Tartaric Acid Has a Specific Rotation of +12.0° — Optical Activity Explained

(+)-Tartaric acid (natural form): [α]D²⁰ = +12.0°

This means: • [α] = specific rotation • D = measured using sodium D-line light (589 nm wavelength) • 20 = temperature of measurement (20°C) • +12.0° = light is rotated 12.0° to the RIGHT (clockwise = dextrorotatory)

All four forms of tartaric acid: • (+)-Tartaric acid (L-form, natural): [α]D = +12.0° → dextrorotatory • (−)-Tartaric acid (D-form, unnatural): [α]D = −12.0° → levorotatory • meso-Tartaric acid: [α]D = 0° → optically inactive (internal compensation) • (±)-Tartaric acid (racemic mixture): [α]D = 0° → optically inactive (external compensation)

Key point: (+)-tartaric acid and (−)-tartaric acid are enantiomers — they are non-superimposable mirror images of each other. They have equal but opposite specific rotations.

The specific rotation is calculated using the formula:

[α] = α / (l × c)

Where: • [α] = specific rotation (in degrees) • α = observed rotation (in degrees, measured by polarimeter) • l = path length of the sample cell (in decimetres, dm; 1 dm = 10 cm) • c = concentration of solution (in g/mL)

For neat (pure) liquids: [α] = α / (l × d) Where d = density of the liquid (in g/mL)

Standard conditions for reporting: • Light source: Sodium D-line (λ = 589 nm) • Temperature: 20°C (or 25°C) • Written as: [α]D²⁰ or [α]²⁰_D

Example calculation: If a solution of tartaric acid (c = 0.5 g/mL) in a 1 dm cell gives an observed rotation of +6.0°: [α] = +6.0 / (1 × 0.5) = +12.0° This confirms the specific rotation of (+)-tartaric acid.

Units: Specific rotation is reported in ° (degrees) but formally has units of °·mL/(g·dm). By convention, the units are usually omitted.

Tartaric acid (C₄H₆O₆) has two chiral centres (C-2 and C-3), giving it the following stereoisomers:

1. (+)-Tartaric acid (L-tartaric acid) • Configuration: (2R,3R) • [α]D = +12.0° (dextrorotatory) • Naturally occurring — found in grapes and wine • Optically active

2. (−)-Tartaric acid (D-tartaric acid) • Configuration: (2S,3S) • [α]D = −12.0° (levorotatory) • Rare in nature — synthesised in lab • Optically active • Mirror image (enantiomer) of (+)-form

3. meso-Tartaric acid • Configuration: (2R,3S) or (2S,3R) • [α]D = 0° (optically inactive) • Has an internal plane of symmetry • Optically inactive despite having chiral centres — internal compensation • NOT an enantiomer — it is a diastereomer of both (+) and (−) forms

4. (±)-Tartaric acid (Racemic tartaric acid) • Equal mixture of (+) and (−) forms (1:1 ratio) • [α]D = 0° (optically inactive) • External compensation — rotations cancel each other out • This is a mixture, not a single compound • Also called racemic acid or DL-tartaric acid

Total unique compounds: 3 (the racemic mixture is not a separate compound)

meso-Tartaric acid is optically inactive even though it has two chiral centres. This is because of internal compensation.

Explanation: • meso-Tartaric acid has the configuration (2R,3S) • The R-centre at C-2 rotates light by +12.0° (to the right) • The S-centre at C-3 rotates light by −12.0° (to the left) • These rotations cancel each other within the same molecule • Net rotation = +12.0° + (−12.0°) = 0°

Internal plane of symmetry: • meso-Tartaric acid has an internal mirror plane that divides the molecule into two halves • The top half is the mirror image of the bottom half • This makes the molecule achiral (non-chiral) despite having stereocentres • A molecule with an internal plane of symmetry is always optically inactive

Key distinction: • meso-compound: optically inactive due to INTERNAL compensation (within one molecule) • Racemic mixture: optically inactive due to EXTERNAL compensation (between two different molecules)

How to identify meso compounds:

1. The molecule has chiral centres
2. There is an internal plane of symmetry
3. One half mirrors the other
4. The stereocentres have opposite configurations (R and S)

In 1848, Louis Pasteur performed a historic experiment that laid the foundation of stereochemistry.

