Polarimetry_v8e.docx
PolarimetryandOpticalRotation
An experiment in which students use a polarimeter to determine the dependence of the optical rotation on
enantiomer, concentration, and path length.
1
1.1
OBJECTIVES
EXPERIMENTAL GOAL
Students measure the optical rotation of the enantiomers of carvone, and determine the effect of path
length and concentration on the measured optical rotation.
1.2
PREREQUISITE SKILLS AND KNOWLEDGE
Students should have completed the Chirality and Optical Activity experiment, or have some familiarity
with the properties of polarized light and optically active materials.
1.3
RESEARCH SKILLS
After this lab, students will have had practice in:
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1.4
following laboratory protocols
using a laboratory notebook
using LabVIEW to control and collect data from a sensor
using a polarimeter to measure optical rotation
organizing data
using Excel to analyze experimental data
using R to fit experimental data
using optical rotation to measure concentration or specific rotation
LEARNING OBJECTIVES
After this lab, students will be able to:
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Use optical rotation to characterize a substance
Measure the specific rotation of an optically active molecule
Use the known specific rotation and the measure rotation to measure the concentration of a
substance
Predict the effect of wavelength on the measured rotation of a substance
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2
2.1
PRE-EXPERIMENT ASSIGNMENT
POLARIZATION AND THE LAW OF MALUS
In the previous experiment, you determined that the intensity of polarized light transmitted through a
polarizer, is described by the equation:
(1)
where I0 is the incident intensity, It is the transmitted intensity and θ is the difference in the angle of the
initial polarization and the axis of the polarizer. This relation is called Malus’ Law, named after physicist
and mathematician Étienne-Louis Malus, an early investigator of the polarization of light.
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In this experiment, you will use Malus’ law to fit your data. The optical rotation angle  shows up as the
fitting parameter p2 in the equation you used to fit your data in the previous experiment:
y = p1 cos2 (x + p2)
(2)
What is p2 for a substance that is not optically active?
What characteristic of the curve does p1 describe?
2.1.1
Optical Rotation
Chiral molecules and crystals will rotate the plane of linearly polarized light. In the early 1800’s, Francois
Jean Dominique Arago observed this phenomenon in quartz crystals, while Jean Baptiste Biot observed it
in liquids and gases of organic substances.
An optically active substance rotates the polarization of the light by an angle that is characteristic of that
substance, but it depends on a number of variables including the temperature, and solvent, if the substance
is in solution.
The degree of rotation  through a solution or a pure liquid depends on the:

Specific rotation of the substance, in units of deg·mL·g-1·dm-1
T
Ambient temperature

Wavelength of the light, in nm
c
Concentration of a solute, in g/mL, or the density of a pure liquid (neat) in g/mL
l
Path length, in dm
This relationship is described by Biot’s equation:
(3)

The specific rotation is a characteristic property of the optically active compound. If the specific rotation
is positive, the compound is said to be dextrorotatory, and if negative, it is said to be levorotatory.
What are the units of specific rotation of a substance?1
Historically, specific rotation measurements have been recorded using light from the excitation spectrum
of sodium. Upon excitation, sodium emits a strong yellow light, a double peak, centered at 589 nm. For
your measurements, you will be using a red laser with a wavelength of 650 nm and a green laser with a
wavelength of 532 nm. Thus, in this experiment, you will also determine how the wavelength of the light
affects the degree of optical rotation.
2.1.1.1 Example calculation
An example is worked out using the data shown below for two runs using the red laser and two runs using
the green laser. In both cases the length of the cell is 10 cm = 1 dm.
