KR online PBQ O-Chem Ch. 2 question 9/10

[stitchontheambo]

Stuck on the answer for this one, and my Google Fu has failed me.

A student measures the optical rotation of L-carnitine as -30 degrees and wonders if the optical rotation might actually be -390 degrees. Is it possible for the student to distinguish between the two possibilities by either doubling or halving the concentration of the sample?

SPOILERS:

correct answer is that only halving the concentration will work, because while specific rotation should be constant, measured rotation can distinguish between the two. If the specific rotation is -30 degrees, then halving the concentration should result in a -15 degree measured rotation; likewise for -390 and -195. Doubling will not work because this would result in -60 and -780, which, accounting for phase, are identical.

Question: to be sure I'm understanding the question right, we need to figure out if a L-carnitine sol'n's optical rotation is -30 or -390. That said, what is phase and why is it unhelpful here? If I understand that, I think the rest will become clear.

---

Members don't see this ad.

 

[NextStepTutor_1]

Hi @stitchontheambo -

Imagine that you are facing due north and then rotate to your right by 90° to face east. Now rotate another 360° (a full circle). You will have rotated 450° (the initial 90° + the new 360°) -- however, you will once more be facing due east, just like you did after your first 90° rotation. Rotate another 360°. Now you will have rotated 810°, but you will still be facing east, just like you did after the first 90° rotation and the subsequent 360° rotation. Therefore, in terms of where you're facing, 90° of rotation is indistinguishable from 450° or 810°. This is what the question means by saying that -60° and -780° are identical when you account for phase -- -780° and -60° are separated by 720° of rotation, which is equal to two 360° circles. In other words, they're the same in terms of where you are pointing.

Phase is usually visualized on a graph with degrees on the X-axis. Consider a standard sine curve -- it will have a value of 1 at 90°, then again at 450°, then again at 810°, and so on at 360° intervals. The explanation for this question is framing rotation in those terms by talking about phase, but it basically boils down to the idea that just like noting that sin(θ) = 1 doesn't tell you what θ is (possible values include 90°, 450°, 810°, etc.), observing a rotation in the direction of 30° is consistent with actually having rotated for 30°, 390°, 750°, etc.

Hope this helps clarify this explanation! This is one of those topics where it can be very helpful to just make a simple model of a clock face and work through it in a hands-on way to really see it. Best of luck!!

 

[stitchontheambo]

Hi @stitchontheambo -

Imagine that you are facing due north and then rotate to your right by 90° to face east. Now rotate another 360° (a full circle). You will have rotated 450° (the initial 90° + the new 360°) -- however, you will once more be facing due east, just like you did after your first 90° rotation. Rotate another 360°. Now you will have rotated 810°, but you will still be facing east, just like you did after the first 90° rotation and the subsequent 360° rotation. Therefore, in terms of where you're facing, 90° of rotation is indistinguishable from 450° or 810°. This is what the question means by saying that -60° and -780° are identical when you account for phase -- -780° and -60° are separated by 720° of rotation, which is equal to two 360° circles. In other words, they're the same in terms of where you are pointing.

Phase is usually visualized on a graph with degrees on the X-axis. Consider a standard sine curve -- it will have a value of 1 at 90°, then again at 450°, then again at 810°, and so on at 360° intervals. The explanation for this question is framing rotation in those terms by talking about phase, but it basically boils down to the idea that just like noting that sin(θ) = 1 doesn't tell you what θ is (possible values include 90°, 450°, 810°, etc.), observing a rotation in the direction of 30° is consistent with actually having rotated for 30°, 390°, 750°, etc.

Hope this helps clarify this explanation! This is one of those topics where it can be very helpful to just make a simple model of a clock face and work through it in a hands-on way to really see it. Best of luck!!

Thanks!