NSFL 5 C/P #28 -- % mixture from specific rotation

[Hospitalized]

Few questions since this is a topic unfamiliar to me.

1.) What is specific rotation?

2.) How are they coming up with the equation they used? Is this some sort of algebra trick I'm failing at?

(low-key feel like this is low-yield material also)

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[theonlytycrane]

(Likely low-yield, I agree). Chiral molecules can rotate plane polarized light in some way, and enantiomers rotate light in the opposite direction.

In the question, R rotates +125.6 so S must rotate -125.6. Some weighted ratio of these enantiomers sums to +62.8 so they just setup a math problem with x being equal to the fraction of R enantiomers and 1 - x being equal to the fraction of S enantiomers.

x * 125.6 + (1 - x) * -125.6 = 62.8

Source: http://chemed.chem.purdue.edu/genchem/topicreview/bp/1organic/chirality.html

 

[Hospitalized]

(Likely low-yield, I agree). Chiral molecules can rotate plane polarized light in some way, and enantiomers rotate light in the opposite direction.

In the question, R rotates +125.6 so S must rotate -125.6. Some weighted ratio of these enantiomers sums to +62.8 so they just setup a math problem with x being equal to the fraction of R enantiomers and 1 - x being equal to the fraction of S enantiomers.

x * 125.6 + (1 - x) * -125.6 = 62.8

Source: http://chemed.chem.purdue.edu/genchem/topicreview/bp/1organic/chirality.html

They didn't even mention the opposite sign thing. That's the piece I needed. Thanks!

 

[BerkReviewTeach]

The concept of enantiomeric excess may or may not be low yield, but it's not a large leap of understanding to go from a 50/50 enantiomeric mixture (racemic mixture) having zero degrees of optical rotation to a mixture of 75/25 having half (75% - 25%) of the maximum value (associated with whichever enantiomer is in excess).

You can find questions in prep materials involving a 75% (+)-enantiomer with 25% (-)-enantiomer mixture as far back as 2005 (probably even earlier). Practice passages on limonene, carvone, and enantiomeric excess date back to 2004 (probably earlier), so this topic would appear to be one that test prep companies have been including in their materials for years.