Data collected using the red diode laser (650 nm) and 20C:
Material in 100 mm cell
p2 (rad)
p2 (rad)
Air
-0.0370
-0.0380
Caraway oil
0.651
0.649
Spearmint oil
-0.867
-0.848
Data collected using the green diode laser (532 nm) ) and 20C:
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Material in 100 mm cell
p2 (rad)
p2 (rad)
Air
-0.0270
-0.0130
Caraway oil
1.079
1.066
Spearmint oil
-1.44
-1.39
First, to calculate the optical rotation  of the sample in the cell, subtract the background for each
measurement.
p2sample
p2airandcell
For the first caraway run using the red laser, the optical rotation of the sample in the cell is
0.651
0.037 = 0.688 rad
Solve equation (3) for the specific rotation:
(4)
The length of the cell in decimeters is 1 and the density of caraway oil can be assumed to be the same as
the density of carvone 0.96 g/mL. Plugging in the values gives:
0.688
1.00
∙ 0.96 /
0.717
Recall that 2π radians = 360. Thus,
0.717
180°
41.1 °
⁄
2.1.1.2 Using an Excel spreadsheet
These calculations are much more easily done using a spreadsheet, which can be prepared before
collecting data. One possible arrangement is detailed below.*
Before any data is collected, you can prepare the spreadsheet for three runs.
To average the runs and calculate the standard deviation, insert the appropriate equations:
*
Note that the polarimetry VI currently reports rotation in degrees, while R works in radians. You can choose to set
up your Excel spreadsheet to work with radians or degrees. You can also choose to add a line to the end of your R
script to convert the final fitting parameter p2 from radians to degrees.
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Excel will complain while the cells are still empty. Check by entering some data.
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Do all the remaining calculations on the mean values:
The dollar sign $ in front of a cell column or row designation means that that row and/or column will be
unchanged, no matter where the equation is placed. Thus when I copy this cell and paste it into the row
below, it will read:
Use equation (4) to complete the next column and (if necessary) convert to degrees for the last column.
Compare your results to these.
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To find the specific rotation at the traditional sodium emission wavelength of 589 nm, you will need to
plot the specific rotations versus wavelength and interpolate:
Setting x=589 nm in each equation gives the specific rotation at 589 nm.
2.1.2
Practice Data
Use the data below to practice the calculations you will be doing in the lab. Note that the concentration, c,
of sucrose in these solutions is given by the proportion. Thus, 10% sucrose has a concentration of 0.10
g/mL.
Data collected using the red diode laser (650 nm):
Material in 100 mm cell
p2 (rad)
p2 (rad)
p2 (rad)
DI Water
0.0380
0.0339
0.0284
10.0% sucrose
0.138
0.140
0.134
20.0% sucrose
0.241
0.236
0.243
Data collected using the green diode laser (532 nm):
2.2
Material in 100 mm cell
p2 (rad)
p2 (rad)
p2 (rad)
DI Water
0.0846
0.0860
0.0832
10.0% Sucrose
0.211
0.203
0.205
20.0% Sucrose
0.331
0.323
0.322
PREPARE FOR THE EXPERIMENT
Read through the entire laboratory manual and make sure you know what you will be doing at each step.
Think carefully about how to answer the questions. Prepare an Excel workbook with space for data and
include all the calculations you will need to make. Practice with the data supplied above. When you feel
ready, test your preparation and your spreadsheet with the pre-experiment quiz on e-Learning.
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3
LABORATORY MANUAL
In this experiment you will measure:
1. The purity of the oils containing each of the carvone enantiomers
2. The pathlength dependence of carvone optical rotation
3.1
MATERIALS CHECK OFF LIST
Each group of 2-3 students will have:
Laptop with LabVIEW and RStudio
SensorDAQ interface with USB cable
Pasco optics bench
Polarizer
Polarization analyzer
Aperture bracket
Vernier light sensor
Rotary motion sensor
2 Adjustable lens holders
Red or green diode laser
Each large group of two small groups will share
2x 100 mm polarimetry cells containing air
100 mm polarimetry cell containing caraway essential oil
100 mm polarimetry cell containing spearmint essential oil
200 mm polarimetry cell containing caraway essential oil
200 mm polarimetry cell containing air
Additional red and green diode lasers
3.2
SAFETY AND WASTE DISPOSAL PROTOCOLS
Do not loosen or tighten the polarimeter cell fittings. Over-tightening can affect the optical properties of
the cell window in addition to causing leaks or breakage. Loosening can lead to leaks, which will also
affect experimental results. Report any leaks immediately.
