STEREOCHEMISTRY - St. Paul's Cathedral Mission College

STEREOCHEMISTRY

PART-2, PPT-2, SEM-1, CC-1B

Dr. Kalyan Kumar Mandal

Associate Professor

St. Paul’s C. M. College

Kolkata

CONTENTS

STEREOCHEMISTRY

PART-2

• Polarimetry and Optical Rotation

• Specific Rotation

• Molar Rotation

Polarimetry and Optical Rotation• The discoveries of polarized light and optical rotation led to the

concept of molecular chirality which, in turn, is basic to the field of

stereochemistry. The dependence of optical activity on

concentration is sometimes called Biot’s law.

• The ability to rotate the plane of polarisation of plane-polarised

light by a certain substance is called optical activity. Substances that

have the ability to rotate the plane of the polarized light passing

through them are called optically active substances. Quartz and

cinnabar are examples of optically active crystals while aqueous

solutions of sugar, tartaric acid are optically active solutions.

• Optical isomerism manifests itself by the rotation that certain

molecules impart to the plane of polarized light when in the

gaseous, liquid, or molten state or in solution (Figure 1).

Polarimeter• The rotation produced by optically active substance is observed

and measured by a rather simple instrument, known as a

polarimeter. Therefore, the instrument used for measuring the

rotatory power of a substance is the polarimeter.

• Essentially it consists of two Nicol prisms, one the polariser (P) and

the other, the analyser (A), and between them a tube (T) which

contains the substance (a liquid or a solution) to be examined

(Figure 2). S is a source of monochromatic light.

• If the substance rotates the plane of polarisation to

the right, i.e., if the analyser has to be turned to

the right (clockwise) to restore the original field,

the substance is said to be dextrorotatory; if to the

left (anticlockwise), levorotatory.

Polarimeter: Used to measure the optical rotation

of molecules in solution

Optical Rotation• The observed angle of rotation of the plane of polarization by an

optically active liquid, solution, or (more rarely) gas or solid is

usually denoted by the symbol α.

• The angle may be either positive (+) or negative (-) depending on

whether the rotation is clockwise, that is, to the right (dextro) or

counter-clockwise, that is, to the left (levo) as seen by an observer

towards whom the beam of polarized light travels. (This is opposite

from the direction of rotation viewed along the light beam).

• It may be noted that no immediate distinction can be made between

rotations of α ±180 n° (n = integer), for if the plane of polarization

is rotated in the field of the polarimeter by ±180°, the new plane

will coincide with the old one.

This Lecture is prepared by Dr. K. K. Mandal, SPCMC, Kolkata

Factors affecting the magnitude of

Optical Rotation

• Factors that affect the magnitude of optical rotation, in addition to

the nature of the sample are:

1. sample thickness (i.e., cell length)

2. sample concentration (or density, in the case of the pure liquid)

3. nature of solvent

4. temperature

5. wavelength of the light used.

• Optical activity is not a colligative property. A colligative property

of a system is one which depends only on the number of particles

and not on the nature of the particles.


Optical Rotation

• In fact optical rotation (α), as measured, is always recorded as being

between -90° and +90°. Thus, for example, no difference appears

between rotations of +50°, +230°, or -130°.

• If solutions of the above rotations were diluted to one-tenth of their

original concentrations, their rotations would become +5°, +23°,

and -13°. Therefore, optical rotation of a solution of a chiral

compound is proportional to its concentration.

• The rotation of the solutions or the pure liquids can also be

measured in a shorter tube. In this case, if a tube of a quarter of the

original length, e.g., 0.25 decimeters (dm) instead of 1dm is used,

the rotations will become +12.5°, +57.5°, and -32.5°.


Biot’s Law and Optical Rotation

• Biot discovered that the observed rotation is proportional to the

length (l) of the cell or tube containing the optically active liquid or

solution and the concentration c (or density in the case of a pure

liquid) (therefore, α ∝ l and α ∝ c), so that:

α = [α] c l (Biot's law),

where [α] is a proportionality constant depending on the nature of

the sample, temperature, solvent, and wavelength of light used.

• Because of the temperature dependence of both concentration (c)

and optical rotation (α), most polarimeter cells are constructed so

that they can be readily thermostated.

• When l is measured in decimeters and c in g mL-1, [α] is called

specific rotation.


