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Representation of Optical Isomers


Different types of representations can be used to depict the optical isomers on paper. There are mainly two types of representations of optical isomers:

  • Wedge Dash
  • Fischer Projection

Wedge Dash Representation

A Wedge Dash, the most popular three-dimensional depiction of a molecule on a two-dimensional surface is in projection (paper). This type of representation is typically used for molecules with chiral centres. This type of representation employs three different types of lines.

Representation of Optical Isomers - JEE

  • Solid wedges or thick lines signify bond projections towards the observer or above the paper's surface. A continuous or regular line denotes a bond in the plane of the paper. 
  • A bond projection away from the observer is indicated by a dashed or broken line.

Fischer Projection

Fischer projections are best used to represent the straight-chain structures of monosaccharides and some amino acids. They represent structural forms that allow one to convey valuable stereochemical information by drawing 3D molecules as flat structures.

Representation of Optical Isomers - JEEFischer Projection

How to Draw Fischer Projection?

In a Fischer projection, the longest chain is drawn vertically. The horizontal lines indicate the bonds with hydrogen, hydroxyl, and amino groups. The four bonds to a chiral carbon make a cross, with the carbon atom at the intersection of the horizontal and vertical lines. The following steps can be employed for an aldohexose.

Representation of Optical Isomers - JEEAldohexose

Step 1: Arrange the molecule so that the chiral carbons and the longest continuous chain are in a vertical line. The aldehyde group representing carbon 1 goes at the top.

Step 2: Draw horizontal lines to make crosses at C-2, C-3, C-4, and C-5.

Step 3: Put the OH groups on the exact side of the cross.

Step 4: Remove C-2, C-3, C-4, and C-5, and the Fischer projection is obtained.

Fischer Projection Rules

The following rules should be kept in mind while working with Fischer projection.

  • Fischer projection may be rotated by 180 degrees without changing its meaning.
  • Fischer projection may not be rotated by 90 degrees. Such a rotation typically changes the configuration to the enantiomer.
  • To find the enantiomer of a molecule drawn as a Fischer projection, exchange the right and left horizontal bonds.

Converting Wedge-Dash Structure to Fischer Projection

The stereochemical formula for (R)-lactic acid can be drawn using the wedge-dashed structure and Fischer projection method. The conversion from wedge-shaped or bond-line structure to Fischer projection is done stepwise.

Examples: 

Q.1. Write the Fischer projection of CH3CH(OH)COOH  

Sol.

Representation of Optical Isomers - JEE

  • Maximum carbon must be in a vertical line.
  • Place higher priority carbon-containing functional group on top of the vertical line.

Q.2 Write Fischer's projection of 

Representation of Optical Isomers - JEE

Sol. 
(i) Place a higher-priority carbon-containing functional group on top of the vertical line.

(ii) Arrange another group according to its clockwise or anti-clockwise position w.r.t. group on the top.

Representation of Optical Isomers - JEE

Q.3. Convert the following wedge-dash figure in the Fischer projection.
Representation of Optical Isomers - JEESol.
Representation of Optical Isomers - JEE

Q.4. Out of the two cross lines in the representation of Fischer projection, what does the horizontal line represent?

Ans: The Fischer Projection consists of both horizontal and vertical lines, where the horizontal lines represent the atoms that are pointed out of the plane while the vertical line represents atoms that are pointed away from the plane. The point of intersection between the horizontal and vertical lines represents the central carbon.

Representation of Optical Isomers - JEE

Q.5. Draw the fisher projection of: 

Representation of Optical Isomers - JEE

Sol.

Representation of Optical Isomers - JEE * Representation of Optical Isomers - JEE

If fourth valency is not given then we assume it to be hydrogen.

Assigning R-S Configuration in Wedge Dash 

Representation of Optical Isomers - JEE R → Rectus → Right → Clockwise.

Representation of Optical Isomers - JEE S → Sinister → Left → Anti-clockwise.

(i) Determining R/S When The #4 Priority Substituent Is In Back (i.e. on a “Dash”)


When the #4 substituent is in the back (on a "dash"), follow the regular rules mentioned above. Here is an example: 

Representation of Optical Isomers - JEE

Note: Designations (R) and (S) bear no relationship to whether a molecule rotates plane-polarized light clockwise (+) or counterclockwise (-).

(ii) Determining R/S When The #4 Priority Substituent Is In Front (i.e. on a “Wedge”)

Let’s first consider the molecule below. The name of this molecule is (R)-1-fluoroethanol. It is listed below with priorities assigned based on atomic number. In this case F>O>C>H. So F is #1 and H is #4. The tricky part here is that the #4 priority is pointing out of the page (on a “wedge”).

