0:02 leah here from leh Versailles calm and
0:05 in this video we're going to look at
0:08 specific rotation calculations when it
0:11 comes to optical activity you can find
0:12 this entire video series on my website
0:15 along with chirality practice quiz and
0:17 cheat sheet by visiting layovers edicom
0:21 slash chirality in the last video we
0:24 looked at the polarimeter and the
0:27 concept that when plane polarized light
0:30 enters the polarimeter that contains a
0:33 pure chiral sample meaning an optically
0:36 active sample the light will be rotated
0:38 either clockwise in the positive
0:41 direction or counterclockwise in the
0:43 negative direction so that when it comes
0:45 out the other end there is some degree
0:48 of observed rotation you can tell that
0:50 the plane polarized light slightly
0:54 change direction this rotation is called
0:57 the alpha value where alpha refers to
1:01 observed rotation there are many things
1:02 that will change the observed rotation
1:06 because it specifically depends on the
1:09 light hitting a molecule and that
1:11 molecule turning yet either to the right
1:14 or the left so what can impact that
1:18 observed rotation concentration if you
1:21 have chiral molecules in a solution as
1:24 the light is passing through the light
1:26 bumps into a chiral molecule it gets
1:28 turned a little bit bumps into another
1:31 molecule gets turned a little more the
1:33 more chiral molecules you have in your
1:35 sample the more the light bumps into
1:38 those molecules and the more the light
1:40 gets turned because every time it hits
1:42 another molecule it turns just a little
1:43 bit more
1:46 another thing that impacts rotation is
1:49 the length of the two the longer the
1:52 length of the polarimeter meaning the
1:54 longer the path the light has to travel
1:57 the more opportunity it has to bump into
2:00 molecules in a short tube
2:02 it goes through hits a couple molecules
2:05 gets out the other end but as that tube
2:07 gets longer and longer it has to travel
2:09 through even more molecules bumps into
2:10 more of them
2:13 and has greater potential to turn that
2:16 length of the tube is considered the
2:18 path length because it's the length of
2:21 the path that light has to travel these
2:23 are directly related to the polarimeter
2:26 the tube that you're using but then we
2:28 have two more outside factors
2:32 temperature remember that temperature is
2:34 a measure of internal energy of a system
2:37 and if you're looking at a higher
2:40 temperature the system is moving faster
2:42 and if it's moving faster that will
2:44 impact how the light travels and hits
2:48 the molecules and finally if what we're
2:50 looking at is the light then changing
2:52 the light source or the wavelength of
2:55 light that we're using is also going to
2:59 impact our numbers if every scientist is
3:01 running their own experiment you need a
3:03 way to be able to refer to what you have
3:06 compared to someone else so that you can
3:09 compare data just like we have SI units
3:12 and IU PAC rules for naming we also have
3:14 a standard system for the optical
3:16 activity and that is the specific
3:22 rotation specific rotation is alpha in
3:24 brackets where the brackets tell us
3:27 standard rather than just an observed
3:30 value and it has a very specific set of
3:33 conditions that includes a concentration
3:36 of one gram per milliliter this is how
3:37 we measure concentration in a
3:40 polarimeter and a path length that is
3:43 equal to 1 decimeter where if you think
3:45 of deci as 1/10
3:48 it's 1/10 of a meter or simply 10
3:51 centimeters but if you're running an
3:54 experiment chances are you don't have
3:56 standard conditions and you need a way
4:00 to equate what you have to this
4:04 specific rotation is specific to that
4:07 molecule it's like a constant like the
4:09 melting point or the boiling point or
4:12 even the KSP value but if you think back
4:15 to Gen chem and KSP it did change
4:18 dependent on temperature that means we
4:20 have to take a look at those final two
4:23 factors so if you have conditions that
4:25 are not specific here's how you set up
4:28 your equation specific rotation which is
4:31 a number that you can get out of a
4:35 reference table is equal to alpha the
4:37 observed rotation divided by
4:41 concentration times path length where
4:45 alpha is the observed rotation
4:47 concentration is measured in grams per
4:50 milliliter and path length is measured
4:53 in decimeters but just like other
4:56 factors in your reference table for
4:59 example KSP that K was temperature
5:01 dependent two more things you want to
5:03 include here with your specific rotation
5:06 would be your temperature and your
5:09 wavelength temperature would be constant
5:11 you set it to a specific temperature and
5:14 the wavelength has to do with the type
5:16 of light source that you're using for
5:21 this experiment for example if I look at
5:25 our 2-bromobutane I looked up the
5:28 specific rotation for our 2-bromobutane
5:32 and this is what I found specific
5:35 rotation 20d is equal to negative 23.1
5:39 and specific rotation 25 D is equal to
5:43 negative 13.5 what is happening here the
5:45 specific rotation changes based on the
5:47 temperature twenty or twenty-five
5:51 degrees Celsius and D tells us not so
5:53 much a wavelength number but the light
5:55 source which has an applied wavelength
5:58 in this case it's the D line of sodium
6:02 at 589 nanometers just an FYI you don't
6:05 have to know this using this information
6:07 I can easily figure out the specific