Effect of Concentration (c) and Path length (l)

on Optical Rotation

• The optical rotatory power is a molecular property. Therefore, the

optical rotation is caused by individual molecules of the optically

active compound. The magnitude of rotation depends on the number

of molecules of the substance that interacts with the plane polarized

light in passing through the polarimeter tube.

• The more concentrated the sample solution (the more molecules per

unit volume), the more molecules will be encountered.

Concentrated solutions and neat samples will have higher optical

rotations than dilute solutions.

• The higher the length of the polarimeter tube higher will be the

number of molecules that will interact with the plane polarized light

and higher will be the optical rotation.

Specific Rotation• The rotatory power of a substance is expressed in terms of specific

rotation, [α]tλ. Specific rotation is defined as the rotation produced

by a solution containing 1 g of the substance per mL when the

length of the column through the light beam passes is 1dm or

10 cm.

• For practical reasons, concentrations are often reported in units of

g/100mL. In this case, a correction factor in the numerator is

necessary.

• Values for specific rotation are reported in units of deg mL g-1 dm-1,

(or 10-1 deg cm2 g-1) which are typically shortened to just degrees.


Specific Rotation• The value of [α], the so-called specific rotation, depends on

wavelength and temperature which are usually indicated as

subscripts and superscripts, respectively; thus [α]25λ denotes the

specific rotation of a substance for light of the wavelength of the

sodium D-line (589 nm) at 25°C.

• When the rotation of a pure liquid is cited, the word “neat” is used

in the parenthesis to specify that the measurement refers to a pure

liquid. When pure transparent liquid (neat sample) is taken, the

expression used is:

where d = density of the liquid in g mL-1 and other have the meaning

as before.

Specific Rotation• The specific rotation is a substance-specific physical parameter.

It is so called because it is specific for a specific substance.

Specific rotation is an intensive property. It does not depend on the

system size or the amount of material in the system.

• In addition to wavelength and temperature, [α]tλ also depends on

the solvent and to some extent on the concentration (in a fashion

not taken into account by the concentration term in Biot’s law),

which must be specified.

• This is usually done by adding such information in parentheses,

thus [α]20589 - 10.8 ± 0.1° (c 5.77, 95% ethanol) denotes the

specific rotation at 20°C for light of wavelength 589 nm in 95%

ethanol solution at a concentration of 5.77 g 100 mL-1.


Specific Rotation versus Solvent

• Some of the changes of specific rotation associated with

temperature, solvent and concentration changes are related to

changes in intermolecular hydrogen bonding and/or the degree of

association or dissociation.

• For example, a sample of atrolactic acid [PhC(CH3)(OH)CO2H],

which is dextrorotatory (i.e., rotates the plane of polarized light to

the right) in benzene is levorotatory (i.e., rotates to the left) in

ether. This is because in benzene there are strong intermolecular

association forces whereas in ether there may be strong hydrogen

bonding between the acidic hydrogen of the acid and the ether

oxygen of the solvent.

• The phenomenon (presumably due to association) is confined to

solvents of low polarity (CHCl3 or CH2Cl2).

Specific Rotation

• A pH dependence of rotation is common in the case of acids and

bases. For example, (S)-(+)-lactic acid, dextrorotatory in water,

whose sodium salt is levorotatory and for L-leucine, which is

levorotatory in water but dextrorotatory in aqueous hydrochloric

acid.

• Since optical rotation is proportional to the number of molecules

encountered by the beam of polarized light, if two substances have

unequal molecular weights but are alike with respect to their power

of rotating polarized light, the substance of smaller molecular

weight will have the larger specific rotation simply by virtue of

having more molecules per unit weight.

• In order to compensate for the effect of differing molecular

weights and to put rotation on a per-mole basis, the term “molar

rotation” is defined.


Molar Rotation• Molar rotation is defined as the product of specific rotation and

molecular weight divided by 100. It is obtained by multiplying

specific rotation with molecular weight of the substance and then

dividing the product by 100.

• The division by 100 is included arbitrarily in the definition in order

to keep its numerical values manageably small and it serves to keep

the numerical value of molar rotation on the same approximate

scale as that of specific rotation.

• For a substance of molecular weight (MW) 100, molar and specific

rotation are the same. Thus, denoting molar rotation by [M] or [Φ],

Numerical Problems

1. Calculate [α] of a 0.1 M solution of lactic acid in a 10 cm cell

when the observed rotation is +0.36°.

