The specific rotation of a pure substance is –5.90°. What is the % of this isomer in a mixture with an observed specific rotation is –2.95°?Correct answer is '75'. Can you explain this answer?

Question

The specific rotation of a pure substance is &ndash;5.90&deg;. What is the % of this isomer in a mixture with an observed specific rotation is &ndash;2.95&deg;?Correct answer is '75'. Can you explain this answer?

Answer

A measure of its ability to rotate the plane of polarized light. It is defined as the angle in degrees through which the plane of polarized light is rotated when passing through a solution of a known concentration of the substance in a cell with a specified length. The specific rotation is a physical property of a substance and is dependent on the wavelength of the light used, the temperature of the solution, and the concentration of the solution. It is expressed as the observed rotation divided by the product of the concentration and the length of the cell. The specific rotation is widely used in the analysis and identification of organic compounds, especially those containing chiral centers.

Answer

Let x% pure and (100-x)% isomer present ...             so,{ X * (-5.90) × (100-x) * 5.90 } ÷ 100 =- 2.95 ... or, X =75

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