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The observed rotation of 2.0 gm of a com...

The observed rotation of 2.0 gm of a compound in 10 mL solution in
a 25 cm long polarimeter tube is `+ 13.4^(@)` . The specific
rotation of compound is :

A

`+30.2^(@)`

B

`-26.8^(@)`

C

`+26.8^(@)`

D

`+40.2^(@)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the specific rotation of the compound, we can follow these steps: ### Step 1: Identify the given values - Observed rotation (α) = +13.4° - Mass of the compound (g) = 2.0 g - Volume of the solution (mL) = 10 mL - Length of the polarimeter tube (L) = 25 cm ### Step 2: Convert the length of the polarimeter tube from cm to dm Since the specific rotation formula requires the path length in decimeters (dm), we convert: - L = 25 cm = 25/10 = 2.5 dm ### Step 3: Calculate the concentration (C) of the solution Concentration is calculated using the formula: \[ C = \frac{\text{mass (g)}}{\text{volume (mL)}} \] Substituting the values: \[ C = \frac{2.0 \text{ g}}{10 \text{ mL}} = 0.2 \text{ g/mL} \] ### Step 4: Use the specific rotation formula The specific rotation ([α]) is given by the formula: \[ [α] = \frac{α}{C \times L} \] Substituting the known values: \[ [α] = \frac{+13.4°}{0.2 \text{ g/mL} \times 2.5 \text{ dm}} \] ### Step 5: Calculate the specific rotation Calculating the denominator: \[ C \times L = 0.2 \times 2.5 = 0.5 \] Now substituting back into the formula: \[ [α] = \frac{+13.4°}{0.5} = +26.8° \] ### Conclusion The specific rotation of the compound is +26.8°. ---
To find the specific rotation of the compound, we can follow these steps: ### Step 1: Identify the given values - Observed rotation (α) = +13.4° - Mass of the compound (g) = 2.0 g - Volume of the solution (mL) = 10 mL - Length of the polarimeter tube (L) = 25 cm ...
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