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:(+)-Mandelic acid has a specific rotation of +158. What would be the observed specific rotation of each of the following mixtures?

a. 50% (-)-mandelic acid and 50% (+)-mandelic acid

b. 25% (-)-mandelic acid and 75% (+)-mandelic acid

c. 75% (-)-mandelic acid and 25% (+)-mandelic acid

Short Answer

Expert verified
  1. 0
  2. +79
  3. -79

Step by step solution

01

Definition of specific rotation-

The observed rotation can be used to calculate the specific rotation at a given temperature and wavelength using the formula-

[饾灙] = 饾灙/ l c

where [饾灙] is the specific rotation,

T is the temperature in degrees Celsius,

l is the wavelength of the incident light (when the sodium D-line is used, l is indicated as D),

蓱 is the observed rotation,

l is the length of the sample tube in decimetres, and

c is the sample concentration in grams per 100 milliliters.

02

Given quantities-

specific rotation of (+)-Mandelic acid = +158

03

Calculation of specific rotation of 50% (-)-mandelic acid and 50% (+)-mandelic acid.

Concentration of (-) Mandelic acid = 50

Concentration of (+) Mandelic acid = 50

Since, it is a racemic mixture, therefore specific rotation of racemic mixture of MSG is 0.

A racemic mixture is an equal mix of two enantiomers with a specific rotation of 0 degrees (Optically Inactive).

04

Calculation of specific rotation of 25% (-)-mandelic acid and 75% (+)-mandelic acid.

Concentration of (-) Mandelic acid = 25

Concentration of (+) Mandelic acid = 75

Therefore, excess of (+) mandelic acid = 75-25= 50%

Enantiomeric excess =脳 100%

50 = (x/158) 脳 100

X = +79

05

Calculation of specific rotation of 75% (-)-mandelic acid and 25% (+)-mandelic acid.

Concentration of (-) Mandelic acid = 75

Concentration of (+) Mandelic acid = 25

Therefore, excess of (-) mandelic acid = 75-25= 50%

Enantiomeric excess = (Observed specific rotation) / (Specific rotation of (+) enantiomer) 脳 100%

50 = (x/158) 脳 100

X = -79

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