Discriminating optical rotations?

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Thoroughbred_Med

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From TBR Orgo Ch.2 phase 1 question 8:

How can a compound with an optical rotation of +233.0 be discerned from a compound with an optical rotation of -127.0?

A. The intensity of light is greater with the positive optical rotation
B. The sample with +233.0 optical rotation when diluted to half of its original concentration would show an optical rotation of +116.5
C. The larger the absolute value of the optical rotation, the greater the density of the compound
D. It is not possible to distinguish the two compounds from one another


I understand why A, C, and D are wrong leaving B the correct answer (good enough to get this question right)... but I don't quite understand how B answers the question stem.

I think my confusion has to due with my misunderstanding that optical rotations of +233.0 and -127.0 give the same reading.... From TBR's answer explanation, "When using a polarimeter, an observed optical rotation of +233.0 and -127.0 would result in the same reading (given that a full circle is 360). To discern one optical rotation from the other, the samples should be diluted to reduce the magnitude of the observed rotation."

Can y'all help me understand this?

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Yes, +233.0 and -127.0 would give you the same reading. That's why you need another way to distinguish these compounds and so you take advantage of the specific rotation formula. Observed rotation is directly related to concentration of a solution. Therefore, if you halve the concentration, you halve the observed rotation.
 
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So if I am not mistaken, you are wondering how +233 and -127 degrees give the same reading? Consider the plot from Mathematica below. The blue shading represents +233 degrees rotation and the white shaded area represents -127 degrees rotation (negative means the other way from the horizontal line). Thus they are the same angle and they will read the same absolute rotation on a detector.

233.png


I hope that helped!
 
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Sorry to bring this back but i was wondering

Why does the magnitude of rotation not depend on the density of the solution if it does depend on concentration?

If you increase the density of the solution wouldnt that also change the concentration and or vice versa?
 
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