Numerical Tricks and Methods:

1. Electronegativity:

   • Remember the Pauling electronegativity values of common elements. For example, F (4.0), O (3.5), N (3.0), C (2.5), H (2.1).
   • Calculate the electronegativity difference (∆EN) by subtracting the electronegativity of the less electronegative element from the more electronegative element.

2. Ionic Bond:

   • Use the Born-Haber cycle to calculate lattice energy by summing the following energy changes:
     • Enthalpy of formation of the compound from its elements
     • Enthalpy of atomization of the elements
     • Enthalpy of ionization of the metal
     • Enthalpy of electron affinity of the non-metal
     • Lattice energy (unknown)

3. Covalent Bond:

   • Determine bond order by counting the number of shared electron pairs between atoms.
   • Use VSEPR theory to predict bond angles based on electron pair geometry.
   • Remember common hybridization types: sp3 (tetrahedral), sp2 (trigonal planar), and sp (linear).

4. Polarity of Bonds:

   • Calculate the dipole moment (µ) using the formula: µ = q × d, where q is the magnitude of the partial charges and d is the distance between them.
   • Electronegativity difference can indicate polarity: ∆EN > 0.4 (polar covalent), ∆EN > 1.7 (ionic).

5. Lewis Structures:

   • Follow the octet rule (except for H, which follows the duet rule) and satisfy all valence electrons.
   • Use formal charge calculations to assess the overall stability of the Lewis structure.

6. Resonance:

   • Identify resonance structures by moving π electrons between atoms without changing atom connectivity.
   • The more resonance structures a molecule has, generally the more stable it is.

7. Molecular Orbital Theory:

   • Construct MO diagrams by combining atomic orbitals of appropriate symmetry.
   • Analyze the molecular orbitals in terms of bonding (σ) or antibonding (σ*) properties.

8. Metallic Bonding:

   • Sea of delocalized valence electrons allows for high electrical and thermal conductivity in metals.

9. Hydrogen Bonding:

   • Identify H-bonding when hydrogen is covalently bonded to an electronegative atom (N, O, F) and the H atom is close to another electronegative atom.

10. Allotropes:

• Compare the structures, properties, and conditions required for the formation of different allotropes.

11. Oxidation States

    • Remember common oxidation states for different elements,
    • Identify the overall charge of an ion/molecule based on its constituent elements.

12. Acid-Base Reactions

    • Memorize strong acids and strong bases.
    • Predict products based on proton transfer.

13. Hydronium and Hydroxide Ion Concentrations:

    • Calculate [H3O+] using [H3O+] = 10^(-pH) or [OH-] using [OH-] = Kw/[H3O+], where Kw is the autoionization constant of water (1.0 × 10^(-14) at 25 °C).

14. Buffer Solutions

    • Calculate [H3O+] of a buffer solution using the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]), where pKa is the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.

15. Solubility Equilibria

    • Determine solubility by calculating the concentration of dissolved solute at equilibrium using the solubility product constant (Ksp) expression.

16. Gas Laws

    • Use the ideal gas law (PV = nRT) to calculate pressure (P), volume (V), temperature (T), or the amount of gas (n) in a system.

17. Equilibrium Constants:

    • Calculate the equilibrium constant (Kp or Keq) from reaction concentrations at equilibrium. Compare with Keq to predict reaction direction.