Background: • Tartaric acid from wine was known to be optically active ([α] = +12.0°) • Racemic acid (from industrial synthesis) had the same chemical formula but was optically inactive • Scientists could not explain why two identical substances had different optical properties

Pasteur's Discovery:

1. He crystallised sodium ammonium tartrate from racemic acid
2. Under a microscope, he noticed two types of crystals — mirror images of each other
3. He manually separated the left-handed and right-handed crystals using tweezers
4. He dissolved each type separately and measured their optical rotation
5. One solution rotated light +12.0° (dextrorotatory)
6. The other rotated light −12.0° (levorotatory)
7. An equal mixture of both showed 0° rotation (racemic)

Significance: • First demonstration that molecules can exist as non-superimposable mirror images (enantiomers) • Proved that optical activity is related to molecular asymmetry • Founded the field of stereochemistry • Pasteur was only 25 years old at the time • Led to the understanding of chirality in chemistry and biology

Optical activity is the ability of a substance to rotate the plane of plane-polarised light.

Key terms: • Plane-polarised light: Light waves vibrating in a single plane • Polarimeter: Instrument used to measure optical rotation • Dextrorotatory (+) or (d): Rotates light to the RIGHT (clockwise) • Levorotatory (−) or (l): Rotates light to the LEFT (anticlockwise) • Optically active: Rotates plane-polarised light • Optically inactive: Does not rotate light

What makes a molecule optically active? • Must be chiral — non-superimposable on its mirror image • Must have no internal plane of symmetry • Usually contains one or more chiral centres (sp³ carbon with 4 different groups)

Important rules:

1. Enantiomers have EQUAL but OPPOSITE specific rotations (+)-tartaric acid = +12.0°, (−)-tartaric acid = −12.0°
2. R/S configuration does NOT predict + or − rotation (R) does not always mean (+), and (S) does not always mean (−) The direction of rotation must be determined experimentally
3. Diastereomers have DIFFERENT (not necessarily opposite) specific rotations
4. A racemic mixture (1:1 enantiomers) always has [α] = 0°
5. Enantiomeric excess (ee) measures optical purity: ee = ([α]_observed / [α]_pure) × 100%

Problem 1: Calculate the observed rotation. A solution of (+)-tartaric acid (c = 0.25 g/mL) is placed in a 2 dm polarimeter tube. [α]D = +12.0°. Find the observed rotation. Solution: α = [α] × l × c = 12.0 × 2 × 0.25 = +6.0°

Problem 2: Find the concentration. A tartaric acid solution in a 1 dm tube shows α = +3.0°. If [α]D = +12.0°, find the concentration. Solution: c = α / ([α] × l) = 3.0 / (12.0 × 1) = 0.25 g/mL

Problem 3: Enantiomeric excess. A mixture of (+) and (−)-tartaric acid shows [α] = +9.0°. Pure (+)-tartaric acid has [α] = +12.0°. Find the ee and composition. Solution: ee = (9.0 / 12.0) × 100 = 75% This means 75% excess of (+)-form. Composition: 87.5% (+)-form and 12.5% (−)-form [Because: if excess = 75%, then (+) = (50 + 75/2)% = 87.5%, (−) = 12.5%]

Problem 4: Racemic mixture. Equal amounts of (+)-tartaric acid ([α] = +12.0°) and (−)-tartaric acid ([α] = −12.0°) are mixed. What is the observed rotation? Solution: [α]_mixture = (+12.0 + (−12.0)) / 2 × 2 = 0°. Racemic mixture is optically inactive.

Problem 5: Identify the form. A tartaric acid sample shows [α]D = 0°. What could it be? Solution: Either meso-tartaric acid (single compound, internal compensation) OR racemic (±)-tartaric acid (1:1 mixture, external compensation). Melting point test can distinguish: meso mp = 140°C, racemic mp = 206°C.