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Home , Optical rotation

STEREOCHEMISTRY

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

Dr. Kalyan Kumar Mandal Associate Professor St. Paul’s C. M. College Kolkata CONTENTS PART-2

• and • • Molar Rotation Polarimetry and Optical Rotation • The discoveries of polarized light and optical rotation led to the concept of molecular 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. and cinnabar are examples of optically active while aqueous solutions of sugar, 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). • 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 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 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. 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.

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

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

This Lecture is prepared by Dr. K. K. Mandal, SPCMC, Kolkata 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 t rotation, [α] λ. 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.

This Lecture is prepared by Dr. K. K. Mandal, SPCMC, Kolkata Specific Rotation • The value of [α], the so-called specific rotation, depends on wavelength and temperature which are usually indicated as 25 subscripts and superscripts, respectively; thus [α] λ 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.

t • In addition to wavelength and temperature, [α] λ 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, 20 thus [α] 589 - 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.

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

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

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

3. The specific rotation of α-D- 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 is (+)-25.10°.

Solution: The rotation of 30% (+)-2-chlorobutane will cancel that of 30% (-) enantiomer to form 60% . 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°.

This Lecture is prepared by Dr. K. K. Mandal, SPCMC, Kolkata Numerical Problems 5. What is the observed rotation when 0.1M solution of (R)-butan-2-ol is mixed with an equal volume of a 0.05M solution of racemic butan-2-ol and the resulting solution is taken in a cell of 5 cm long tube in a polarimeter? The specific 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 Problems 6. 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 (-) . 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.

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