Question

Polarimetry Lab calculations:

Isomer	Observed Degree of Rotation(Raw data)
(+) Carovene	158.75°
(-) Carovene	229.75°
Blank	200.75°
Unknown (X)	175.25°

I would like some help to figure out how to do this; I want to make sure that I am doing it correct. Here is what I have done so far:

1. Find specific rotations for all the isomers:

I believe these are the equations to use:

X _observed= X _raw - Blank             l= 0.8 dm and c= 0.9600 g/cm³

[X]= X _observed / lc

Can someone show me the calculations for all of them, this is what I did for Unknown:

My Unknown (X): I did x observed= 175.25-200.75= -25.5°

[X]= X _observed / lc -25.5°/(0.8*0.9600)= -33.20°

2. Find the Enantiomer Excess:

The equations our teacher gave were:

EE= [X] _observed / [X]_pure * 100

([X]_pure can be found by [X]= X_pure/ lc

I don’t know how to find x pure. What even is that, where can I get it from the numbers. After I get EE,

I need to find how much of (-) and (+) is in the enantiomer (the equation given for that is

EE= [X]₊ XA + [X]_- (1-X₊)

[X]₊ and [X]_- are supposed to be answers from number 1.

Answer 1

Let [X]+ is the specific rotation of (+) carovene

[X]+ = observed rotation / lc

given l = 0.8 dm

        c =0.96 g /cc

       lc = 0.8 x 0.96 = 0.768

[X]+ = (158.75 - 200.75) / 0.768

       = -42/0.768

       = 54.7 ⁰

similarly [X]- the specific rotation of (-) carovene is given by

{X]- = (229.75 - 200.75)/0.768

      = +29/0.768

      = +37.8 ⁰

[X]_unknown = ( 175.25 - 200.75)/0.768

               = -33.2 ⁰

since the unknown has the specific rotation in negative, it must have excess of [X]+ enantiomer.

Therefore enantiometric excess = EE ={ [X]_unknown/ [X]+ }* 100

we have taken [X]+ because that enantiomer is present in excess.

                                          EE = [-33.2 / -54.7] * 100

                                                = 61%                                               

Let y% be the amount of [X]+ enantiomer in the unknown. then (100-y)% is the amount of [X]- enantiomer in the unknown.

61 = y - (100-y)

    = 2y-100

2y = 161 or y = 80.5%

i.e (+) carovene in the unknown sample = 80.5%

    (-) carovene in the unknown sample = 19.5 %

EE = 80.5 - 19.5 = 61 %

Note:

If we use the other formula for find out ' y '

[X]_unknown = { [X]+ * y/100 } + { [X]- * (100-y)/100 }

   -33.2 = -54.7 y/100 + 37.8 (100 -y)/100

    -3320 = -54.7y + 3780 - 37.8y

-7100 = -92.5y

y = 7100/92.5 = 77%

i.e (+) carovene in the unknown sample = 77%

    (-) carovene in the unknown sample = 23 %

EE = 77-23 = 54 %