Suppose that a 0.2 g/mL solution of (S)-ibuprofen in a 2 dm long cell rotates plane-polarized light +10°. What is the specific rotation for (S)-ibuprofen?

Question

Suppose that a 0.2 g/mL solution of (S)-ibuprofen in a 2 dm long cell rotates plane-polarized light +10°.  What is the specific rotation for (S)-ibuprofen?

Quizplus · Accepted Answer

11ecba2d_12a0_69a9_a3bf_41402d907487_MD0008_00 Chiral molecules are optically active because they rotate plane-polarized light. The angle of rotation is known as the specific rotation and contains both direction (+ or −) and magnitude (degrees). A rotation in the clockwise direction is classified as (+) whereas counterclockwise rotation is classified as (−). Specific rotation is unique to each chiral molecule and must be determined experimentally. The observed rotation is dependent on the sample concentration and sample cell length; the specific rotation is standardized to show what the rotation would be if the pathlength were 1 decimeter (dm) and the concentration were 1 g/mL. This is calculated via the following equation: 11ecba2d_12a0_69aa_a3bf_1dfdfed961fd_MD0008_00 where [α] is the specific rotation, α_obs is the observed rotation (degrees), c is the concentration (g/mL), and l is the sample cell length (dm). The units of specific rotation are (degrees · mL) / (g · dm) but are typically expressed as degrees for simplicity. The observed rotation for a 0.2 g/mL sample of (S)-ibuprofen in a 2 dm long cell is +10°. The specific rotation is calculated as follows: 11ecba2d_12a0_69ab_a3bf_133dbf0eff46_MD0008_00 11ecba2d_12a0_69ac_a3bf_0ff98d60ac7f_MD0008_00 (Choices A and D) A specific rotation of −50° or +50° is obtained if the sample cell length is not accounted for and the observed rotation is divided only by the concentration. The specific rotation should be negative only when the observed rotation is negative. (Choice B) A specific rotation of −25° is obtained by correctly using the specific rotation equation and dividing the observed rotation by the sample's concentration and sample cell length but then incorrectly changing the sign of the angle. Because the observed rotation is positive, the specific rotation should also be positive. Educational objective: Specific rotation is the angle by which chiral molecules rotate plane-polarized light and contains direction (+ or −) and magnitude (degrees). The observed rotation α_obs is dependent on the concentration (c in g/mL) and sample cell length (l in dm). Therefore, the specific rotation is standardized to account for these experimental parameters: 11ecba2d_12a0_90bd_a3bf_8d226e86e3e5_MD0008_00 __________

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