2. Calculate the specific rotation of an optically active compound

in solution containing 0.75g/10ml, when measured in a 10 cm

tube of a polarimeter at 25°C shows a rotation +1.2°.


Numerical Problems

3. The specific rotation of α-D-glucose is (+)-112°. Assuming that 2

tablespoons weighs 18 g and a small glass tube 5 cm in

diameter holds 200 mL of solution. Calculate how much

rotation should have been observed in a polarimetric

experiment.

Numerical Problems

4. Calculate the specific rotation of a mixture of 30% (+)-2-

chlorobutane and 70% (-)-2-chlorobutane, [α]D of pure

enantiomer is (+)-25.10°.

Solution: The rotation of 30% (+)-2-chlorobutane will cancel that of

30% (-) enantiomer to form 60% racemic mixture. Therefore,

enantiomeric mixture contains 40% optically pure (-)- enantiomer.

As the racemic portion shows no resultant rotation, the observed

rotation will be due to 40% of pure (-)- enantiomer. 100% (-)-

enantiomer exhibits [α]D = - 25.10° [ because pure (+) enantiomer

has a [α]D = + 25.10°], therefore, 40% of pure (-)- enantiomer will

exhibit a specific rotation, 40 x (-25.10°)/100 = (-)- 10.04°.


Numerical Problems5. What is the observed rotation when 0.1M solution of

(R)-butan-2-ol is mixed with an equal volume of a 0.05Msolution of racemic butan-2-ol and the resulting solution istaken in a cell of 5 cm long tube in a polarimeter? Thespecific rotation of (R)-butan-2-ol is (+)-13.9°.

Solution: The racemic butan-2-ol has no contribution to the optical

activity. Hence, when a solution of racemic butan-2-ol is added, the

only effect of its addition on the observed rotation is to dilute the

solution of (R)-enantiomer by a factor of two. Therefore, the

concentration of the solution containing (R)-butan-2-ol after dilution is

0.05M. The molecular weight of butan-2-ol is 74.

Numerical Problems6. A 0.1M solution of a pure chiral compound X has an observed

rotation (+)-0.2° in a 10 cm polarimeter cell. The molecular weight

of the compound is 180.

(i) What is the [α]D of X?

(ii) What is the observed rotation if this solution is mixed with an

equal volume of a solution that is 0.1M in (-)-enantiomer?

(iii) What is the observed rotation of solution of X, if the solution is

diluted with an equal volume of the same solvent?

(iv) What is the specific rotation of X after the dilution described in

(iii)?

(v) What is the specific rotation of (-)-enantiomer, the enantiomer of

X?

(vi) What is the observed rotation of 100 mL of a solution that

contains 0.01M of (+) and 0.005M of (-) enantiomers. Assume a

1dm polarimeter tube. What is the specific rotation?

Numerical Problems

(ii) When an equal volume of 0.1M solution (-)- enantiomer is added

to a solution containing optically pure chiral compound of (+)

variety, a racemic mixture is formed. The observed rotation is,

therefore, 0°.

(iii) Observed rotation ‘α’ is directly proportional to the concentration

of the solution containing optically active compound. Hence, the

observed rotation will be (+)-0.1°, as the concentration of the

solution becomes half.


Numerical Problems

(iv) Specific rotation, [α]D is independent on the concentration of the

solution. It depends on the nature of the solvent, length of the

polarimer tube, experimental temperature and the wavelength of

the plane polarized light used. Therefore, specific rotation will

have the same value, (+)-11.11°.

(v) Since, a pair of enantiomers have equal but opposite sign of

rotation, the specific rotation of enantiomer is (-)-11.11°.

(vi) When 0.005 mole of (-)-enantiomer is added to 0.01 mole of (+)-

enantiomer, 0.005 mole of (+)-enantiomer forms racemate with

0.005 mole of (-)-enantiomer. Therefore, rotation due to

(0.01 - 0.005) = 0.005 mole of (+)-enantiomer (volume of the

solution = 100 mL) will be observed. In this case, 0.009 g mL-1,

which is half of the value mentioned in (i). Therefore, the observed

rotation α = 0.2°/2 = 0.1°.

• The specific rotation will remain unaffected.

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