specific rotation

Meaning: Specific rotation is the angle a chiral compound rotates plane-polarized light, normalized to a path length of 1 dm and a concentration of 1 g/mL. Because of this normalization it is a physical constant, reported with temperature and wavelength (usually the sodium D line, 589 nm), as in [α]D²⁵. Clockwise rotation is dextrorotatory (+); counterclockwise is levorotatory (−). Enantiomers have equal magnitude and opposite sign. A racemic mixture shows no net rotation.

Equation: [α] = α / (l × c), where α is the observed rotation (degrees), l is the path length (dm, where 1 dm = 0.1 m), and c is the concentration (g/mL). Units are conventionally degrees·mL·g⁻¹·dm⁻¹, often left unwritten.

On the MCAT: A passage gives α, tube length and concentration, and you calculate [α]. Or you compare a mixture with a pure enantiomer: optical purity = (observed [α] ÷ [α] of pure enantiomer) × 100%, which equals enantiomeric excess. A sample that is 75% R and 25% S has 50% ee, so it rotates half as much as pure R. Questions also ask what happens to α if concentration or tube length changes.

Common confusion: Observed rotation α depends on concentration and path length. Specific rotation [α] does not. Also, the sign (+ or −) cannot be predicted from R or S; it is measured experimentally, so an R compound may be either (+) or (−).