Carvone at full strength is an irritant that can harm skin, eyes, and lungs. Use care while handling the
carvone-containing cells.
Both the red and green lasers can damage the eye. Goggles must be worn during this experiment.
All materials should be saved to use again.
3.3
3.3.1
EXPERIMENTAL PROCEDURE
General Instructions for Measuring Optical Rotation
Before you start, check to make sure your laser is aligned through the middle of the polarimetry cell and
into the light sensor. Follow the same procedure you used in the previous experiment when you measured
the dependence of light intensity on rotational angle in air.
For each measurement, you will also need to measure the optical rotation of a blank cell. For the carvone
measurements, the blank cell will be a cell containing only air.
Q1. Why is a blank cell measurement needed? Explain why the blank cell for carvone contains only air.
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For each measurement follow these steps:
1. Record the wavelength of your laser.
2. Choose one of the polarimeter cells and place it carefully in place on the mounts.
3. Record the run number and all relevant information about the cell in your data table and in your
notebook
4. Use a piece of paper to verify that the laser light is aligned through the cell and into the light
sensor.
5. Load your VI and make sure the settings are correct.
6. Start data acquisition and slowly rotate the polarizer attached to the rotary motion sensor through
360°.
7. Rotate the polarizer back until the angular position reads 0.00 degrees on the digits scale. Press
‘Stop’.
8. Fit this curve using Malus’ Law, equation (2). Record the results of the fit in your data table.
Repeat these steps for each of the remaining cells.
Record at least three curves for each rotation measurement. Average the rotations, and report the sample
standard deviation (STDEV.S) as the error in each measurement.
3.3.2
Measurement of Optical Rotation of Enantiomers of Carvone
Collect the cells containing essential oils of caraway and spearmint from your instructor. Be sure you also
have the appropriate blank cell.
Record and fit the rotation curves for each cell.
Q2. What do you notice about the two curves?
Replace the red diode laser with the green diode laser and repeat the above measurements.
3.3.2.1 Analysis
Q3. Calculate the specific rotation and error in rotation of each essential oil for both the red diode laser
(650 nm) and the green diode laser (532 nm). The density of carvone is 0.96 g/mL.
The accepted specific rotations of S- and R-carvone are +61° / (dm·g/mL) and -61° / (dm·g/mL),
respectively. These values were measured using light at the wavelength of the sodium D line (589 nm).
Since you have measurements at two wavelengths on either side of this wavelength, you can interpolate
your measurements to make them comparable to the accepted values.
Q4. What is your interpolated value at 589 nm?
Q5. Paste a snip of your interpolation graph here:
Q6. Which oil is S-carvone and which is R-carvone? Briefly explain the reasoning behind your answer.
Q7. Assuming that any differences from the published values are due to lack of purity, calculate the %
purity of each essential oil.
3.3.3
Pathlength Dependence of Carvone Optical Rotation
Q8. Predict the relationship between path length and optical rotation. Be specific. (For example, do you
expect the relationship to be linear or non-linear?) Explain your reasoning.
To test your hypothesis, you may use polarimetry cells of three different lengths (0 mm, 100 mm and 200
mm), each of which contains caraway oil.
Plan an experiment that will allow you to determine the relationship between path length and optical
rotation.
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Q9. Describe your planned experiment.
Carry out your experiment.
Q10. Describe your results graphically.
Q11. What equation fits your data?
3.4
POST-LAB ASSIGNMENT
Work with your group to submit a one-page abstract in class, describing the experiment you just
completed. Include relevant, publishable figures in your abstract.
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