6:10 rotation for s remembering that R and s
6:13 are enantiomers so if R is
6:16 lever rotatory it turns light to the
6:19 left or the negative direction as in
6:22 this case only will be dextrorotatory
6:24 meaning turns light in the positive
6:27 direction s at 20 degrees will be
6:29 positive twenty three point one s at
6:31 twenty five degrees will be positive
6:33 thirteen point five going back to our
6:36 equation your professor won't always be
6:38 so nice and sometimes you'll be asked to
6:40 calculate different values for example
6:43 what is the expected observed rotation
6:46 given conditions what do you do you want
6:49 to isolate your alpha knot in brackets
6:52 your regular alpha for observed by using
6:54 simple algebra to move everything over
6:56 to the other side so we'll multiply both
7:00 sides by concentration and path length
7:04 that allows C&L to cancel concentration
7:06 of path length on the other side which
7:09 gives us a new equation that alpha or
7:13 observed rotation is equal to alpha in
7:15 brackets specific rotation times
7:19 concentration times path length let's
7:23 try an example a student attempts to
7:26 separate R and s 2 butanol the final
7:30 solution is 0.25 molar and 25 degrees
7:32 was the students successful if a
7:35 ten-centimeter self shows a negative 2.5
7:38 rotation using the D line of sodium
7:40 we're given the following information
7:43 from a reference table and we want to
7:45 figure out if the student was successful
7:47 in separating between R and s when
7:49 you're given a problem like this there's
7:50 a whole lot of words and that makes it
7:53 very confusing what you want to do is
7:55 see if you can pull out the numbers from
7:58 the story and come up with a simple
8:01 equation in this situation if we are
8:04 given a specific rotation and an
8:06 observed rotation and asked if we're
8:09 successful what we're translating this
8:12 to is simple does the Alpha observed
8:16 match the alpha specific or is something
8:18 wrong here meaning is the solution not
8:21 pure if the solution was properly
8:23 separated we should be able to calculate
8:25 one from the other and I purposely made
8:27 the example this way because some professor
8:27 professor
8:28 we'll ask you to calculate alpha
8:30 specific sum we'll ask you to calculate
8:32 alpha observed and I want to make sure
8:35 you can do both recognize that some of
8:38 this information is very nice to have if
8:39 you're doing this in lab but we honestly
8:42 don't care on paper for example 25
8:45 degrees Celsius great this is at 25
8:46 degrees Celsius so we're good we don't
8:49 need to worry about it and these simply
8:51 tells us what type of light we're using
8:54 in this case the d-line of sodium it has
8:56 nothing to do with dextro or level
8:57 rotatory so we don't care about that
9:00 note that it's there ignore it move on
9:02 to the problem the fact that we have a
9:05 negative observed rotation and negative
9:08 13.5 to 4 R we know that we're looking
9:11 at the our sample but is it just R or is
9:13 there some s still left in there
9:16 we'll use the equation specific rotation
9:19 is equal to observed rotation divided by
9:22 concentration times path length and in
9:24 the first version we're going to plug in
9:27 all the experimental data and see if
9:30 this is correct meaning if it gives us
9:32 the correct specific rotation if it does
9:34 we know we're good if it does not we
9:36 know that the solution is not what we
9:39 expected it's not pure R so what do we
9:41 have an observed rotation of negative
9:45 two point five degrees concentration of
9:49 0.25 molar and a path length as 10
9:51 centimeters problem is we don't want
9:53 centimeters we want decimeters 10
9:56 centimeters is equal to one decimator so
9:59 that simply gives us a 1 punching this
10:02 into the calculator you get negative 10
10:04 degrees which is what we would expect
10:07 for the specific rotation if this was
10:09 the observed rotation of pure R which it
10:12 is not telling us the student did not do
10:15 a proper separation to solve it the
10:18 other way let's see what a pure our
10:21 solution would give us for the observed
10:24 rotation under these conditions one more
10:26 time we start with the equation specific
10:28 rotation equals observed rotation
10:30 divided by concentration times length
10:33 move concentration times length over to
10:35 the other side to cancel out that allows
10:38 us to isolate observed rotation giving
10:40 us the new equation
10:43 alpha observed is equal to specific
10:48 rotation times C times L and then we
10:51 plug in the numbers we are given
10:53 negative thirteen point five two degrees
10:56 for specific rotation multiply that by
10:59 0.25 molar for concentration and 1
11:02 decimeter for path line plugging all
11:05 that into the calculator we get negative
11:09 three point three eight degrees as the
11:12 ideal observed rotation if this was just
11:15 an our solution the fact that the
11:18 observed rotation is less than negative
11:20 three point three eight it's negative
11:22 two point five tells us there's some s
11:23 remaining in there
11:25 the next question your professor might
11:27 ask is figure out what percent of the
11:31 solution is R or s or figure out the
11:34 enantiomeric excess of what we have also
11:37 known as optical purity and that is
11:38 exactly what we'll cover in the next
11:41 video which you can find along with the
11:43 stereochemistry practice quiz and cheat
11:46 sheet by visiting my website layer four
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