Contents
Classification of polarization
In this experiment the rate of reaction between sucrose and water catalyzed by hydrogen ion is followed by measuring the angle of rotation of polarized light passing through the solution. The angle of rotation of polarized light passing through the solution is measured using a polarized beam of He-Ne laser and polarizer. The reaction is:
C12H22O11(sucrose) + H2O + H+ => C6H12O6(fructose) + C6H12O6(glucose) + H+
Sucrose is dextrorotatory, but the resulting mixture of glucose and fructose is slightly levorotatory because the levorotatory fructose has a greater molar rotation than the dextrorotatory glucose. As the sucrose is used up and the glucose-fructose mixture is formed, the angle of rotation to the right (as the observer looks in the direction opposite to that of the light propagation) becomes less and less, and finally the light is rotated to the left.
The reaction of sucrose inversion can be catalyzed not only by hydrogen ions but also by enzymes (for example by ß-fructofuranidase). The basic mechanism for enzyme catalyzed reactions was first proposed Michaelis and Menten in 1913 and was confirmed by a study of the kinetics of the sucrose inversion.
The experiment includes two parts. In the first part you will learn the properties of the polarized light from He-Ne laser, and in the second you will study the chemical kinetics of the hydrogen ion catalyzed inversion of sucrose.
1. Malus Law.
2. Polarized light (linear and circular).
3. Optical activity.
4. Chemical Kinetics.
5. Specific rotation.
6. Operation principles of: He-Ne laser, photodiode and polarizer.
Light in the form of a plane wave in space is said to be linearly polarized. Light is a transverse electromagnetic wave, but natural light is generally unpolarized, all planes of propagation being equally probable. If light is composed of two plane waves of equal amplitude by differing in phase by 90°, then the light is said to be circularly polarized. If two plane waves of differing amplitude are related in phase by 90°, or if the relative phase is other than 90° then the light is said to be elliptically polarized.
A plane electromagnetic wave is said to be linearly polarized. The transverse electric field wave is accompanied by a magnetic field wave as illustrated.
Circularly polarized light consists of two perpendicular electromagnetic plane waves of equal amplitude and 90° difference in phase. The light illustrated is right- circularly polarized.
If light is composed of two plane waves of equal amplitude by differing in phase by 90°, then the light is said to be circularly polarized. If you could see the tip of the electric field vector, it would appear to be moving in a circle as it approached you. If while looking at the source, the electric vector of the light coming toward you appears to be rotating clockwise, the light is said to be right-circularly polarized. If counterclockwise, then left-circularly polarized light. The electric field vector makes one complete revolution as the light advances one wavelength toward you. Circularly polarized light may be produced by passing linearly polarized light through a quarter- wave plate at an angle of 45° to the optic axis of the plate.
The
component of
A, Acosθ
is transmitted and
Asinθ
is blocked out.
Recall
that the intensity is proportional to the square of amplitude, so that the
intensity transmitted is:
where
is the intensity of light incident
on polarizer.
If
unpolarized light
falls on the polarizer, ideally
only half of the light (i.e.
) is transmitted (the field of the incident wave has components parallel and
perpendicular to the polarizing axis. The incident light is a random mix of both
so each component is equal).
If
a second polarizer is now placed in the beam, with vibration direction
θ
relative to the first polarizer,
the intensity transmitted is thus
Note that the polarization direction of the light after passing the polarizer is identical to the to the polarizer orientation, however the intensity is reduced according to Malus law. When a polarized light passes a optically active substance the polarization direction changes, however the intensity remains unchanged.
Two compounds are called isomers if they have the same molecular formula but different chemical structures. Optical isomers are those in which two compounds have not only the same molecular formula but also identical bonding connections between the various atoms. A pair of optical isomers remain distinct from each other, however. because they are nonsuperimposable mirror images of each other. One optical isomer cannot be superimposed on the other, just as your left hand cannot be superimposed on your right hand. Compounds that exist as optical isomers are frequently referred to as chiral compounds, and each member of a pair of optical isomers is named an enantiomer. Molecules such as H2O and CH4, which do not exist as nonsuperimposable pairs. are called achiral. A few examples of chiral compounds are presented in Figure 1.
Fig. 1
Enantiomers have identical atoms and bonds, but the two different forms have different optical properties. If plane polarized light is passed through a solution of a chiral compound. the plane of polarization of the light is rotated either clockwise or counterclockwise. The extent of this rotation depends on the nature of the compound and the path length of the solution, as well as environmental factors such as temperature. Under the same conditions, enantiomers rotate light to the same extent, except that one rotates the plane of polarized light to the left and the other structure rotates it to the right.
