Question

A student measured the optical activity of an unknown sugar at two different concentrations. The results of his measurements are shown below. Given that the sample cell had a path length of 10.0 cm, calculate the specific rotation for the unknown sugar. (Hint: Consider each measurement of plane polarized light has a true reading and a "ghost" reading 180° from the true reading).

concentration observed rotation 2.00 g sugar in 10.0 mL water +159.1∘

5.00 g sugar in 10.0 mL water +127.8∘

Answer=-105∘ . WHY? Please write out steps

Answer 1

Specific rotation ([α]) is a property of a chiral compound. It is defined as the change in orientation of monochromatic planepolarized light, per unit distance–concentration product, as the light passes through a sample of a compound in solution

    Compounds which rotate light clockwise are said to be dextrorotary, and correspond with positive specific rotation values, while compounds which rotate light counter clockwise are said to be levorotary, and correspond with negative values. Specific rotation is given by the following equation

when c is the concentration of the solution in gm/ml , α is observed rotation, d is the cell length in decimeter.

here l= 1 dm

For the first case , specific rotation= (-180 +159.1)^o x 10/1 x 2 = (-20.9 ^ox 10)/1 x 2  = -104.5^o

For the second case , specific rotation= (-180 +127.8)^o x 10/1 x 5 = (-52.2 ^ox 10)/1 x 5 = -104.4^o

^{Therefore if we take the average of the above two results, specific rotation of the unknown sugar soution will be -104.45 or 105 degree}