Specific Rotation Calculation:

To calculate the specific rotation of an optically active compound, we need to use the formula:

Specific Rotation (α) = (θ × 100) / (c × l)

Where:
α = Specific Rotation
θ = Observed optical rotation in degrees
c = Concentration of the compound in g/mL
l = Path length of the sample tube in dm

Given Data:
θ = 5.8 degrees
c = 4 g / 100 mL = 0.04 g/mL
l = 20 cm = 0.2 dm

Applying the formula:
Specific Rotation (α) = (5.8 × 100) / (0.04 × 0.2)
Specific Rotation (α) = 1450 / 0.008
Specific Rotation (α) = 181250

Therefore, the specific rotation of the compound is 181250 degrees per g·cm^3·dm.

Explanation:

- The specific rotation of an optically active compound is a measure of its ability to rotate the plane of polarized light.
- The formula for specific rotation relates the observed optical rotation (θ) to the concentration (c) and path length (l) of the sample.
- The concentration of the compound is given as 4 g in 100 mL, which can be converted to 0.04 g/mL.
- The path length of the sample tube is given as 20 cm, which can be converted to 0.2 dm.
- Substituting the given values in the formula, we can calculate the specific rotation.
- The specific rotation is a unitless quantity, but it is often expressed in degrees per g·cm^3·dm.
- In this case, the specific rotation of the compound is calculated to be 181250 degrees per g·cm^3·dm.