IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
OBJECT:
The purpose of this experiment is to introduce you to molecular spectroscopy and the extraction of
molecular parameters and thermodynamic properties from an analysis of the vibrational fine
structure of an electronic band spectrum of gaseous iodine.
REFERENCES:
Your physical chemistry text.
G. Gaydon, “Dissociation Energies and Spectra of Diatomic Molecules,” 3rd. ed. Chapman and
Hall, London, 1968.
Energy Levels of Neutral Iodine.
http://physics.nist.gov/PhysRefData/Handbook/Tables/iodinetable5.htm
M. Karplus and R. N. Porter, “Atoms and Molecules”, W. A. Benjamin, Menlo Park, CA, 1971.
EXPERIMENTAL:
Measure the gas-phase visible absorption spectrum of I2 using the Cary 300 spectrophotometer.
Instructions on the use of the Cary 300 are given in the following section. The instructor will
provide two 10 cm cylindrical quartz cells. One will be empty and will serve as the reference cell;
the other will contain iodine vapor in equilibrium with an excess of solid iodine. In handling the
cells, take care to avoid scratching the cell windows. Fingerprints can permanently damage the
optical surfaces if they are not washed off immediately with a reagent grade or better solvent.
USE OF THE CARY 300 SPECTROPHOTOMETER:
This section describes how to use the Cary 300 spectrometer to measure the visible spectrum of
gaseous molecular iodine. This document describes selected features of the instrument and will
evolve as we develop experience with the new acquisition. For a full description of the instrument,
consult the extensive Help files that constitute its manual.
I) Initialization of the computer and spectrophotometer
A) Turn on the surge protector if it is off.
B) Turn on the computer, printer, and monitor if they are off. Wait for the operating system,
Windows 95, to be loaded.
C) Click on the Cary UV Win icon to open the software window.
D) You will be measuring absorbance versus wavelength and will be using the Scan module.
Click on the Scan icon.
E) Remove any cells from the spectrophotometer, insert the cylindrical cell holder, and then
turn on the spectrophotometer.
F) Observe the messages on the left side of the status line (second from the bottom). These
messages will document the status of the initialization of the spectrophotometer. Record any
error messages as they will provide clues for repairs if the spectrophotometer is not functioning
properly. The spectrophotometer is ready when the "idle" message appears and when
numbers in the windows in the upper left and upper right that display the absorbance and
wavelength, respectively, are red.
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
II) Setup of the spectrophotometer.
A) Click on the Setup button on the left side of the window. You will access the setup
subwindow whose functions are selected by clicking on the tabs on the top of the window.
Make the following changes in the following sections:
1) Cary
a) Set the Start (higher) and Stop (lower) wavelengths in nm. In preparation for
running a baseline, these should be 650 nm and 490 nm. After the baseline is
run, the range that is scanned is set via these values. However, the spectrum
can only be scanned within the limits set in the baseline step. For example, if
the Start and Stop limits for the baseline determination are set at 650 nm and
490 nm, respectively, the spectrum could be run in the range 520-490 nm but
not 520-480 nm.
b) Set the data interval to 0.05 nm. According to the Nyquist theorem of
sampling, the data interval should be half the resolution (spectral band width) or
less.
2) Options
a) Set the spectral band width (SBW) or resolution to 1 nm.
b) Click on the Vis (visible) button under source. Only the visible lamp is
needed in this experiment and the hydrogen lamp is turned off.
c) Select the signal-to-noise mode.
d) Set the Acceptable S/N to 1000. This will configure the instrument to
measure long enough so that the signal-to-noise ratio is 1000. You may want
to increase this number to obtain better sensitivity in the vicinity of the
bandhead.
e) Set the S/N Timeout to 1 sec. This is the sampling time per data interval. If it
is long enough, the selected S/N will be achieved. If it is too low, a non-lethal
error message will appear. The value needs to be increased in this case.
3) Baseline
a) Select the Zero/Baseline option.
4) Autostore
a) Select the Store Off option unless you want to store your baseline spectrum.
5) When done with these changes, click on OK.
B) Running the baseline.
1) Wait for the wavelength window to show the starting wavelength. The message "idle"
will appear in the message line when the spectrophotometer is ready.
2) Click on the Baseline button on the left. You will be prompted to insert the blank cell
in the spectrophotometer. Click on OK when the cell has been inserted. The instrument
will automatically measure the baseline.
3) The instrument will now prompt you to block the sample light beam. Click on OK after
you have inserted an opaque card for this purpose.
4) After the completion of this step, the spectrophotometer is now ready.
