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Specific Rotation and Observed Rotation Calculations in Optical Activity
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leah here from leh Versailles calm and
in this video we're going to look at
specific rotation calculations when it
comes to optical activity you can find
this entire video series on my website
along with chirality practice quiz and
cheat sheet by visiting layovers edicom
slash chirality in the last video we
looked at the polarimeter and the
concept that when plane polarized light
enters the polarimeter that contains a
pure chiral sample meaning an optically
active sample the light will be rotated
either clockwise in the positive
direction or counterclockwise in the
negative direction so that when it comes
out the other end there is some degree
of observed rotation you can tell that
the plane polarized light slightly
change direction this rotation is called
the alpha value where alpha refers to
observed rotation there are many things
that will change the observed rotation
because it specifically depends on the
light hitting a molecule and that
molecule turning yet either to the right
or the left so what can impact that
observed rotation concentration if you
have chiral molecules in a solution as
the light is passing through the light
bumps into a chiral molecule it gets
turned a little bit bumps into another
molecule gets turned a little more the
more chiral molecules you have in your
sample the more the light bumps into
those molecules and the more the light
gets turned because every time it hits
another molecule it turns just a little
bit more
another thing that impacts rotation is
the length of the two the longer the
length of the polarimeter meaning the
longer the path the light has to travel
the more opportunity it has to bump into
molecules in a short tube
it goes through hits a couple molecules
gets out the other end but as that tube
gets longer and longer it has to travel
through even more molecules bumps into
more of them
and has greater potential to turn that
length of the tube is considered the
path length because it's the length of
the path that light has to travel these
are directly related to the polarimeter
the tube that you're using but then we
have two more outside factors
temperature remember that temperature is
a measure of internal energy of a system
and if you're looking at a higher
temperature the system is moving faster
and if it's moving faster that will
impact how the light travels and hits
the molecules and finally if what we're
looking at is the light then changing
the light source or the wavelength of
light that we're using is also going to
impact our numbers if every scientist is
running their own experiment you need a
way to be able to refer to what you have
compared to someone else so that you can
compare data just like we have SI units
and IU PAC rules for naming we also have
a standard system for the optical
activity and that is the specific
rotation specific rotation is alpha in
brackets where the brackets tell us
standard rather than just an observed
value and it has a very specific set of
conditions that includes a concentration
of one gram per milliliter this is how
we measure concentration in a
polarimeter and a path length that is
equal to 1 decimeter where if you think
of deci as 1/10
it's 1/10 of a meter or simply 10
centimeters but if you're running an
experiment chances are you don't have
standard conditions and you need a way
to equate what you have to this
specific rotation is specific to that
molecule it's like a constant like the
melting point or the boiling point or
even the KSP value but if you think back
to Gen chem and KSP it did change
dependent on temperature that means we
have to take a look at those final two
factors so if you have conditions that
are not specific here's how you set up
your equation specific rotation which is
a number that you can get out of a
reference table is equal to alpha the
observed rotation divided by
concentration times path length where
alpha is the observed rotation
concentration is measured in grams per
milliliter and path length is measured
in decimeters but just like other
factors in your reference table for
example KSP that K was temperature
dependent two more things you want to
include here with your specific rotation
would be your temperature and your
wavelength temperature would be constant
you set it to a specific temperature and
the wavelength has to do with the type
of light source that you're using for
this experiment for example if I look at
our 2-bromobutane I looked up the
specific rotation for our 2-bromobutane
and this is what I found specific
rotation 20d is equal to negative 23.1
and specific rotation 25 D is equal to
negative 13.5 what is happening here the
specific rotation changes based on the
temperature twenty or twenty-five
degrees Celsius and D tells us not so
much a wavelength number but the light
source which has an applied wavelength
in this case it's the D line of sodium
at 589 nanometers just an FYI you don't
have to know this using this information
I can easily figure out the specific
rotation for s remembering that R and s
are enantiomers so if R is
lever rotatory it turns light to the
left or the negative direction as in
this case only will be dextrorotatory
meaning turns light in the positive
direction s at 20 degrees will be
positive twenty three point one s at
twenty five degrees will be positive
thirteen point five going back to our
equation your professor won't always be
so nice and sometimes you'll be asked to
calculate different values for example
what is the expected observed rotation
given conditions what do you do you want
to isolate your alpha knot in brackets
your regular alpha for observed by using
simple algebra to move everything over
to the other side so we'll multiply both
sides by concentration and path length
that allows C&L to cancel concentration
of path length on the other side which
gives us a new equation that alpha or
observed rotation is equal to alpha in
brackets specific rotation times
concentration times path length let's
try an example a student attempts to
separate R and s 2 butanol the final
solution is 0.25 molar and 25 degrees
was the students successful if a
ten-centimeter self shows a negative 2.5
rotation using the D line of sodium
we're given the following information
from a reference table and we want to
figure out if the student was successful
in separating between R and s when
you're given a problem like this there's
a whole lot of words and that makes it
very confusing what you want to do is
see if you can pull out the numbers from
the story and come up with a simple
equation in this situation if we are
given a specific rotation and an
observed rotation and asked if we're
successful what we're translating this
to is simple does the Alpha observed
match the alpha specific or is something
wrong here meaning is the solution not
pure if the solution was properly
separated we should be able to calculate
one from the other and I purposely made
the example this way because some professor
professor
we'll ask you to calculate alpha
specific sum we'll ask you to calculate
alpha observed and I want to make sure
you can do both recognize that some of
this information is very nice to have if
you're doing this in lab but we honestly
don't care on paper for example 25
degrees Celsius great this is at 25
degrees Celsius so we're good we don't
need to worry about it and these simply
tells us what type of light we're using
in this case the d-line of sodium it has
nothing to do with dextro or level
rotatory so we don't care about that
note that it's there ignore it move on
to the problem the fact that we have a
negative observed rotation and negative
13.5 to 4 R we know that we're looking
at the our sample but is it just R or is
there some s still left in there
we'll use the equation specific rotation
is equal to observed rotation divided by
concentration times path length and in
the first version we're going to plug in
all the experimental data and see if
this is correct meaning if it gives us
the correct specific rotation if it does
we know we're good if it does not we
know that the solution is not what we
expected it's not pure R so what do we
have an observed rotation of negative
two point five degrees concentration of
0.25 molar and a path length as 10
centimeters problem is we don't want
centimeters we want decimeters 10
centimeters is equal to one decimator so
that simply gives us a 1 punching this
into the calculator you get negative 10
degrees which is what we would expect
for the specific rotation if this was
the observed rotation of pure R which it
is not telling us the student did not do
a proper separation to solve it the
other way let's see what a pure our
solution would give us for the observed
rotation under these conditions one more
time we start with the equation specific
rotation equals observed rotation
divided by concentration times length
move concentration times length over to
the other side to cancel out that allows
us to isolate observed rotation giving
us the new equation
alpha observed is equal to specific
rotation times C times L and then we
plug in the numbers we are given
negative thirteen point five two degrees
for specific rotation multiply that by
0.25 molar for concentration and 1
decimeter for path line plugging all
that into the calculator we get negative
three point three eight degrees as the
ideal observed rotation if this was just
an our solution the fact that the
observed rotation is less than negative
three point three eight it's negative
two point five tells us there's some s
remaining in there
the next question your professor might
ask is figure out what percent of the
solution is R or s or figure out the
enantiomeric excess of what we have also
known as optical purity and that is
exactly what we'll cover in the next
video which you can find along with the
stereochemistry practice quiz and cheat
sheet by visiting my website layer four
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