Question

A 0.06 g/mL solution of (S)-1-phenylethanol placed in a 5 cm long polarimeter tube shows an optical rotation of 1.2^o . The specific rotation is ______ ^o .
(round off to the nearest integer)

Answer 1

Correct Answer: 39 - 41

Specific Rotation Calculation 

To determine the specific rotation, we use the formula:

[α] = \( \frac{\alpha_{\text{obs}}}{l \cdot c} \), where [α] is the specific rotation, \( \alpha_{\text{obs}} \) is the observed rotation, \( l \) is the length of the polarimeter tube in decimeters, and \( c \) is the concentration in g/mL.

Given Values:

• \( \alpha_{\text{obs}} = 1.2^\circ \)
• \( l = 5 \, \text{cm} = 0.5 \, \text{dm} \)
• \( c = 0.06 \, \text{g/mL} \)

Substituting Values into the Formula:

The formula becomes:

\[ [\alpha] = \frac{1.2}{0.5 \times 0.06} \]

Calculation:

Calculating the specific rotation:

\[ [\alpha] = \frac{1.2}{0.03} = 40^\circ \]

Verification:

The calculated specific rotation of \( 40^\circ \) is within the expected range of 39 to 41.

Final Answer:

The specific rotation is \( 40^\circ \).