You can “simply” rotate the molecule in your head so that the #4 priority is on a dash. Then you can traditionally assign R or S. This “simple” advice is not always an easy task for beginners.

Representation of Optical Isomers - JEERotating the Molecule

Here’s another way around this. When the #4 priority is on a wedge you can just reverse the rules. So now we have two sets of rules:

If the #4 priority is on a dash:

  • Clockwise = R
  • Counterclockwise = S

If the #4 priority is on a wedge, reverse the typical rules:

  • Clockwise = S
  • Counterclockwise = 
    Representation of Optical Isomers - JEE
    Applying the Opposite Rule

(iii) Determining R/S when the Lowest Priority Group is in the Plane of the Page

If the Lowest Priority Group group is in the plane of the page, swapping any two groups will change the configuration from R to S or vice versa. To determine the configuration:

  • Swap the #4 substituent with the substituent in the back.
  • Redraw the chiral center and determine R/S on the new configuration with the #4 group in the back.
  • Flip the result to its opposite to account for the single swap made in step #1.

Representation of Optical Isomers - JEEWhen the Lowest Priority Group is in the Plane of Page

Calculating the Total no. of Optically Active Isomers

1. If a compound has 'n' different chiral carbons then the total no. of optically active isomers = 2n

No. of meso form = 0

e.g.

Representation of Optical Isomers - JEE

no. of different chiral carbon = 4

total optical isomer = 2n = 24 = 16

  • There will be no meso as the compound does not have identical chiral carbon.
  • If a compound has n identical chiral centre (symmetrical) ⇒ There must be symmetry from somewhere.

Example: (Glucose)

Representation of Optical Isomers - JEE

Total no. of different chiral carbon = 4
Total Optical Isomers = 24 = 16

(i) If n is even

  • number of optical isomers (a) = 2n-1
  • meso forms (m) = 2n/2-1
  • total number of optical isomers = a + m

(ii) If n is odd

Representation of Optical Isomers - JEE

Total optical isomers =  Representation of Optical Isomers - JEE = 2n-1

 Example 1: 

 Representation of Optical Isomers - JEE

  • When there is an odd no. of identical carbon atoms (i.e. symmetrical) then this compound will certainly contain pseudo chiral w.r.t. which compound is symmetrical (i.e. POS).
  • Other meso compounds of the above compound will form by changing the place Br and H around pseudo-chiral carbon.

Representation of Optical Isomers - JEE

Total meso forms = 2

Total optical isomers  = Representation of Optical Isomers - JEE

Representation of Optical Isomers - JEE

= 22 - 2

= 4 - 2 = 2
Here are the two Optical Isomers: 

Representation of Optical Isomers - JEE

Example 2: 

Representation of Optical Isomers - JEE

Total no. of even chiral = 4

Number of optical isomers = a = Representation of Optical Isomers - JEE = Representation of Optical Isomers - JEE = 23 = 8

Meso forms = m = Representation of Optical Isomers - JEE = Representation of Optical Isomers - JEE = 22-1 = 21 = 2

Total number of optical isomers = 8 + 2 = 10

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Diastereoisomers through Fischer Projection

For a single chiral center, there is no diastereoisomer. The stereoisomers which are not related as object and mirror images. They may be optically active or optically inactive.

Representation of Optical Isomers - JEEInactiveRepresentation of Optical Isomers - JEEActiveFor a compound having 2 chiral centers, Fix one chiral carbon

Representation of Optical Isomers - JEE

After one inter-change, if (R, R) → (R, S), then we get diastereomers.
Representation of Optical Isomers - JEE

For a compound having 3 chiral carbon to get diastereoisomer, fix two chiral carbon and one interchange with the left carbon or fix one chiral carbon and interchange with other two,

Representation of Optical Isomers - JEERepresentation of Optical Isomers - JEERepresentation of Optical Isomers - JEE

(I)                                (II)

Total isomer = 23 = 8

Representation of Optical Isomers - JEERepresentation of Optical Isomers - JEERepresentation of Optical Isomers - JEE

(III)                               (IV)

(I) and (III), I and (IV), (II) and (III), (II) and (IV) are diastereoisomers.

Some Solved Examples

Q.1. 

(I)    Representation of Optical Isomers - JEE                

(II)       Representation of Optical Isomers - JEE            

 (III)      Representation of Optical Isomers - JEE

                                                                                        

 (IV) Representation of Optical Isomers - JEEWhat is the relation among the above compounds? 

