Weak Interactions

These types of forces are responsible for formation of liquids and solids in covalently bonded species.

Ion-dipole

Coulombic attraction; usually a cation with a dipole

E = energy Z = ion charge μ = dipole moment, ε_o = permittivity of free space

r = distance between ion and center of the dipole

Order of magnitude of the energy:

For Z = 1 (=1.602×10^–19 C); μ = 1 D (= 3.336×10^–30 C·m); 4πε_o = 1.113×10^–10 J^–1C²m^–1; r = 1 nm (= 1×10^–9 m); N_A = 6.022×10²³ mol^–1

E = –(1.602×10^–19 C)(3.336×10^–30 C·m)(6.022×10²³ mol^–1)/ (1.113×10^–10 J^–1C²m^–1)(1×10^–9 m)² = ~ –3000 J/mol

Dipole-dipole

Requires either a molecular dipole or a bond dipole

directional, shorter range

Order of magnitude of the energy:

For μ = 1 D (= 3.336×10^–30 C·m); 4πε_o = 1.113×10^–10 J^–1C²m^–1; r = 1 nm (= 1×10^–9 m); N_A = 6.022×10²³ mol^–1

E = –(3.336×10^–30 C·m)²(6.022×10²³ mol^–1)/ (1.113×10^–10 J^–1C²m^–1)(1×10^–9 m)³ = ~ –60 J/mol

Ion-Induced Dipole

α is the polarizability of the neutral

Order of magnitude of the energy:

For Z = 1 (=1.602×10^–19 C); α = 1 ų (= 1×10^–30 m³); 4πε_o = 1.113×10^–10 J^–1C²m^–1; r = 1 nm (= 1×10^–9 m); N_A = 6.022×10²³ mol^–1

E = –(1.602×10^–19 C)²(1×10^–30 m³)(6.022×10²³ mol^–1)/ 2(1.113×10^–10 J^–1C²m^–1)(1×10^–9 m)⁴ = ~ –70 J/mol

Dipole-Induced Dipole

Order of magnitude of the energy:

For μ = 1 D (= 3.336×10^–30 C·m); α = 1 ų (= 1×10^–30 m³); 4πε_o = 1.113×10^–10 J^–1C²m^–1; r = 1 nm (= 1×10^–9 m); N_A = 6.022×10²³ mol^–1

E = –(3.336×10^–30 C·m)²(1×10^–30 m³)(6.022×10²³ mol^–1)/ (1.113×10^–10 J^–1C²m^–1)(1×10^–9 m)⁶ = ~ –0.06 J/mol

Instantaneous Dipole-Induced Dipole (van der Waal's or London Dispersion)

E = –3IPα²/4r⁶

IP = ionization potential

Order of magnitude of the energy:

For IP = 1000 kJ/mol (= 1000000 J/mol); α = 1 ų (= 1×10^–30 m³); 4πε_o = 1.113×10^–10 J^–1C²m^–1; r = 1 nm (= 1×10^–9 m);

E = –3(1000000 J/mol)(1×10^–30 m³)²/(1×10^–9 m)⁶ = ~ –3 J/mol

van der Waal's interaction explain the condensation of nonpolars:

Hydrogen Bonding

A special case of dipole-dipole (maybe), but is relatively common and has large energies (approaching covalent bond energies)

Characteristics:

1. Directional

2. Linear or near linear bond angles

3. Covalent-like bond energies 10-15 kcal/mole, 40-60 kJ/mole

4. Occurs between H^δ+ and elements more electronegative than H^δ+ (O, N, F)

liquid water (E. Grunwald, J. Am. Chem. Soc., 1986, 108, 5719 and 5726)

Coordination Number = 4.2-4.5 !

HF has very unusual properties because of strong H-bonding

1. high bp

	hydrogen halide	bp(oC,1atm)
	HF	+9
	HCl	-87
	HBr	-67
	HI	-35

2. oligomeric in the gas phase (HF)₆ cyclic hexamer

3. weak acid in water, K_a ~ 10^–4

HF(aq) + H₂O(l) ⇄ H₃O⁺(aq) + F^–(aq)

2 HF(aq) ⇄ H₂F⁺(aq) + F^–(aq)

HF(aq) + F^–(aq) ⇄ H₂F^–(aq)

multiple competing equilibria