Optical purity calcs

[Bobby Fischer]

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Would someone give me a quick explanation regarding calculating the answer to this question clearly? The explanation isn't cutting it and I do not have my organic chem text handy to look it up. I remember doing this during the semester but forgot.

Q: An organometallic chromium catalyst is developed that is able to perform the following reaction stereo selectively. You isolate the product at 70% optical purity and you obtain 50mg of total product. How many milligrams of the desired (major) enantiomer do you have?

A: Optical purity is defined as the difference of percentages. Optical purity = % of one enantiomer - % of the other enantiomer. So 70 percent optical purity is a 85/15 ratio, not a 70/30 ratio. 85% of 50 is 42.5. (Note that as you do not have a calculator for this section of the DAT, you might find it easier to determine that 85% of 100 is 85 and 85% of fifty would be 85/2 or 42.5.)

 

[Troyvdg]

It tells you that you have 70% optical purity, which just means that you have 70% more of one enantiomer than the other. The other 30% is a racemic mixture between the two enantiomers (which is why it is not optically active). From this we know that we have .7(50mg) of the desired enantiomer, but we also have to remember to include the 15% that is in the racemic mixture (the racemic mixture is made up of 15% of the major enantiomer and 15% of the other giving a total of 30%).

.7 + .15 = .85
.85(52)= 42.5mg of desired enantiomer

 

[Bobby Fischer]

It tells you that you have 70% optical purity, which just means that you have 70% more of one enantiomer than the other. The other 30% is a racemic mixture between the two enantiomers (which is why it is not optically active). From this we know that we have .7(50mg) of the desired enantiomer, but we also have to remember to include the 15% that is in the racemic mixture (the racemic mixture is made up of 15% of the major enantiomer and 15% of the other giving a total of 30%).

.7 + .15 = .85
.85(52)= 42.5mg of desired enantiomer

That is a great explanation. Thank you👍