Only chiral compounds rotate light in this way, and for this reason chiral compounds are often called optically active compounds (and achiral compounds are referred to as optically inactive). The reason chiral compounds rotate polarized light is complex and is fully explained only by a quantum mechanical treatment of the interaction of electromagnetic radiation with chiral compounds. One way of thinking about optical rotation, however, is to consider linearly polarized light as a superposition of right-handed and left-handed circularly polarized light. Because circularly polarized light has a handedness like chiral molecules, it is not surprising that right- and left-handed circularly polarized light interact differently with chiral molecules. Specifically, the index of refraction of a chiral substance is different for left- and right-handed circularly polarized light. Thus, the right- and left-handed components of linearly polarized light travel through a chiral medium with different velocities, and one handedness of light is retarded with respect to the other. The net effect of this retardation is to rotate the direction of the polarization of the linearly polarized light.
No easy method can predict whether a particular chiral compound will rotate light clockwise or counterclockwise. Distinguishing between two enantiomers by the direction in which they rotate the polarization of light is often convenient. By convention. left-rotating enantiomers are labeled (-) and right-rotating ones (+). Some chiral compounds rotate light more than others, and chiral compounds can be assigned specific rotation values (often designated in tables by the symbol [a]), which tell to what extent the compound rotates light. The specific rotation is defined as
where a refers to the rotation (in degrees) the electric field vector of the light undergoes in traveling a distance l (in dm) through a solution with a concentration c (in g/mL).
Note that g/mL means gramm per mL of the total solution! The procedure of preparation of a given concentration is as follows: First dilute a necessary amount of substance in small amount of a solvent and than add a solvent up to desired total volume.
The specific rotation of a solution should be independent of the concentration of the solution, because implicit in the definition of specific rotation is the assumption that the rotation of the light is directly proportional to the concentration of the solution. The specific rotation of a solution does depend. however, on the temperature of the solution and the wavelength of light traveling through it. Thus, specific rotations are often labeled with a superscript that indicates the temperature (in 0C) and a subscript that indicates the wavelength of light (in nm). The specific rotation of the solutions in this experiment might be reported as
if a He-Ne laser is used, because the wavelength of light produced by a red He-Ne laser is 632.8 nm.
The bottle that you will get in the lab will be
marked by
, while
the subscript D means 589 nm Na- D-line standard.
Chirality is an especially important concept in organic chemistry, because a vast number of organic compounds are chiral. The chiral nature of organic compounds usually results from an asymmetric carbon atom, which is one that is bonded to four different substituents. A simple example of a chiral organic molecule is CHCIBrI. The two enantiomers can be thought of as having two of the attached atoms reversed, causing the two forms to be nonsuperimposable. Many organic compounds have more than one asymmetric carbon, each of which is called a chiral center. In these compounds each chiral center has 2, or 2n total possible configurations. where n is the number of chiral centers. Some of these configurations are mirror images of each other and are called enantiomeric pairs. Any given pair of these molecules are not necessary mirror images, however, and in general are called diasteriomers.
The vast majority of important biological compounds, such as sucrose, have at least one chiral center. The structures of sucrose and quinine are shown in Figure .
Amino acids and sugars have a special labeling system to distinguish between different diasteriomers. The letters D and L. from the Latin dexter (right) and laevus (left), are used to indicate how the -H and -OH groups are attached to a particular carbon atom. Despite their names, the labels do not indicate which way the light is rotated
Interestingly, in almost all life forms, only L forms of amino acids are produced, whereas the D forms of sugars predominate. Although there is no intuitive reason for one configuration to predominate over the other, biological systems have evolved such that for many chiral compounds, only one isomer is observed in nature. This fact has profound implications for the pharmaceutical industry. Because many drugs are chiral. different isomers of the same drug can have entirely different effects on the body. One isomer of a drug may have the desired healing effect, while another may have no effect or even be harmful. Thus, controlling the chirality of biological compounds when they are being synthesized is almost always necessary, and chiral selectivity presents a key challenge for the pharmaceutical industry in developing safe and effective drugs.
Chemical
kinetics, a topic in several chemistry courses, illustrates the connection
between mathematics and chemistry. Chemical kinetics deals with chemistry
experiments and interprets them in terms of a mathematical model. The
experiments are perfomed on chemical reactions as they proceed with time.
The models are differential equations for the rates at which reactants
are consumed and products are produced. By combining models with experiments,
chemists are able to understand how chemical reactions take place at the
molecular level.
These
are characterized by the property that their rate is proportional to the amount
of reactant. It follows that the differential rate law contains the amount (or
concentration) of reactant and a proportionality constant (the rate constant):
Mathematicians
call equations that contain the first derivative but no higher derivatives first
order differential equations. Chemists call the equation d[A]/dt = -k[A] a first
order rate law because the rate is proportional to the first power of
[A]. Integration of this ordinary differential equation is elementary,
giving:
A
common way for a chemist to discover that a reaction follows first order
kinetics is to plot the measured concentration versus the time on a semi-log
plot. Namely, the concentration versus time data are fit to the following
equation:
A
plot of ln([A]) versus t is a straight line with slope -k. Alternatively, a plot
of rate versus [A] is a straight line with slope -k. From experimental data the
rate constant can be found from the slope of the appropriate plot.
