An attempt at synthesizing a certain optically active compound resulted in a mixture of all enantiomers.


Screenshot 2024 01 20 091032

Screenshot 2024 01 20 091032

Step 1 of 2

Given data: The mixture had an observed specific rotation of +13.6 degree, the R enantiomer is -35.8 degree.

Find: Determine the percentage of each isomer in the mixture.

Explanation:

To determine the percentage of each isomer in the mixture, we can use the observed specific rotation and the specific rotation of the R enantiomer.

Step 2 of 2

The formula for the calculation of the Optical rotation is:

Specific rotation of mixture={(% of R enantiomer / 100)* (specific rotation of R enantiomer)}+ {(% of S enantiomer / 100)* (specific rotation of S enantiomer)}

For R enantiomer:

Let % = x %

Specific rotation = –38.3°

For S enantiomer:

% = 100 – x

(2 enantiomers in mixture)

Specific rotation = 38.3° (Opposite direction of R enantiomer)

Given, Observed specific rotation of mixture = 12.0°

Thus,

12∘=X/100×(−38.3∘)+(100−x)/100×(−38.3∘)

Solving for x, we get that:

x = 34.33 %

Explanation:

Therefore, % of S enantiomer is 100% – 34.33% = 65.97%

Final solution

Percentage of R enantiomer = 34.33 %

Percentage of S enantiomer = 65.67 %

 

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