Calculate the specific rotations of the following samples taken at 25 °C using the sodium D line.
(a) 1.00 g of sample is dissolved in 20.0 mL of ethanol. Then 5.00 mL of this solution is placed in a 20.0-cm polarimeter tube. The observed rotation is 1.25° counterclockwise.
(b) 0.050 g of sample is dissolved in 2.0 mL of ethanol, and this solution is placed in a 2.0-cm polarimeter tube. The observed rotation is clockwise 0.043°.
Here we have to calculate the specific rotations of the samples.
Mass of sample = 1.00gm
Volume of ethanol = 20.0mL
Volume of sample = 5mL
Width of polarimeter tube = 20.0cm= 2dm
Counter clockwise rotation = -1.25°
Specific rotation can be calculated as follows:-
[α]lT = α/lc
[α]lT = specific rotation in degrees. (The correct units are deg cm2 g-1, but are usually just given as degrees). l is the wavelength of light used for the observation (usually 589 nm, the D line of a sodium lamp unless otherwise specified. This wavelength is responsible for the orange-yellow color of the common sodium vapor street light). T is the temperature in oC.
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...