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
III) Running spectra
A) Insert the sample cell containing I2 in the spectrophotometer.
B) Click on the Start button (the green stop light) to begin acquisition of the spectrum. You will
be prompted to enter a name for the run. The spectrum will appear on the screen as it is being
acquired.
C) Expand the spectrum and print it. The spectrum can be expanded automatically by clicking
on the button with the vertical double-headed arrow at the top of the menu.
D) Three series of transitions originating from v" = 0, 1, and 2 can be resolved if the
appropriate scanning parameters are used. The relevant parameters are SBW, data interval,
and S/N timeout. Scan the region between 560-590 nm, making adjustments in these
parameters until the spectrum clearly shows the three series. There is no need to scan the
entire spectrum during this phase of the experiment; if the spectral features in the region 560590 nm are resolved, then all resolvable features in the entire spectrum will also be resolved.
Make sure to record in your notebook the affect that changing various parameters make on the
appearance of your spectrum.
E) Once you have developed a method, record your best set of parameter settings in your
notebook and then scan the entire spectrum using these parameters. After recording the
spectrum, determine the wavelengths of the individual resolved bands. Expanding and plotting
the spectrum section by section will be necessary to display all the features in the spectrum.
You can read off the frequencies from the plotted spectrum or read the data directly from the
screen by using the cursor mode. If you use the “peak pick” feature of the software, be wary of
what is selected as the peak position.
F) You will note after completion of the previous step that the resolved bands at 510 nm or less
become increasingly more closely spaced and weaker. As the energy of the photon absorbed
by the molecular iodine approaches the value sufficient to dissociate the molecule, the spacing
approaches zero. The point where the spacing reaches zero is called the bandhead. It is
desirable to measure transitions as close to the bandhead as possible. The transitions close
to the bandhead are very weak so increasing the signal-to-noise is necessary to observe these
features. Your final task is to vary the signal-to-noise ratio in the hope of squeezing additional
and very valuable information from the spectrum. After determining the parameters that give
you the best resolution in the bandhead region, record these parameters in your notebook and
scan a region that contains definite peaks and goes past the bandhead region. Determine the
wavelengths of the resolved bands in this region.
G) Miscellaneous details.
1) The computer can store spectra called traces from multiple runs. To access a
particular trace, click on Graph and a submenu including a list of traces will appear.
Click on the name of the trace that you wish to display.
2) The software has a feature that calculates the first derivative of the spectrum. The
first derivative spectrum sometimes shows details that are poorly resolved in the normal
spectrum.
To calculate the first derivative with respect to wavelength versus
wavelength, perform the following steps:
a) Select a trace.
b) Click on the calculator icon to open the Math window.
c) Clear the window by clicking on the red C button.
d) Select the Derivative 1 option under Operation.
e) Set the filter interval equal to the data interval.
f) Play with various values of the filter size. Each point in the derivative spectrum is
based on filter-size points in the normal spectrum.
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
g) Click on Selected Trace to select the spectrum being manipulated.
h) Select New Graph.
i) To perform the operation, click on Apply and then the red = (equals) button. Click
OK in response to the prompt. Shortly a new window with the first derivative
spectrum will appear. Compare it with the normal spectrum.
H) Calibration of the spectrophotometer.
The last step prior to turning off the spectrophotometer is the calibration of the wavelength drive.
First remove the sample cell and then perform the following steps:
a) From the Windows Desktop, start the Validate program by clicking on the
Validate icon. The calibration routines are not accessible from the Cary UV Win
program.
b) Click on the Setup button on the left and click on the OK button which will
appear.
c) Click on the Zero button on the left and wait until the zeroing procedure has
been completed.
d) Click on the Tests button on the left. When the configuration menu appears,
select “Instrument Performance Tests” in the Enable Test Section and
“Wavelength Accuracy D2” in the Test Order section. Click on the OK button to
configure the test routine with the options that you have selected.
e) Execute the test routine by clicking on Command and then on Start in the
Command menu. The results will appear in a window. Several minutes will be
required to run the tests. You will use the calibration data at 486.00 nm and
656.10 nm. For example, if the report reads that the 486.00 nm line was found
at 486.02 nm, then the wavelength reading is 0.02 nm high and hence a
correction of –0.02 nm needs to be added to all wavelengths in the near vicinity
of 486 nm.
4) To shut down, remove the cell from the spectrophotometer, turn off the
spectrophotometer, and exit from the software. Unless otherwise instructed, leave the
computer on.
CALCULATIONS:
I)
Calculation of the transition frequencies in wavenumber (cm-1).
