
× mol. wt.
× At. wt.
?
? At. wt.
 mol. wt.
Mass
  
Density :
Specific gravity = 
C 4 at water of density
ce tan subs the of density
?
For gases :
Absolute density (mass/volume) = 
gas the of volume Molar
gas the of mass Molar
? ? =  
RT
PM
Vapour density      V.D.= 
2
H
gas
d
d
 = 
RT H
RT gas
2
PM
PM
 = 
2
H
gas
M
M
 = 
2
M
gas
M
gas
 = 2 V.D.
Mole-mole analysis :
Mass
??At. wt. / Mol. Wt.
Mole
Mole-mole 
relationship 
of equation
Mole
× 22.4 lt
Volume at STP
× mol. wt./At. wt.
Mass
Concentration terms :
Molarity (M) :
? Molarity (M) = 
inml
V ) solute of wt . Mol (
1000 w
?
?
Molality (m) :
Molality = 
1000
gram  in  solvent  of  mass
solute  of  moles  of  number
?
 = 1000 w
1
 / M
1
w
2
Mole fraction (x) :
? Mole fraction of solution (x
1
) = 
N n
n
?
? Mole fraction of solvent (x
2
) = 
N n
N
?
x
1
 + x
2
 = 1
  
% Calculation :
(i) % w/w = 
100
gm in  solution  of  mass
gm  in  solute  of  mass
?
(ii) % w/v = 
mass  of  solute  in  gm
100
Volume  of  solution  in  ml
?
(iii) % v/v = 
Volume  of  solute  in  ml
100
Volume  of  solution
?
Derive the following conversion :
1. Mole fraction of solute into molarity of solution M = 
2 2 1 1
2
x M M x
1000 x
?
? ?
2. Molarity into mole fraction x
2
 = 
2
1
MM 1000
1000 MM
? ? ?
?
3. Mole fraction into molality m = 
1 1
2
M x
1000 x ?
4. Molality into mole fraction x
2
 = 
1
1
mM 1000
mM
?
5. Molality into molarity M = 
2
mM 1000
1000 m
?
? ?
6. Molarity into Molality m = 
2
MM 1000
1000 M
? ?
?
M
1
 and M
2
 are molar masses of solvent and solute. ? is density of solution
(gm/mL)
M = Molarity (mole/lit.), m = Molality (mole/kg), x
1
 = Mole fraction of
solvent, x
2
 = Mole fraction of solute
Average/Mean atomic mass :
A
x
 = 
100
x a ..... x a x a
n n 2 2 1 1
? ? ?
Mean molar mass or molecular mass :
M
avg.
 = 
n 2 1
n n 2 2 1 1
n .... n n
M n ...... M n M n
? ?
? ?
    or M
avg.
 = 
?
?
?
?
?
?
n j
1 j
j
n j
1 j
j j
n
M n
Page 5


  
Planck's Quantum Theory :
Energy of one photon = h?  =
?
hc
Photoelectric Effect :
h? = h?
0
 + 
2
1
m
e
?
2
Bohr?s Model for Hydrogen like atoms :
1. mvr = n 
? 2
h
(Quantization of angular momentum)
2. E
n
 = ? 
2
1
n
E
 z
2
 = ?2.178 × 10
?18
 
2
2
n
z
 J/atom  =   ?13.6 
2
2
n
z
eV
E
1
 = 
2
4 2
n
me 2? ?
3. r
n
 = 
Z
n
2
 × 
m e 4
h
2 2
2
?
 = 
Z
n 529 . 0
2
?
 Å
4. v = 
nh
ze 2
2
?
 = 
n
z 10 18 . 2
6
? ?
 m/s
De?Broglie wavelength :
? = 
p
h
mc
h
?
(for photon)
Wavelength of emitted photon :
?
1
 = ? = 
?
?
?
?
?
?
?
?
?
?
?
2
2
2
1
2
n
1
n
1
RZ
PHYSICAL CHEMISTRY
ATOMIC STRUCTURE
  
No. of photons emitted by a sample of H atom :
2
) 1 n ( n ? ? ?
Heisenberg?s uncertainty principle :
?x.?p > 
? 4
h
or m ?x.?v ? 
? 4
h
or ?x.?v ? 
m 4
h
?
Quantum Numbers :
* Principal quantum number (n) = 1, 2, 3, 4 .... to ?.
* Orbital angular momentum of electron in any orbit  = 
? 2
nh
.
* Azimuthal quantum number (?) = 0, 1, ..... to (n ? 1).
* Number of orbitals in a subshell = 2? + 1
* Maximum number of electrons in particular subshell = 2
 
