Polarimeter: How To Calculate Optical Purity And SOR (With 7+ FAQs)

Polarimeter

A polarimeter is an instrument used to measure the angle by which the plane of polarised light is rotated as it passes through an optically active substance, due to the substance’s ability to rotate the polarisation of light.

Principle of Polarimeter

• Polarised light is passed through an optically active sample.
• The plane of polarised light rotates as it travels through the sample.
• This rotation occurs because the substance can rotate the plane of vibration of polarised light.
• The angle of rotation (α) depends on:
  • Nature of the compound
  • Concentration or path length
  • Wavelength of light
  • Temperature

How To Calculate Specific Optical Rotation (SOR)?

SOR is calculated by using the following formula-1:

Formula-1

Note:

• For pure liquids, c = density (g/mL
• [α] = Specific optical rotation (°·dm⁻¹·g⁻¹·mL for solution or °·dm⁻¹ for pure substances)
• c = Concentration of the solution (g/mL or g/100 mL, depending on system)

What is Optical Activity?

• A substance is optically active if it can rotate the plane of polarised light.
• Dextrorotatory (denoted as (+)- or d-): Rotates light clockwise.
• Levorotatory (denoted as (–)- or l-): Rotates light counterclockwise.

Factors affecting optical activity:

• Molecular structure (presence of chiral centres)
• Wavelength and temperature
• Solvent used

How to Calculate Optical Purity using a Polarimeter?

Optical purity is a measure of the amount of one enantiomer in excess over the racemic mixture. It is calculated by the following formula-2 using the polarimeter:

Formula-2:

Case Study 1: How to calculate the optical purity of a pharmaceutical using a polarimeter?

A pharmaceutical company is developing a chiral drug where only one enantiomer is biologically active. The inactive (or harmful) enantiomer must be minimised.

Objective: Determine the optical purity of a synthesised sample using a polarimeter.

Procedure:

1. The observed rotation (α) of the sample is measured at 20°C using a 1 dm tube.
2. The sample concentration is 0.6 g/mL.
3. The known specific rotation of the pure enantiomer is +50°.

Calculation:

Observed rotation α = +30°

Specific rotation [α]=(30/1 x 0.6) = 50° (Using formula-1)

Enantiomer’s specific rotation is +50°
Let’s recalculate optical purity using the correct logic:

Optical purity = (30/50) x 100 = 60% (Usimg formula-2)

Conclusion:

The enantiomeric excess is 60%, indicating that the drug contains 80% of the desired enantiomer and 20% of the undesired one.

Case Study 2: How to calculate Sugar concentration in a food product?

A quality control team at a juice manufacturing company wants to verify the sugar content using polarimetry, as sugar is optically active.

Objective: Determine the concentration of sucrose in a juice sample.

Procedure:

1. A polarimeter tube of 2 dm is used.
2. Observed rotation: α = +13.2°
3. Specific rotation of sucrose: [α]_D^20​ = +66.5°

c = (α/[α] xl) = (13.2/66.5 x2) = 0.0992 g/mL

Multiply by 1000 to convert to g/L: 0.0992×1000=99.2 g/L

Note: The sugar concentration in the juice sample is approximately 99.2 g/L, matching the expected sweetness and caloric content.

Conclusion

In conclusion, the polarimeter is a vital tool in analysing optically active substances by measuring the angle of optical rotation. Understanding its working principle, methods for calculating specific optical rotation and optical purity, along with practical case studies, provides valuable insight into its applications in fields such as chemistry, pharmaceuticals, and food science. The FAQs further clarify common doubts, making this article a comprehensive guide to the use and significance of polarimetry.

Related

• Relative Response Factor (RRF) in Pharmaceutical Analysis

FAQs

Why is path length measured in decimeters?

The standard unit for polarimetry is dm (1 dm = 10 cm), which simplifies the SOR formula and ensures consistency.

What kind of light source is used in polarimetry?

Typically, a sodium lamp emitting monochromatic light at 589 nm (D-line) is used.

Is optical rotation a physical or chemical property?

It is a physical property because it does not involve a chemical change, but it is specific to molecular structure (chirality).

Does temperature affect optical rotation?

Yes. Optical rotation varies with temperature, so measurements often include temperature and wavelength

Further Reading

• Polarimeter Chiral Detectors in Enantioseparations