First correct the wavelengths directly obtained from the spectrum using the results from the
calibration. The calibration will yield corrections at two wavelengths that flank the region of
interest. Use linear interpolation to obtain the correction for any wavelength between the two.
Since the measurements were made in air, the wavelengths must be converted to
wavelengths in vacuum. The relationship used for this adjustment is:
vac = nair where n is
the refractive index of air at the wavelength involved and the relevant temperature and
pressure. In the wavelength region scanned at ambient temperature and pressure, n 
1.0002680.
II)
Assignment of the Spectrum.
Close inspection of the iodine spectrum under very high-resolution [c.f. Mecke, Ann. Physik,
71, 104 (1923)] reveals 10 series in the region 500-605 nm. Most of these series are not
resolved on the Cary so do not attempt to assign the region at wavelengths greater than 605
nm. However, the Cary 300 is capable of resolving the three series of bands for which v” = 0,
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
1, and 2. These are found in the region of the spectrum where the wavelength is less than 605
nm. Use the progressions in intensity and wavelength to discover where one series ends and
another begins. The older literature on iodine is replete with errors. The long standing
assignment of the transitions was corrected by Steinfeld et al. [J. I. Steinfeld, L. Jones, M.
Lesk, and W. Klemperer, J. Chem. Phys., 42, 25 (1965)]. The following correctly assigned
transitions should be useful in beginning the assignment of vibrational quantum numbers to
each resolved component of the spectrum.
v”
v’
vac(nm)
2
2
1
0
1
0
13
17
15
22
24
29
595.666
581.803
581.278
553.400
554.758
536.866
III) Fitting of the Data to a Model.
The electronic transition being observed is the B3+ouX1+g of molecular iodine. (Refer to Figure
1 at the end of this section. As can be seen in the figure, the ground electronic state of I2
dissociates into two ground electronic state (2P1.5) iodine atoms whereas I2 in the excited B state
dissociates into a ground state iodine atom and an iodine atom in the 2P0.5 excited electronic
state.) If one references the bottom of the ground-state potential energy surface to zero (a
common spectroscopic convention), one can derive the following expressions where all
parameters are in wavenumber:
E(X1+g) = 0 + G”(v”)
(1)
E(B3+ou) = Te + G’(v’)
(2)
Te + De’ = Eat + De”
(3)
(cm-1) = E(B3+ou) – E(X1+g)
(4)
In the above expressions, ” refers to the ground electronic state; ’ refers to the excited electronic
state. G refers to the vibrational energy eigenvalue. It can be shown that a Taylor-series
expansion of the potential energy function about re translates into an expression for G that is a
Taylor series in powers of v + ½.
G(v) = (v + ½)e – (v + ½)2exe + … (5)
The quantum number v” of the resolved transitions covers the narrow range 0-2 where the
harmonic oscillator approximation is quite good. Consequently, you will not be able to determine
the value of e”xe” directly from the data. In contrast, the quantum number v’ for the same
transitions covers a wide range and e”xe” can be determined. Combining equations (1), (2), (4),
and (5), one obtains
 = Te - (v” + ½)e” + (v’ + ½)e’ - (v’ + ½)2e’xe’
(6)
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
The method of multivariate linear regression provides a means of obtaining all four parameters in
equation (6) in one step. Multivariate linear regression is an extension of the standard linear least
squares method that employs one independent variable. Note that the frequency depends linearly
on the parameters and that the equation has three independent variables: -(v” + ½), (v’ + ½), and
–(v’ + ½)2. The parameter e is associated with the independent variable -(v” + ½) and so on.
The multivariate linear regression can be performed using the multiple regression module of
NCSS. Set up an NCSS spreadsheet with the frequencies in the first column, v” in the second
column, and v’ in the third column. Use spreadsheet techniques to define the independent
variables identified above in the next three columns. Once your spreadsheet is setup, access the
regression module with following sequence of mouse clicks: Analysis, Regression/Correlation, and
Multiple Regression. After you have fit the data to the model discussed above, pay careful
attention to the table of residuals, the differences between the observed and predicted values of
the frequency. Large deviations indicate an input error or an incorrectly assigned transition. You
can estimate using a propagation-of-errors analysis the anticipated error in the wavenumber from
the wavelength resolution of the Cary 300.
