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.
Cl_{2} ----- Cl_{2 } , VWFOA is in between two chlorine molecules
V_{R} > M_{R} > C_{R}
V_{R} = vander waal's
M_{R} = metallic radius
C_{R} = 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
2s^{2}2p^{2} 2s^{2}2p^{3} 2s^{2}2p^{5}
As it has half filled ⇒ more stable.
Zn 4s^{2}3d^{10} 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 n^{th} shell → 0.35
electrons from (n − 1) shell → 0.85
electrons (n − 2) and inner shells → 1.0
C : 1s^{2} 2s^{2} 2p^{2}
1s^{2} 2s^{2} 2p^{1} + \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) IE_{1} → 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 Enthalpy(Δ_{eg}H) :
X_{(g)} + e^{-}\rightarrow X_g^{{-}}, \triangle H = -EA_{1}
Note : except for Be, Mg, N, He, Ne, Ar, Kr, Xe
EA_{1} 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 | |
sp^{3} | 25 % | 2.55 |
sp^{2} | 33.33 % | 2.75 |
sp | 50 % | 3.25 |
sp > sp^{2} > sp^{3}
Electronegativity Applications :
% of ionic character = 16 (X_{A} − X_{B}) + 3.5(X_{A} − X_{B})^{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}
[Distance_{A-A} = radius of A + radius of A]
2. For heterodiatomic molecule AB, d_{A-B} = r_{A} + r_{B} + 0.09 (X_{A}-X_{B})
where, X_{A} and X_{B} 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.)
E_{A-B}, E_{A-A} and E_{B-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, Z_{eff} 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
r_{covalent} 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