ORG-16

Specific optical rotation

[α] = α / (c l). Polarimetry of a chiral sample.

Reading speed

StereochemistryBiot

Governing equation

[\alpha]=\alpha/(c\,\ell)

$c \in \left[0.001, 1\right]$

where

\alpha: Observed rotation (°)
c: Concentration (g/mL)
\ell: Path (dm)
[\alpha]: Specific rotation (° mL g^{-1} dm^{-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.

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①

Governing law — red

[\alpha]=\alpha/(c\,\ell)

$c \in \left[0.001, 1\right]$

$c = 0.001$ $[\alpha] = 1200$

Along the curve

②

Domain of the variable — blue

c_{\min} = 0.001,\quad c_{\max} = 1

$c \in \left[0.001, 1\right]$

$c = 0.001$ $c = 0.001$

Along the curve

③

Response curve — green

[\alpha]=\alpha/(c\,\ell)

$c \in \left[0.001, 1\right]$

$c = 0.001$ $[\alpha] = 1200$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}[\alpha]}{\mathrm{d}c}

$c \in \left[0.001, 1\right]$

$c = 0.007$ $[\alpha]^{\prime} = -88456.2$

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-16 — Specific optical rotation) is the form associated with Biot. Working symbols: $\alpha$ , $c$ , $\ell$ $\rightarrow$ $[\alpha]$ . c in g/mL, l in dm. [α]_D^{20} is reported for the sodium D-line at 20 °C.

Purpose

Purpose: compute

[\alpha]

from

\alpha

c

\ell

in Organic chemistry via

[\alpha]=\alpha/(c\,\ell)

[α] = α / (c l). Polarimetry of a chiral sample. 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

\alpha = 1.200\,\mathrm{^{\circ}}

c = 0.100\,\mathrm{g/mL}

\ell = 1.000\,\mathrm{dm}

, the governing relation

[\alpha]=\alpha/(c\,\ell)

yields

[\alpha] = 12.00\,\mathrm{^{\circ} mL g^-1 dm^-1}

. Homogeneous solution, 1 dm path default. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Observed rotation \alpha1.2 °Concentration c0.1 g/mLPath \ell1 dm

Outputs

Specific rotation [\alpha]12.00 ° mL g^{-1} dm^{-1}

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Narration of this film

Homogeneous solution, 1 dm path default.

c in g/mL, l in dm. [α]_D^{20} is reported for the sodium D-line at 20 °C.

Reading speed

Watch on YouTube