Periodic Classification of Elements - Formula Sheet

Core Equations and Ratios of Periodic Classification

The following are the key mathematical expressions, periodic rules, and industrial ratios presented in this chapter:

1. Covalent Atomic Radius (Homoatomic Molecules)

\[r_A = \\frac{d(A-A)}{2}\]

• r_A: Covalent radius of atom \(A\) in Angstroms (Å) or picometers (pm)
• d(A-A): Interatomic distance (bond length) between the nuclei of two identical, single-bonded atoms of element \(A\)

2. Electronegativity Difference and Bond Character

\[|\\chi_A - \\chi_B| = 1.7 \\implies \\text{50% Ionic, 50% Covalent}\]

\[|\\chi_A - \\chi_B| > 1.7 \\implies \\text{Dominantly Ionic Character}\]

\[|\\chi_A - \\chi_B| < 1.7 \\implies \\text{Dominantly Covalent Character}\]

• χ_A, χ_B: Electronegativities of the two bonded atoms \(A\) and \(B\) (relative units on Pauling's scale)

3. Hydrated Ferric Oxide (Rust Chemical Formula)

\[\\text{Fe}_2\\text{O}_3 \\cdot x\\text{H}_2\\text{O}\]

• Fe₂O₃: Ferric oxide (Iron(III) oxide)
• x: Variable integer coefficient indicating the degree of hydration (water of crystallization) depending on environmental moisture

4. Iron Smelting Charge Ratio (Blast Furnace)

\[\\text{Ore} : \\text{Coke} : \\text{Limestone} = 8 : 4 : 1\]

• Roasted Ore: 8 parts by weight of haematite ore (\(\\text{Fe}_2\\text{O}_3\), provides source metal)
• Coke: 4 parts by weight of carbon (\(\\text{C}\), serves as fuel and generates reducing gas \(\\text{CO}\))
• Limestone: 1 part by weight of calcium carbonate (\(\\text{CaCO}_3\), serves as basic flux to remove acidic silica gangue)