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- [Narrator] Let's do some calculations
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using optical activity.
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So for our first problem,
let's say we have
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.300 grams of natural cholesterol.
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So here's the dot structure
for natural cholesterol,
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it's an optically active compound,
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and we dissolve our cholesterol
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in 15.0 milliliters of chloroform.
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And we put that solution
in a 10.0 centimeter
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polarimeter tube, the observed
rotation at 20 degrees C,
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using the D line of sodium,
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it turns out to be negative .630 degrees.
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And our goal is to calculate the specific
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rotation of cholesterol.
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We saw how to do this in the last video.
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The specific rotation is equal
to the observed rotation,
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divided by the concentration
times the path length.
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So let's plug in some numbers, here.
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The specific rotation is equal
to the observed rotation,
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which is negative .630
degrees, so we put that in.
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Negative .630 degrees.
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We divide by the concentration,
which is in grams per mL.
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So that's .300 grams, divided by 15.0 mLs.
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So .300 grams
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divided by 15.0 mLs.
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We multiply that by the path length,
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and the path length needs
to be in decimeters.
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So we have a 10.0 centimeter tube,
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10.0 centimeters is 1 decimeter,
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so that makes our math easy, here.
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So this would be 1.00 decimeter.
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All right, let's do the math.
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So let's get out the calculator,
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and let's solve for the specific rotation.
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That would be negative .630
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divided by,
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we have .300 divided by 15.0.
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And then we multiply that by one.
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I don't really need to do that,
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but I'll go ahead and do it anyway.
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So that's multiplied by 1.00, here.
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And we get negative 31.5.
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So that is our specific rotation.
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So let's write that down, here.
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So we have our specific
rotation at 20 degrees C,
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so we put a 20 here, using
the D line of sodium,
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so we put a D here,
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and this is equal to negative 31.5.
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Now, sometimes you see
this with a degrees sign,
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so sometimes you'll see
it written like that,
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but I'm going to take that
out, because normally,
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we don't have any units
for our specific rotation.
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So it just depends on what
book you're looking in.
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For our next problem, problem two,
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let's talk about percent
enantiomeric excess,
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or optical purity.
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This is where you take the
percentage of one enantiomer,
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and from that you subtract the percentage
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of the other enantiomer.
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So for part A, let's calculate the percent
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enantiomeric excess for
a solution that contains
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a single enantiomer.
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So if we have only one enantiomer,
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this is like the first
problem that we did,
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with natural cholesterol.
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That means you have
100% of this enantiomer,
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and obviously 0% of the other one.
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So the percent enantiomeric excess
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would just be 100 minus zero,
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or 100%.
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So we have 100% optical purity,
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so this is an optically pure solution.
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For part B, let's do this
for a solution that contains
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equal amounts of both enantiomers.
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So when that happens, it's
called a racemic mixture.
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So if we have equal amounts of both,
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that must mean we have
50% of one enantiomer,
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and 50% of the other.
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So the percent enantiomeric excess
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would be equal to 50 minus 50,
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which of course is equal to zero.
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So this has an optical purity of 0%,
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and a racemic mixture
is not optically active.
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You get a net rotation of zero
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if you have equal amounts
of both enantiomers.
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For part C, we have a
solution that contains
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75% of one enantiomer,
and 25% of the other.
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So the percent enantiomeric
excess is equal to,
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this would be 75% minus 25%,
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which of course is equal to 50%.
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So we have 50% excess of this enantiomer,
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and we have a 50% optically pure solution.
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For our last problem, we have a mixture
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of natural cholesterol and its enantiomer.
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And our mixture has a specific
rotation of negative 27.
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Our goal is to calculate the
percent enantiomeric excess
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of this mixture, and we can do that
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using this equation up here.
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So the percentage enantiomeric excess
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is equal to the observed
specific rotation,
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divided by the specific
rotation of the pure enantiomer.
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And to get a percentage,
we multiply it by 100.
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So the percent enantiomeric
excess is equal to
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the observed specific rotation,
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which is negative 27, so
we write that in here.
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So negative 27.
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We divide that by the specific rotation
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of the pure enantiomer.
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And for natural cholesterol,
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we saw what the specific rotation
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of the pure enantiomer
was in the first problem.
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We got negative 31.5.
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So I'll write in here, negative 31.5.
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And we multiply it by 100.
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So that gives us our
percent enantiomeric excess.
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So let's get out the calculator, here.
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We don't need to worry
about negative signs,
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so we can just take 27
and divide that by 31.5,
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and multiply it by 100, and we get 85.7.
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And let's round that to 86%.
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So our percent enantiomeric excess is 86%.
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So we're done with our calculation, here.
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Our next question is, what
percentage of the mixture
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is natural cholesterol?
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Well, 86%, this was our
enantiomeric excess.
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So if we think about this as being
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86% of natural cholesterol,
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so let me write this down, here.
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86% of natural cholesterol.
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And the remaining 14%
must be a racemic mixture.
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So if the remaining 14%
is a racemic mixture,
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that means half of it
is natural cholesterol,
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and half of it is the enantiomer.
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So that means that 7% is
our natural cholesterol,
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and 7% is the enantiomer.
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So seven plus seven is,
of course, equal to 14.
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So what's the total percentage
of natural cholesterol
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in our mixture?
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That would be 86 plus seven,
which of course is 93%.
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So that's our answer.
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So 93% of our mixture
is natural cholesterol.
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This can get a little
bit confusing sometimes,
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so you can check this answer
to make sure it's correct.
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You know that the total
of natural cholesterol
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and its enantiomer should be 100%,
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so if natural cholesterol is 93%,
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and its enantiomer is 7%,
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obviously 93% plus 7% is 100%.
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Also, we know from the previous problem
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that the percentage enantiomeric excess
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is equal to the percent of one enantiomer
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minus the percent of the other enantiomer.
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So we can say that the
percent enantiomeric excess
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is equal to 93% minus 7%.
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And 93 minus 7 is 86%,
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which is what we got in
our calculation down here.
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So that's just a nice
little check to make sure
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you did the problem correctly.