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**ATOMIC STRUCTURE**

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

The radius of a nucleus : R = R_{0} (A)^{1/3} cm

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

Photoelectric Effect:

**Bohr’s Model for Hydrogen like atoms :**

- mvr = n(h/2π) (Quantization of angular momentum)

**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 (x_{1}) = ∴ Mole fraction of solvent (x_{2}) =

**% Calculation:**

**Derive the following conversion :**

- Mole fraction of solute into molarity of solution M =
- Molarity into mole fraction x
_{2}= - Mole fraction into molality m =
- Molality into mole fraction x
_{2}= - Molality into molarity M =
- Molarity into Molality m =

M_{1} and M_{2} are molar masses of solvent and solute, ρ 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 :**

**Mean molar mass or molecular mass:**

**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) =**

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 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:**

**Volume strength of H _{2}O_{2}:**

20V H_{2}O_{2} means one litre of this sample of H_{2}O_{2} on decomposition gives 20 It. of O_{2} 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.

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