× (2? + 1)
* Orbital angular momentum L = 
? 2
h
 ) 1 ( ? ? ? = ? ) 1 ( ? ? ?
?
?
?
?
?
?
?
?
2
h
?
STOICHIOMETRY
? Relative atomic mass (R.A.M) = 
atom carbon one of mass
12
1
element an of atom one of Mass
?
= Total Number of nucleons
? Y-map
Mole
× 22.4 lt
? 22.4 lt
Volume at STP
? N
A
× N
A
Number
× mol. wt.
× At. wt.
?
? At. wt.
 mol. wt.
Mass
  
Density :
Specific gravity = 
C 4 at water of density
ce tan subs the of density
?
For gases :
Absolute density (mass/volume) = 
gas the of volume Molar
gas the of mass Molar
? ? =  
RT
PM
Vapour density      V.D.= 
2
H
gas
d
d
 = 
RT H
RT gas
2
PM
PM
 = 
2
H
gas
M
M
 = 
2
M
gas
M
gas
 = 2 V.D.
Mole-mole analysis :
Mass
??At. wt. / Mol. Wt.
Mole
Mole-mole 
relationship 
of equation
Mole
× 22.4 lt
Volume at STP
× mol. wt./At. wt.
Mass
Concentration terms :
Molarity (M) :
? Molarity (M) = 
inml
V ) solute of wt . Mol (
1000 w
?
?
Molality (m) :
Molality = 
1000
gram  in  solvent  of  mass
solute  of  moles  of  number
?
 = 1000 w
1
 / M
1
w
2
Mole fraction (x) :
? Mole fraction of solution (x
1
) = 
N n
n
?
? Mole fraction of solvent (x
2
) = 
N n
N
?
x
1
 + x
2
 = 1
  
% Calculation :
(i) % w/w = 
100
gm in  solution  of  mass
gm  in  solute  of  mass
?
(ii) % w/v = 
mass  of  solute  in  gm
100
Volume  of  solution  in  ml
?
(iii) % v/v = 
Volume  of  solute  in  ml
100
Volume  of  solution
?
Derive the following conversion :
1. Mole fraction of solute into molarity of solution M = 
2 2 1 1
2
x M M x
1000 x
?
? ?
2. Molarity into mole fraction x
2
 = 
2
1
MM 1000
1000 MM
? ? ?
?
3. Mole fraction into molality m = 
1 1
2
M x
1000 x ?
4. Molality into mole fraction x
2
 = 
1
1
mM 1000
mM
?
5. Molality into molarity M = 
2
mM 1000
1000 m
?
? ?
6. Molarity into Molality m = 
2
MM 1000
1000 M
? ?
?
M
1
 and M
2
 are molar masses of solvent and solute. ? is density of solution
(gm/mL)
M = Molarity (mole/lit.), m = Molality (mole/kg), x
1
 = Mole fraction of
solvent, x
2
 = Mole fraction of solute
Average/Mean atomic mass :
A
x
 = 
100
x a ..... x a x a
n n 2 2 1 1
? ? ?
Mean molar mass or molecular mass :
M
avg.
 = 
n 2 1
n n 2 2 1 1
n .... n n
M n ...... M n M n
? ?
? ?
    or M
avg.
 = 
?
?
?
?
?
?
n j
1 j
j
n j
1 j
j j
n
M n
  
Calculation of individual oxidation number :
Formula : Oxidation Number  =  number of electrons in the valence shell
? number of electrons left after bonding
Concept of Equivalent weight/Mass :
For elements, equivalent weight (E) =  
factor - Valency
weight Atomic
For acid/base,        
Acidity / Basicity
M
E?
Where M = Molar mass
For O.A/R.A,        
lost / gained e of moles of . no
M
E
?
?
Equivalent weight (E) = 
v.f.
weight moleculear or Atomic
(v.f. = valency factor)
Concept of number of equivalents :
No. of equivalents of solute = 
M/n
W
E
W
wt. Eq.
Wt
? ?
No. of equivalents of solute = No. of moles of solute × v.f.
Normality (N) :
Normality (N) = 
litres) (in solution of Volume
solute of s equivalent of Number
Normality  = Molarity × v.f.
Calculation of valency  Factor :
n-factor of acid =  basicity = no. of H
+
 ion(s) furnished per molecule of the
acid.
n-factor of base = acidity = no. of OH
?
 ion(s) furnised by the base per
molecule.
At equivalence point :
N
1
V
1
 = N
2
V
2
n
1
M
1
V
1
 = n
2
M
2
V
2