ORG-22

Hansen solubility distance

Ra² = 4(δD1−δD2)² + (δP1−δP2)² + (δH1−δH2)². Like-dissolves-like metric.

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SolubilityHansen

Governing equation

R_a^2=4(\delta_{D1}-\delta_{D2})^2+(\delta_{P1}-\delta_{P2})^2+(\delta_{H1}-\delta_{H2})^2

$\delta_{D2} \in \left[10, 25\right]$

where

\delta_{D1}: δD solute (MPa^{1/2})
\delta_{P1}: δP solute (MPa^{1/2})
\delta_{H1}: δH solute (MPa^{1/2})
\delta_{D2}: δD solvent (MPa^{1/2})
\delta_{P2}: δP solvent (MPa^{1/2})
\delta_{H2}: δH solvent (MPa^{1/2})
R_0: Interaction radius (MPa^{1/2})
R_a: Hansen distance (MPa^{1/2})
RED: Relative energy difference (—)

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.

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①

Governing law — red

R_a^2=4(\delta_{D1}-\delta_{D2})^2+(\delta_{P1}-\delta_{P2})^2+(\delta_{H1}-\delta_{H2})^2

$\delta_{D2} \in \left[10, 25\right]$

$\delta_{D2} = 10$ $R_a = 16.28$

Along the curve

②

Domain of the variable — blue

\delta_{D2}_{\min} = 10,\quad \delta_{D2}_{\max} = 25

$\delta_{D2} \in \left[10, 25\right]$

$\delta_{D2} = 10$ $\delta_{D2} = 10$

Along the curve

③

Response curve — green

R_a^2=4(\delta_{D1}-\delta_{D2})^2+(\delta_{P1}-\delta_{P2})^2+(\delta_{H1}-\delta_{H2})^2

$\delta_{D2} \in \left[10, 25\right]$

$\delta_{D2} = 10$ $R_a = 16.28$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R_a}{\mathrm{d}\delta_{D2}}

$\delta_{D2} \in \left[10, 25\right]$

$\delta_{D2} = 10.09$ $R_a^{\prime} = -1.965$

Along the curve

Lecture brief

Historical brief

Hammett (1937) and Taft linear free-energy, E-factor green metrics, Woodward–Fieser UV and Claisen equilibria are how organic chemistry became predictive. The lab is substituent, waste and tautomer. This sheet (ORG-22 — Hansen solubility distance) is the form associated with Hansen. Working symbols: $\delta_{D1}$ , $\delta_{P1}$ , $\delta_{H1}$ , $\delta_{D2}$ , $\delta_{P2}$ , $\delta_{H2}$ , $R_0$ $\rightarrow$ $R_a$ , $RED$ . Hansen split Hildebrand δ into dispersion, polar and hydrogen-bond. RED = Ra/R0 < 1 means soluble.

Purpose

Purpose: compute

R_a

RED

from

\delta_{D1}

\delta_{P1}

\delta_{H1}

\delta_{D2}

\delta_{P2}

\delta_{H2}

R_0

in Organic chemistry via

R_a^2=4(\delta_{D1}-\delta_{D2})^2+(\delta_{P1}-\delta_{P2})^2+(\delta_{H1}-\delta_{H2})^2

Ra² = 4(δD1−δD2)² + (δP1−δP2)² + (δH1−δH2)². Like-dissolves-like metric. Use it when a real organic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\delta_{D1} = 18.000\,\mathrm{MPa^1/2}

\delta_{P1} = 8.000\,\mathrm{MPa^1/2}

\delta_{H1} = 7.000\,\mathrm{MPa^1/2}

\delta_{D2} = 16.000\,\mathrm{MPa^1/2}

\delta_{P2} = 8.000\,\mathrm{MPa^1/2}

\delta_{H2} = 10.000\,\mathrm{MPa^1/2}

R_0 = 10.000\,\mathrm{MPa^1/2}

, the governing relation

R_a^2=4(\delta_{D1}-\delta_{D2})^2+(\delta_{P1}-\delta_{P2})^2+(\delta_{H1}-\delta_{H2})^2

yields

R_a = 5.00\,\mathrm{MPa^1/2}

RED = 0.500\,\mathrm{—}

. Two substances, δ in MPa^{1/2}. Optional R0 for RED. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

δD solute \delta_{D1}18 MPa^{1/2}δP solute \delta_{P1}8 MPa^{1/2}δH solute \delta_{H1}7 MPa^{1/2}δD solvent \delta_{D2}16 MPa^{1/2}δP solvent \delta_{P2}8 MPa^{1/2}δH solvent \delta_{H2}10 MPa^{1/2}Interaction radius R_010 MPa^{1/2}

Outputs

Hansen distance R_a5.00 MPa^{1/2}
Relative energy difference RED0.500 —

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Narration of this film

Two substances, δ in MPa^{1/2}. Optional R0 for RED.

Hansen split Hildebrand δ into dispersion, polar and hydrogen-bond. RED = Ra/R0 < 1 means soluble.

Reading speed

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