Important Formulas: Physical Chemistry

Atomic Structure

Estimation of closest distance of approach (derivation) of α-particle :

The radius of a nucleus : R = R₀ (A)^1/3 cm

Planck's Quantum Theory : Energy of one photon = hv = (hc/λ)

Photoelectric Effect:

Bohr's Model for Hydrogen like atoms :

1. mvr = n(h/2π) (Quantization of angular momentum) 
2. 
3. 
4. 

De-Broglie wavelength :

Wavelength of emitted photon :

No. of photons emitted by a sample of H atom :

Heisenberg's uncertainty principle:

Or

Or

Quantum Numbers:

• Principal quantum number (n) = 1,2, 3, 4 .... to∞.
• Orbital angular momentum of electron in any orbit = nh/2π.
• Azimuthal quantum number (l) = 0 , 1 .... to (n - 1).
• Number of orbitals in a subshell = 2l + 1
• Maximum number of electrons in particular subshell = 2x (2l+ 1)
• Orbital angular momentum L =  

Stoichiometry

• Relative atomic mass (R.A.M)=  Total Number of nucleons
• Y-map

Density:

For gases:

Absolute density (mass/volume) =

Vapour density

M_gas = 2 V.D.

Mole-mole analysis:

Concentration terms:

Molarity (M):

∴

Molality (m):

Mole fraction (x):

∴ Mole fraction of solution (x₁) = ∴ Mole fraction of solvent (x₂) = 

% Calculation:

Derive the following conversion:

1. Mole fraction of solute into molarity of solution M =
2. Molarity into mole fraction x₂ =
3. Mole fraction into molality m =
4. Molality into mole fraction x₂ =
5. Molality into molarity M =
6. Molarity into Molality m =

M₁ and M₂ are molar masses of solvent and solute, ρ is density of solution (gm/mL) 

M = Molarity (mole/lit.), m = Molality (mole/kg), x₁ = Mole fraction of solvent, x₂ = Mole fraction of solute

Average/Mean atomic mass:

Mean molar mass or molecular mass:

Calculation of individual oxidation number :

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) = 

Equivalent weight (E) =  (v.f. = valency factor)

Concept of number of equivalents:

No. of equivalents of solute =

No. of equivalents of solute = No. of moles of solute x v.f.

Normality (N): 

Normality = Molarity x v.f.

Calculation of valency Factor:

• n-factor of an acid = basicity = number of H⁺ ions furnished per molecule of the acid in the reaction considered.
• n-factor of a base = acidity = number of OH^- ions furnished per molecule of the base in the reaction considered.

At equivalence point:

Volume strength of H₂O₂:

20V H₂O₂ means one litre of this sample of H₂O₂ on decomposition gives 20 It. of O₂ gas at S.T.P.

Measurement of Hardness:

Calculation of available chlorine from a sample of bleaching powder :

 where x = molarity of hypo solution and v = mL. of hypo solution used in titration.