Question

A 20g of cane sugar is dissolved in water to make 50 cc of solution. A 20 cm length of tube filled with this solution causes +53\(^{\circ}\)30' optical rotation. What will be the specific rotation?

• A. 66.9 degree (decimeter)\(^{-1}\) (g/cc)\(^{-1}\)
• B. 7.09 degree (decimeter)\(^{-1}\) (g/cc)\(^{-1}\)
• C. 76.9 degree (decimeter)\(^{-1}\) (g/cc)\(^{-1}\)
• D. 6.69 degree (decimeter)\(^{-1}\) (g/cc)\(^{-1}\)

Hint:

Pay close attention to units when calculating specific rotation. The path length must be in decimeters and the concentration in g/cc or g/mL. A common mistake is forgetting to convert from centimeters to decimeters.

Answer 1

The Correct Option is A

Step 1: Recall the formula for specific rotation. Specific rotation \([\alpha]\) is defined as: \[ [\alpha] = \frac{\theta}{l \times c} \] where \(\theta\) is the observed optical rotation in degrees, \(l\) is the path length in decimeters (dm), and \(c\) is the concentration of the solution in g/cc (or g/mL).
Step 2: Convert the given units to the required units. - Observed rotation: \(\theta = 53^{\circ}30' = 53.5^{\circ}\). - Path length: \(l = 20 \, \text{cm} = 2 \, \text{dm}\) (since 1 dm = 10 cm). - Concentration: Mass = 20 g, Volume = 50 cc. \[ c = \frac{\text{mass}}{\text{volume}} = \frac{20 \, \text{g}}{50 \, \text{cc}} = 0.4 \, \text{g/cc} \]
Step 3: Calculate the specific rotation. \[ [\alpha] = \frac{53.5}{2 \times 0.4} = \frac{53.5}{0.8} = 66.875 \]
Step 4: Match the result with the options. The calculated value is approximately 66.9 degree (decimeter)\(^{-1}\) (g/cc)\(^{-1}\).