Sol. I and II are identical
III and IV are identical
II and III are diastereo isomer
I and IV are diastereo isomer

Q.2. Find the total isomers obtained by dichlorination of cyclopentane. 

Sol.

Representation of Optical Isomers - JEE

Total isomers = 3 + 3 + 1 = 7

Optically isomers = 6, Optically active isomers = 4

Q.3. Find the total isomers obtained by trichlorination of propane. 

Sol.

Representation of Optical Isomers - JEE

Representation of Optical Isomers - JEE

Total isomers = 6

optically isomers = 2

Q.4. Find total isomers obtained by dichlorination of n-butane  

Sol.

Representation of Optical Isomers - JEE1

Representation of Optical Isomers - JEE2

Representation of Optical Isomers - JEE2

Representation of Optical Isomers - JEE1

Representation of Optical Isomers - JEE1

Representation of Optical Isomers - JEE3 (2 optically 1 meso ) Total isomers = 10 (6 optically active + 1 meso + 3 structural)

Q.5. How many stereoisomers of 1,2,3-cyclohexantriol are there?

Sol.

Representation of Optical Isomers - JEE No. of Chiral carbon = 3 (identical) symmetrical)

a = Representation of Optical Isomers - JEE = Representation of Optical Isomers - JEE = 4- 2

m = 2

total stereoisomers = 2 + 2 = 4

Representation of Optical Isomers - JEEMeso

Representation of Optical Isomers - JEE

Mesoform is optically inactive due to internal compensation and racemic mixture is optically inactive due to external compensation.

Q.6. A and B are enantiomers of each other. The specific rotation of A is 20 º. Rotation of mixture of A and B = -5º What is the percentage of the racemic part?
Sol. x mol A, 1-x mol B

x × 20 + ( 1- x ) (-20) = -5

20 x - 20 + 20x = - 5

40 x = 15 ⇒ x = 3/8 = 0.375

moles of A = 3/8

moles of B = Representation of Optical Isomers - JEE = Representation of Optical Isomers - JEE

Representation of Optical Isomers - JEE moles of A and Representation of Optical Isomers - JEE moles of B will form racemic mixture.

Enantiomer excess or optical purity = Representation of Optical Isomers - JEE - Representation of Optical Isomers - JEE = Representation of Optical Isomers - JEE

Q.7.

Representation of Optical Isomers - JEEWhat is the rotation of the mixture?  

Sol. Rotation will be due to B only,

= 0.3 × (-20º)

= - 6º

► Chiral compound → optically active compound

Q.8. Which of the following compounds is Chiral (Optically active)?

(A)

Representation of Optical Isomers - JEE

(B)

Representation of Optical Isomers - JEE

(C) Both 

(D) None

Ans. (D)

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FAQs on Representation of Optical Isomers - JEE

1. What is the significance of assigning R-S configuration in wedge dash representation of optical isomers?
2. How can we calculate the total number of optically active isomers?
Ans. To calculate the total number of optically active isomers, we need to consider the number of chiral centers in the molecule. Each chiral center can have two possible configurations (R or S), so the total number of optically active isomers can be calculated using the formula 2^n, where n is the number of chiral centers.
3. What are diastereoisomers and how can they be represented through Fischer projection?
Ans. Diastereoisomers are stereoisomers that are not mirror images of each other. They have different physical and chemical properties. Fischer projection is a way to represent diastereoisomers by showing the three-dimensional structure of the molecule in a two-dimensional drawing. In Fischer projection, the horizontal lines represent bonds coming out of the plane towards the observer, while the vertical lines represent bonds going into the plane away from the observer.
4. How can the representation of optical isomers be helpful in the JEE exam?
Ans. Understanding the representation of optical isomers is crucial for solving questions related to stereochemistry in the JEE exam. Questions on assigning R-S configuration, determining the number of optically active isomers, and analyzing diastereoisomers through Fischer projection are commonly asked in the exam. Having a clear understanding of these concepts will help in accurately answering such questions.
5. What are some common misconceptions or mistakes students make when dealing with optical isomers?
Ans. Some common misconceptions or mistakes students make when dealing with optical isomers include confusing the terms enantiomers and diastereoisomers, incorrectly assigning R-S configuration, not considering the presence of chiral centers, and misinterpreting Fischer projections. It is important for students to practice and understand the concepts thoroughly to avoid these mistakes during the JEE exam.
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