When an optically active compound is placed in a 10 dm tube, is present 20 g in a 200 mL solution rotates the plane polarized light by 3 0 ∘ . Calculate the angle of rotation and specific angle of rot

Question

When an optically active compound is placed in a 10 dm tube, is present 20 g in a 200 mL solution rotates the plane polarized light by 3 0 ∘ . Calculate the angle of rotation and specific angle of rotation if above solution is diluted to 1 L .

TestHub · Accepted Answer

Explanation Question: Asking about the specific rotation and observed rotation.

Concept: Based on polarimeter tube experiment.

Solution: Following formula is used to find $[α]$

Specific rotation $[α] = \frac{Observed rotation ( θ )}{Tube lengh ( ℓ ) \times concenration of solution ( C )}$

Units - $θ$ in degree

$\to ℓ$ in decimeter (dm)

$\to C$ in gram / ml.

Given $⟶ θ = 3 0^{\circ}$

$\to ℓ = 10 dm$

$\to C = 20 gm$ in 200 ml

$[α] = n$

$\frac{3}{10 \times \frac{20}{200}} = \frac{30 \times 200}{10 \times 20} = 30$

Specific rotation does no depend upon ℓ & C so on dilution (α) remains same.

* Observed rotation on dilution to 1L.

$θ = [α] l . C$

$θ = 30 \times 10 \times \frac{20}{1000} = 6$ °

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