Optical Activity

Calculate optical rotation from specific rotation, concentration, and path length with wavelength/temperature corrections.

Model: Textbook approximation

α = [α] c l (Biot; α > 0 dextrorotatory), [α]_T = [α]_{20 °C} [1 + k (T − 20 °C)]

output azimuth = θ_in − α, [M] = [α] M / 100 (deg·cm²·dmol⁻¹, M in g/mol)

sucrose: NIST SRM 17e / ICUMSA dispersion (used by NIST from 546 to 883 nm); custom: [α] ∝ 1/(λ² − λ₀²)

Vacuum wavelength λ (nm)Concentration c (g/100 mL)Path length l (dm)Molar mass M (g/mol)Temperature (°C)Temperature coefficient k (1/°C)Input azimuth θ_in (°)

Sucrose: [α] = 66.524 deg·mL·g⁻¹·dm⁻¹ at 20 °C and 589.44 nm (vacuum); NIST uses the dispersion equation from 546.2 to 882.6 nm. The default k is Schönrock's value for the normal sugar solution (26.016 g/100 mL), a linear fit for a few degrees around 20 °C. Concentration is mass per solution volume made up at 20 °C; [α] is taken as independent of concentration.

[α] at λ and 20 °C

66.524 deg·mL·g⁻¹·dm⁻¹

[α] at 20.0 °C

66.524 deg·mL·g⁻¹·dm⁻¹

Observed rotation α

34.614°

dextrorotatory (+): clockwise, seen looking toward the source

Output azimuth

-34.614°

θ_in − α = -34.614° (a line repeats every 180°)

Molar rotation [M]

227.71 deg·cm²·dmol⁻¹

Seen looking toward the source.

Solid: input θ_in. Dashed: output. Arrow: α (reduced to ±180°).

Specific rotation against wavelength at 20 °C

NIST SRM 17e ICUMSA curve over 546.2–882.6 nm; the marker is the current wavelength.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Biot α = [α]cl, [α] independent of c. Sucrose: NIST SRM 17e, ICUMSA dispersion 546–883 nm (vacuum λ); custom: one-term Drude. Linear T term, k = −4.61 × 10⁻⁴ /°C (26 g/100 mL), a few K around 20 °C.

NIST (2003). Certificate of Analysis, SRM 17e Sucrose (optical rotation): [α] at 589.44 nm and 20 °C (lot at 99.965 °Z), ICUMSA rotatory dispersion equation 546–883 nm. tsapps.nist.gov
Bates F. J., Blake J. C. (1907). The influence of basic lead acetate on the optical rotation of sucrose in water solution. Bull. Bur. Stand. 3(1), 105: Schönrock's temperature coefficient −0.000461 /°C. doi:10.6028/bulletin.057
Condon E. U. (1937). Theories of optical rotatory power. Rev. Mod. Phys. 9(4), 432–457: the Drude dispersion formula. doi:10.1103/RevModPhys.9.432

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Optical Activity

Calculate optical rotation from specific rotation, concentration, and path length with wavelength/temperature corrections.

α = [α] c l (Biot; α > 0 dextrorotatory), [α]_T = [α]_{20 °C} [1 + k (T − 20 °C)]

output azimuth = θ_in − α, [M] = [α] M / 100 (deg·cm²·dmol⁻¹, M in g/mol)

sucrose: NIST SRM 17e / ICUMSA dispersion (used by NIST from 546 to 883 nm); custom: [α] ∝ 1/(λ² − λ₀²)

Vacuum wavelength λ (nm)Concentration c (g/100 mL)Path length l (dm)Molar mass M (g/mol)Temperature (°C)Temperature coefficient k (1/°C)Input azimuth θ_in (°)

[α] at λ and 20 °C

66.524 deg·mL·g⁻¹·dm⁻¹

[α] at 20.0 °C

66.524 deg·mL·g⁻¹·dm⁻¹

Observed rotation α

34.614°

dextrorotatory (+): clockwise, seen looking toward the source

Output azimuth

-34.614°

θ_in − α = -34.614° (a line repeats every 180°)

Molar rotation [M]

227.71 deg·cm²·dmol⁻¹

Seen looking toward the source.

Solid: input θ_in. Dashed: output. Arrow: α (reduced to ±180°).

Specific rotation against wavelength at 20 °C

NIST SRM 17e ICUMSA curve over 546.2–882.6 nm; the marker is the current wavelength.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

NIST (2003). Certificate of Analysis, SRM 17e Sucrose (optical rotation): [α] at 589.44 nm and 20 °C (lot at 99.965 °Z), ICUMSA rotatory dispersion equation 546–883 nm. tsapps.nist.gov
Bates F. J., Blake J. C. (1907). The influence of basic lead acetate on the optical rotation of sucrose in water solution. Bull. Bur. Stand. 3(1), 105: Schönrock's temperature coefficient −0.000461 /°C. doi:10.6028/bulletin.057
Condon E. U. (1937). Theories of optical rotatory power. Rev. Mod. Phys. 9(4), 432–457: the Drude dispersion formula. doi:10.1103/RevModPhys.9.432

Report a problem