INO-08

Coulomb lattice snapshot

U ∝ |Z+ Z−| / r. Bare ionic attraction of a pair.

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LatticeCoulomb

Governing equation

U=-\dfrac{k|Z_+Z_-|}{r}

where

Z_+: Cation charge (—)
Z_-: Anion charge (—)
r: Separation (Å)
U: Pair energy (kJ/mol)

Lecture brief

Historical brief

Pauling and Allred–Rochow electronegativity, Kapustinskii lattice energy, CFSE and Goldschmidt radii organise the periodic solid. The sheets predict bond character and crystal packing. This sheet (INO-08 — Coulomb lattice snapshot) is the form associated with Coulomb. Working symbols: $Z_+$ , $Z_-$ , $r$ $\rightarrow$ $U$ . The pedagogical ancestor of Madelung: one pair, no summation, no repulsion.

Purpose

Purpose: compute

U

from

Z_+

Z_-

r

in Inorganic chemistry via

U=-\dfrac{k|Z_+Z_-|}{r}

U ∝ |Z+ Z−| / r. Bare ionic attraction of a pair. Use it when a real inorganic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Z_+ = 2.000\,\mathrm{—}

Z_- = 2.000\,\mathrm{—}

r = 2.100\,\mathrm{Å}

, the governing relation

U=-\dfrac{k|Z_+Z_-|}{r}

yields

U = -2646.4\,\mathrm{kJ/mol}

. Point charges, r in Å, kJ/mol for a mole of pairs. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cation charge Z_+2 —Anion charge Z_-2 —Separation r2.1 Å

Outputs

Pair energy U-2646.4 kJ/mol

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Narration of this film

Point charges, r in Å, kJ/mol for a mole of pairs.

The pedagogical ancestor of Madelung: one pair, no summation, no repulsion.

Reading speed

Watch on YouTube