INO-03

Kapustinskii lattice energy

U = 1202 ν |Z+ Z−| / r0 × (1 − 0.345/r0) kJ/mol, r0 in Å.

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LatticeKapustinskii 1956

Governing equation

U=\dfrac{1202\,\nu|Z_+Z_-|}{r_0}\left(1-\dfrac{0.345}{r_0}\right)

where

\nu: Ions per formula (—)
Z_+: Cation charge (—)
Z_-: Anion charge (—)
r_0: Internuclear r0 (Å)
U: Lattice 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-03 — Kapustinskii lattice energy) is the form associated with Kapustinskii 1956. Working symbols: $\nu$ , $Z_+$ , $Z_-$ , $r_0$ $\rightarrow$ $U$ . An empirical Madelung-plus-repulsion formula that needs only the ionic radii and charges.

Purpose

Purpose: compute

U

from

\nu

Z_+

Z_-

r_0

in Inorganic chemistry via

U=\dfrac{1202\,\nu|Z_+Z_-|}{r_0}\left(1-\dfrac{0.345}{r_0}\right)

U = 1202 ν |Z+ Z−| / r0 × (1 − 0.345/r0) kJ/mol, r0 in Å. 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

\nu = 2.000\,\mathrm{—}

Z_+ = 1.000\,\mathrm{—}

Z_- = 1.000\,\mathrm{—}

r_0 = 2.800\,\mathrm{Å}

, the governing relation

U=\dfrac{1202\,\nu|Z_+Z_-|}{r_0}\left(1-\dfrac{0.345}{r_0}\right)

yields

U = 752.8\,\mathrm{kJ/mol}

. Binary salt, r0 = r+ + r− in Å. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Ions per formula \nu2 —Cation charge Z_+1 —Anion charge Z_-1 —Internuclear r0 r_02.8 Å

Outputs

Lattice energy U752.8 kJ/mol

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Narration of this film

Binary salt, r0 = r+ + r− in Å.

An empirical Madelung-plus-repulsion formula that needs only the ionic radii and charges.

Reading speed

Watch on YouTube