INO-15

Ionic potential φ = Z/r

φ = Z / r. Polarising power of a cation.

Reading speed

BondingCartledge

Governing equation

\varphi=Z/r

$r \in \left[0.2, 1.8\right]$

where

Z: Charge (—)
r: Ionic radius (Å)
\varphi: Ionic potential (\mathrm{\AA}^{-1})

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

\varphi=Z/r

$r \in \left[0.2, 1.8\right]$

$r = 0.2$ $\varphi = 15$

Along the curve

②

Domain of the variable — blue

r_{\min} = 0.2,\quad r_{\max} = 1.8

$r \in \left[0.2, 1.8\right]$

$r = 0.2$ $r = 0.2$

Along the curve

③

Response curve — green

\varphi=Z/r

$r \in \left[0.2, 1.8\right]$

$r = 0.2$ $\varphi = 15$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\varphi}{\mathrm{d}r}

$r \in \left[0.2, 1.8\right]$

$r = 0.21$ $\varphi^{\prime} = -68.14$

Along the curve

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-15 — Ionic potential φ = Z/r) is the form associated with Cartledge. Working symbols: $Z$ , $r$ $\rightarrow$ $\varphi$ . High φ (small, highly charged) polarises anions and leans covalent — Fajans.

Purpose

Purpose: compute

\varphi

from

Z

r

in Inorganic chemistry via

\varphi=Z/r

φ = Z / r. Polarising power of a cation. 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 = 3.000\,\mathrm{—}

r = 0.640\,\mathrm{Å}

, the governing relation

\varphi=Z/r

yields

\varphi = 4.688\,\mathrm{mathrmAA^-1}

. r in Å, Z the formal charge. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Charge Z3 —Ionic radius r0.64 Å

Outputs

Ionic potential \varphi4.688 \mathrm{\AA}^{-1}

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

r in Å, Z the formal charge.

High φ (small, highly charged) polarises anions and leans covalent — Fajans.

Reading speed

Watch on YouTube