Classification of Elements and Periodicity in Properties

Atomic Radii, Ionic Radii, Ionization Energy, Electron affinity, Electronegativity


Periodicity and Properties :

Repetition of similar properties at regular intervals
→ IA, II A, 0 → 2, 8, 8, 18, 18, 32
→ III A - VI A → 8, 18, 18, 32

  • Atomic Radius
  • Ionization potential
  • Electron Affinity
  • Electron Negativity
  • Metallic and Non-metallic
  • Valency
  • Electropositivity
  • Nature of oxides.

Atomic Radius :
Distance between nucleus and outermost electron. expressed in Å, nm, and pm etc ....Experimental determination of atomic radius is not possible. Atoms have no sharp boundary.

⇒ Radius of H - atom \frac{D_{H - H}}{2}=\frac{0.74}{2} = 0.37Å

Crystal Radius / Metallic Radius :
Half of the inter nuclear distance between two nucleus

r_{Na} = \frac{d_{{Na} - {Na}}}{2}

Vander Waal's Radius :
→ minimum force between particles
→ size increases vander waal's force of attraction(VWFOA) increases.
Cl2 ----- Cl , VWFOA is in between two chlorine molecules
   
VR > MR > CR
VR = vander waal's
MR = metallic radius
CR = crystal radius

Factors influencing atomic radius :
effective nuclear charge (Z*)
\tt Z^{*} = \left(\frac{No.of \ protons}{No.of \ electrons}\right)
Na^{+} = \frac{11}{10},\ Mg^{+2} = \frac{12}{10}, \ Al^{+3} = \frac{13}{10}

Factors influencing ionization energy :
→ Atomic radius :
IP \ (or) \ IE \propto \frac{1}{AR}
Nuclear charge : Increases left to right
Screening / shielding effect :
s > p > d > f
IP \propto \frac{1}{Screening}

Half - filled and completely filled sub-shells :
   C            N          O
2s22p2  2s22p3  2s22p5
As it has half filled ⇒ more stable.
Zn 4s23d10 completely filled-more stable.

Effective nuclear charge (Z*) and screening constant :
Z* = Z − σ (Z = atomic number)

Screening Constant(σ) :
following slates rule
electrons from nth shell → 0.35
electrons from (n − 1) shell → 0.85
electrons (n − 2) and inner shells → 1.0
C : 1s2 2s2 2p2
1s2 2s2 2p1 + \upharpoonleft
σ = 3(0.35) + 2(0.85) = 2.75
Z* = 6 − 2.75 = 3.25

Lanthanoid Contraction :
→ differentiating e enters into deep seated 4f - orbitals
shielding : s > p > d > f
→ due to poor shielding capacity of 4f - orbitals
→ size decreases gradually.

Consequences of Lanthanoid Contraction :
→ atomic size of 4d, 5d series elements are almost same.
eg : Zr - Hf, Nb - Ta ----
→ IP values of 5d - series elements are more than those of 4d - series elements.
Basic nature and covalent nature of hydroxides decreases from Ce(OH)3 → Lu(OH)3

Ionization Potential :
Amount of energy required to remove the most loosely held electron from an isolated neutral gaseous atom.
Xg + IP (or) IE1 X_g^{+} + e
ΔH = +IE
1 e.V = 3.35 × 10-20 cal/atom
= 1.6 × 10-19 J/atom
= 96.45 kJ/mol
= 23.06 kcal/mol.

Electron Gain EnthalpyegH) :
X_{(g)} + e^{-}\rightarrow X_g^{{-}}, \triangle H = -EA_{1}
Note : except for Be, Mg, N, He, Ne, Ar, Kr, Xe
EA1 is always positive
\triangle_{eg}H = -E_{A} - \frac{5}{2}RT
X_{(g)}^- + e^{-} \rightarrow X_{(g)}^{2-} ; \triangle H_{2} = +EA_{2} is endothermic

Electronegativity : Tendency of the bonded atom to attract the bonding e

Pauling Scale of EN :
X_{A} - X_{B} = 0.208\sqrt{\triangle}
Δ is in kcal/mole
X_{A} - X_{B} = 0.1017\sqrt{\triangle}
Δ is in kJ/mole
\triangle = \left(E_{A - B}\right)_{exp} - \frac{1}{2}\left(E_{A - A} - E_{B - B}\right)_{theoretical}

Mulliken's Scale of EN :
EN = \frac{IP + EA}{2}
case (1) EN = \frac{I_{P} + E_{A}}{2 \times 2.8}
= \frac{IP + EA}{5.6} (in \ e.V)
= \frac{IP + EA}{130}(kcal / mol)
= \frac{IP + EA}{544}(kJ / mol)

Hybridization :
As the s - character of hybrid orbital increases EN ↑

  %S EN
sp3 25 % 2.55
sp2 33.33 % 2.75
sp 50 % 3.25

 
                 sp > sp2 > sp3

Electronegativity Applications :
% of ionic character = 16 (XA − XB) + 3.5(XA − XB)2
electronegativity difference = 1.7 ⇒ 50% covalent character
                                                          ⇒ 50% ionic character
                                                   = 0  ⇒ 100% covalent character
                                                 < 1.7 ⇒ more than 50% covalent
                                                 > 1.7 ⇒ more than 50% ionic

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1. Atomic radius,\tt r_{A}=\frac{r_{A}+r_{A}}{2}=\frac{d_{A-A}}{2}
[DistanceA-A = radius of A + radius of A]

2. For heterodiatomic molecule AB, dA-B = rA + rB + 0.09 (XA-XB)
where, XA and XB are electronegativities of A and B.

3. Mulliken scale
Electronegativity (x) =\tt \frac{IE+\Delta He_{g}}{2}

4. Pauling scale: The difference in electronegativity of two atoms A and B is given by the relationship \tt x_{B}-x_{A}= 0.208\sqrt{\Delta}
where, \tt \Delta = E_{A-B}-\sqrt{E_{A-A}\times E_{B-B}}
(Δ is known as resonance energy.)
EA-B, EA-A and EB-B represent bond dissociation energies of the bonds A - B, A - A and B - B respectively.

5. Allred and Rochow's scale
Electronegativity =\tt 0.744+\frac{0.359\ Z_{eff}}{r^{2}}
where, Zeff is the effective nuclear charge = Z − σ
where, σ is screening constant. It's value can be determined by Slater's rule.

6. Covalent radius
rcovalent or \tt r_{c}= \frac{1}{2} [bond length]

7. The screening effect and effective nuclear charge are very closely related, i.e,
                      Z' = Z − σ
where,  Z' = effective nuclear charge
              Z = atomic number
              σ = screening constant