With the spectroscopic parameters in hand, estimate the value of De’ by using the approximate
expression
De  e2/4exe
(7)
Equation (7) gives a fairly accurate estimate of De when the electronic potential energy function is
well described by a Morse potential as is the case with the B state of iodine. De”, the desired
dissociation energy of the ground electronic state, can be obtained via a thermodynamic cycle (c.f.
equation (3) and the figure below). To this end, you will need an accurate value of Eat which can
be obtained from the cited NIST Web site or from Charlotte E. Moore’s monumental opus Atomic
Energy Levels. D0’ and can be obtained from De’ and De” by applying the zero point energy, i.e.
G(v = ½). An approximation for e”xe” can also be obtained from Eq. (7).
III)
Thermodynamic Calculations.
Using the ground-state parameters obtained from the analysis of the spectrum and standard
results from statistical mechanics (c.f. the summary included with the write-up), calculate values of
Cp at 25ºC and the equilibrium constant Kp at 25C for the dissociation reaction I2(g) = 2 I(g). The
ground-state bond length of iodine is 2.666 Å. The ground state of atomic iodine is 2P1.5 with a
degeneracy of 4. The electronic degeneracy of the ground electronic state of molecular
iodine(1+g) is one.
The following short discussion is included to steer the student past some of the reefs in the
calculation of Kp. The simplest route to the equilibrium constant is the well known result
G = -RTlnK
(8)
G = H - TS
(9)
The standard entropy change is calculated from the stoichiometry of the dissociation reaction:
S = 2S(I) - S(I2)
(10)
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
The standard entropy of each chemical component is calculated using statistical mechanics.
Employ the appropriate equations as provided on the information sheet to calculate the various
contributions to the entropy for I and I2.
A different approach is required to calculate the standard enthalpy change. What we want is the
entropy change for the reaction at 298K, H ro 298K  . Looking at Figure 1, we can see that the
internal energy change at absolute zero, Ero 0 K  , is D0”, since all molecules will be in the ground
electronic-vibrational-rotational-translational state. Remember also that, for an ideal gas
H = E + pV = E + nRT
(11)
We can use this information in a cyclic process to then calculate H ro 298K  as follows:
I2(298K)
H ro 298K 

H o I 2 ,0K   H o I 2 ,298K 
I2(0K)
2I(298K)

2 H o I ,298K   H o I ,0 K 
H ro 0 K 
2I(0K)
From this graph, the equation for H ro 298K  can be easily derived. The enthalpy difference,
Hº(298K) – Hº(0K), is simply the enthalpy change associated with heating the substance from 0K
to 298K and can be calculated from statistical mechanics.
IV)
Statistics.
The NCSS report for the multivariate regression will yield the standard deviation (error) for the
parameters Te, e”, e’, and e’xe’. Using the appropriate Student’s t value, calculate the 95%
confidence interval of each parameter. Calculate an uncertainty for De’ and e”xe” using a
propagation of errors analysis. For De’, do not overlook the contribution of the covariance term.
You may use this result as an estimate of the uncertainties of Do”, De”, and Do”. Ponder the basis
for this short cut. Employ the following hints in calculating the uncertainty for Kp. The error in Kp
is dominated by the error in Do” and Kp is proportional to exp(-NAhcDo”/RT). Do not estimate an
uncertainty for Cp.
V)
Report.
Include the following with your report: the report sheet, all notebook entries and computer output,
the assigned spectrum, the NCSS spreadsheet, the NCSS regression report, and notes on all of
your calculations.
For the long report, in addition to sections on the experimental method and the analysis of the
spectrum, you should include a discussion section describing what you learned about the
molecule including a description of the orbitals involved in the transition and their relative bonding
properties as determined from the dissociation energies and the force constants.
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
Revised FJG Jan. 3, 2002
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
Figure 1: Potential Energy Surfaces of Iodine
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IODINE ABSORPTION SPECTRUM (CARY 300 VERSION)
IODINE ABSORPTION SPECTRUM REPORT SHEET
Date Expt. Completed: ________________
NAME: _____________________________________
Date Report Due:
________________
Date Report Submitted: ________________
Spectroscopic
Parameter
Experimental Result
Literature Value
Te
_________________________
_________________________
e”
_________________________
_________________________
e”xe”
_________________________
_________________________
e’
_________________________
_________________________
e’xe’
_________________________
_________________________
De’
_________________________
Do’
_________________________
De”
_________________________
Do”
_________________________
_________________________
Kp (298 K)
_________________________
_________________________
Cp (298 K)
_________________________
_________________________
_________________________
Literature Sources: ______________________________________________________________________
______________________________________________________________________________________
Instrument Parameters:
Main spectrum
Bandhead Region
data interval
______________________
______________________
SBW
______________________
______________________
S/N
______________________
______________________
S/N Timeout
______________________
______________________
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