Second
Order Reactions are characterized by the property that their rate is
proportional to the product of two reactant concentrations (or the square of one
concentration). Suppose that A ---> products is second order in A, or suppose
that A + B ---> products is first order in A and also first order in B.
Then the differential rate laws in these two cases are given by differential
rate laws:
In
mathematical language, these are first order differential equations
because they contain the first derivative and no higher derivatives. A chemist
calls them second order rate laws because the rate is proportional to the
product of two concentrations. By elementary integration of these differential
equations integrated rate laws can be obtained:
where
a and b are the initial concentrations of A and B (assuming a not equal to b),
and x
is the extent of reaction at time t. Note that the latter can also be written:
A
common way for a chemist to discover that a reaction follows second order
kinetics is to plot 1/[A] versus the time in the former case, or ln(b(a-x)/a(b-x)
versus t in the latter case.
A
plot of 1/[A] versus t is a straight line with slope k.
Determining
the Specific Rotation
The
observed rotation is dependent upon the path length of the light passing through
the sample compartment and is also dependent upon the number of molecules of the
isomer. The observed rotation is converted to a specific rotation by using the
following formula:
Specific
Rotation = Observed Rotation / (conc,g/ml) (length of sample tube, decimeters)
Let's
take an example: Suppose that the observed rotation of an optically active
isomer produced an observed rotation of +13.00 degrees. The sample had a
concentration of 1000g/liter and the length of the sample tube was 20 cm in
length. What would be the reported specific rotation of this dextrorotatory
isomer?
1.
Convert the concentration to g/ml
1000g / liter X 1 liter / 1000 ml = 1.0 g/ml
2.
Convert the length of the tube to decimeters knowing that 10 cm = 1 decimeter.
20
cm X 1 dm / 10 cm = 2 dm
3.
Using the above formula plug in the observed rotation, the length and
concentration.
Specific
Rotation = +13.00 / (1.0 g/ml) (2 dm) = +6.50 degrees
Let's
see if you can do one of these. Suppose that the observed rotation was -45.5
degrees of rotation. The concentration was 3.00 grams/ml and the length of the
tube was 20 cm. Identify whether this is a dextrorotatory or levorotatory isomer
and determine the specific rotation.
Answer:
The
following procedure is followed:
1.
Convert the length of the tube to dm
20
cm X 1 dm / 10 cm = 2 dm
2.
Plug in the concentration in g/ml and the length of the tube into the formula.
Specific
Rotation = -45.5 degrees / (3.0 g/ml) (2 dm)= -7.58 degrees rotation.
Since
the rotation is negative it will be the levorotatory isomer.
Design and build optical scheme that provides the rotation of polarization by 90o using two mirrors. Read about it here.
Using polarizer and photodiode to measure the intensity of the laser beam you have to check the Malus law for determination of the light intensity passed through the polarizer.
The main aim of this experiment is to measure the dependence of the reaction rate constant on acid concentration in order to validate chemical mechanism of the reaction. You have to measure the dependence of the rotation angle on time of the reaction for different initial acid concentration. Compare obtained results with literature data.
1. Specific rotation of Sucrose, Glucose and Fructose.
2. Molecular mass of Sucrose, Glucose and Fructose.
1. The unpolarized light with intensity I0 propagates through two
crossed polarizers. The intensity of the light after second polarizer is obviously equal to zero. The third
polarizer is placed between first and second polarizer. The angle between its axis and the that of the
first polarizer is equal to 30 o. What is the intensity of the light after second polarizer now?
2. Which molecules can not be optically active: H2, CH4, CHClBr2,
CHClBrF,
3. 15 g sucrose were added to 100 ml of water. What is the rotational angle if the polarized light passes through 10 cm of such solution? Assume that solution density is 1.07 g/cm3 and specific rotation is equal to 66.40 ?
4. Through what angle should an analyzer be rotated from the incoming plane of polarization to reduce the intensity to one-fourth?
a description of the experiment can be found here:
F.Daniels et al. Experimental Physical Chemistry 7th edition.
for basic knowledge in chemical kinetics:
R. A. Alberty, R.J.Silbey Physical Chemistry, second edition, John Wiley and Sons, N.Y., 1996 pp. 710 - 729.
P.W. Atkins, Physical Chemistry, sixth edition, Oxford University Press, 1998, pp.761 - 784.
for basic principles of He-Ne laser, photodiode, polarizers, light polarization etc. :
B.E.A. Saleh, M.C. Teich Fundamentals of Photonics John Wiley & Sons, Inc 1991
Eugine Hecht, Alfred Zajac Optics Addison-Wesley Publishing Company.