Question

An aqueous solution containing 6.31 g of an optically pure compound was diluted to 600.0 mL with water and placed in a polarimeter tube 20.0 cm long. The measured rotation was –2.91° at 25 °C. Calculate the specific rotation of the compound.

Answer 1

[α]_l^T = α/lc

[α]_l^T = specific rotation in degrees. l is the wavelength of light used for the observation

α = observed rotation in degrees.

l = cell path length in decimeters. (1 decimeter = 1 dm = 10 cm. A standard polarimeter tube is 1.00 dm in length.)

c = concentration in g ml^-1 for a pure liquid compound (i.e., the liquid's density), or g 100 ml^-1 for a solution.

Solving the specific rotation equation for observed rotation, we get [α]_l^T = α/lc. The sample size is 6.31 g, but this has been diluted to 600.0 mL, so the sample concentration is 6.31 g in 600 ml. Plugging in the numbers, we get   [α]_l^T = -2.91 ⁰C / (2.00 dm) (6.31 g / 600 ml). Solving, we find [α]_l^T = -138.35 ^oC.