Bonding Continuum
Bonding isn't binary — it exists on a spectrum defined by electronegativity.
The Van Arkel-Ketelaar Triangle
We often simplify bonding into Ionic, Covalent, and Metallic. In reality there is a continuum. The Bonding Triangle predicts bonding type using two parameters:
X-Axis: Average Electronegativity
\( \bar{\chi} = \frac{\chi_A + \chi_B}{2} \)
- Low \(\bar{\chi}\): Electrons held loosely (Metallic).
- High \(\bar{\chi}\): Electrons held tightly (Covalent).
Y-Axis: Electronegativity Difference
\( \Delta\chi = |\chi_A - \chi_B| \)
- Low \(\Delta\chi\): Electron sharing (Covalent / Metallic).
- High \(\Delta\chi\) (>1.8): Electron transfer (Ionic).
The Three Zones
Ionic
Top Vertex — High Δχ, Medium \(\bar{\chi}\).
Ex: CsF (Brittle, Insulator)
Metallic
Bottom Left — Low Δχ, Low \(\bar{\chi}\).
Ex: Na, Cs (Conductive, Malleable)
Covalent
Bottom Right — Low Δχ, High \(\bar{\chi}\).
Ex: F₂, CH₄ (Insulator)
Intermediates
Compounds on the borders show intermediate properties. Silicon falls in the "Semiconductor" zone. SiC sits on the covalent-metallic boundary, explaining its hardness and semi-conductivity.
Think About It
Where would HF sit on the Van Arkel-Ketelaar triangle? Is it ionic, covalent, or somewhere in between?
χ(H) = 2.2, χ(F) = 4.0. So Δχ = 1.8 (borderline ionic) and average χ = 3.1 (high, indicating covalent character). HF sits in the upper-right region — it has very strong polar covalent character with significant ionic contribution. This explains its unusually high boiling point and strong hydrogen bonding.