The specific rotation of sucrose in water is +66.5°.
Understanding Specific Rotation
Specific rotation, denoted as $[\alpha]_D^T$, is a fundamental physical property used to characterize optically active substances like sucrose. It quantifies the degree to which a compound rotates plane-polarized light at a specific temperature ($T$) and wavelength (indicated by $D$ for the sodium D-line). This value is crucial for identifying pure compounds, determining enantiomeric excess, and understanding molecular structure.
The specific rotation is calculated using the following formula:
$[\alpha]D^T = \frac{\alpha{obs}}{c \times l}$
Where:
- $[\alpha]_D^T$ is the specific rotation (in degrees).
- $\alpha_{obs}$ is the observed rotation (in degrees).
- $c$ is the concentration of the solution (in g/mL).
- $l$ is the path length of the polarimeter tube (in dm, where 1 dm = 10 cm).
For a deeper dive into the principles of optical activity and specific rotation, you can refer to resources on polarimetry.
Specific Rotation of Sucrose
Sucrose, a common disaccharide, exhibits optical activity. When dissolved in water, it rotates plane-polarized light to the right (clockwise). This property makes it a dextrorotatory compound, hence its specific rotation value is positive.
The specific rotation of sucrose in water is +66.5°. This value is typically measured at a standard temperature (e.g., 20°C or 25°C) and using the sodium D-line as the light source.
Factors Influencing Specific Rotation
While specific rotation is a characteristic constant for a given compound, its observed value can be influenced by several factors:
- Temperature: Changes in temperature can affect molecular vibrations and solvent interactions, leading to slight variations in rotation.
- Wavelength of Light: The degree of rotation is dependent on the wavelength of light used, hence the specification of the D-line (589 nm).
- Solvent: The solvent used can impact the specific rotation due to solvent-solute interactions. For sucrose, water is the standard solvent for this measurement.
Practical Application: Calculating Observed Rotation
Understanding specific rotation allows for the calculation of observed rotation under different experimental conditions. Let's consider a practical example:
Imagine you have a solution of sucrose and want to predict the observed rotation when placed in a polarimeter.
Example Scenario:
- Substance: Sucrose
- Concentration: 2 grams of sucrose dissolved in 100 mL of water.
- Path Length: A polarimeter tube with a length of 5 cm.
Calculation Steps:
-
Determine the concentration ($c$):
- $c = \text{mass of solute} / \text{volume of solution}$
- $c = 2 \text{ g} / 100 \text{ mL} = 0.02 \text{ g/mL}$
-
Convert the path length ($l$) to decimeters:
- $l = 5 \text{ cm} / 10 \text{ cm/dm} = 0.5 \text{ dm}$
-
Use the specific rotation formula to find observed rotation ($\alpha_{obs}$):
- $\alpha_{obs} = [\alpha]_D^T \times c \times l$
- Given $[\alpha]_D^T = +66.5^\circ$ (for sucrose in water)
- $\alpha_{obs} = +66.5^\circ \times 0.02 \text{ g/mL} \times 0.5 \text{ dm}$
- $\alpha_{obs} = +66.5^\circ \times 0.01$
- $\alpha_{obs} = +0.665^\circ$
Therefore, under these specific conditions, the observed rotation for the sucrose solution would be +0.665°.
Key Properties of Sucrose
To summarize, here are some key optical and chemical properties of sucrose:
| Property | Value |
|---|---|
| Specific Rotation | +66.5° (in water, typically at 20°C or 25°C, sodium D-line) |
| Chemical Formula | C₁₂H₂₂O₁₁ |
| Classification | Disaccharide (composed of glucose and fructose) |
| Optical Activity | Dextrorotatory (rotates plane-polarized light to the right) |
| Polarimetric Behavior | Undergoes hydrolysis into D-glucose and D-fructose, causing a change in specific rotation from positive to negative, hence the term "inversion of sucrose." |
Sucrose's consistent specific rotation value is vital for quality control in the food industry, particularly for sugar production and analysis, ensuring product purity and concentration.
