EXPERIMENT 6
ABSORPTION SPECTROPHOTOMETRY: MULTI-COMPONENT DETERMINATIONS USING
ABSORBANCE AND FIRST-DERIVATIVE DATA
This is a group experiment. All groups in each laboratory will share one set of standard solutions.
I. INTRODUCTION
This experiment involves the use of absorption spectrophotometry to quantify
concentrations of three metal ions, Co(II), Cu(II), and Ni(II) based on differences in the absorption
spectra of EDTA complexes of the ions. Principal purposes of the experiment are to illustrate:
• the use of chelating agents to develop colored complexes with metal ions,
• the use of solid-state imaging detectors for quantitative spectrophotometry,
• the use of first-derivative spectroscopy to compensate for possible instrumental drift, and
• the combined use of multiwavelength data with matrix algebra to resolve multi-component
samples without a separation step.
II. OVERVIEW
A. Options for mixtures
Most practical quantitative determinations require the quantitation of two or more
components in each sample. Two general approaches used to quantify different components in
common samples are a) to use procedures with built-in selectivity for the individual components
and b) to separate the individual components prior to the measurement step. This experiment
illustrates the first option, namely the use of a procedure with built-in selectivity for the three
components of interest. Specifically, a complexing agent, ethylenediaminetetraacetic acid
(EDTA), is used to form complexes with three metal ions that have different absorption spectra.
Then, differences in the absorption spectra are used to resolve the three components from one
another.
B. Rationale
If different components in a sample have different absorption spectra and if there are no
interactions among the components, then the absorbance at each wavelength will be the sum of
the absorbances of the individual species. By measuring the absorbances at a number of
wavelengths equal to or greater than the number of components in the sample, it is possible to
write a series of simultaneous equations in terms of the absorbances, path lengths, molar
absorptivities, and concentrations of the different species. If the path length and molar
absorptivities are known, it is possible to solve the simultaneous equations for the concentration
of each of the species in the sample. The process works best for wavelengths involving
maximum differences among the absorptivities of the different species.
C. Specific example
Metal ions such as Co(II), Cu(II), and Ni(II) react with dihydrogen form of EDTA to form
complex ions as follows:
M2+ + H2EDTA2- º MEDTA2- + 2H+
(1)
Many of the complex ions produced by such reactions are colored and absorb light in the visible
region of the spectrum. The absorption of light can be used to quantify concentrations of the
metal ions in solution.
The solid curve in Fig. 1A is the spectrum of a mixture of the EDTA complexes of Co(II),
Cu(II), and Ni(II). The other plots represent spectra of the individual complexes. Careful
examination of the shape of the spectrum of the mixture at selected wavelength regions shows
that the shape reflects features of the individual spectra. Accordingly, it is possible to select
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regions of the spectrum that emphasize spectral features of each individual component relative to
the others.
The arrows at the top of the figure represent wavelengths near points of maximum
differences among the individual components. Absorbances at these wavelengths should permit
the resolution of the three complex ions from one another. The procedure is to use standards to
calculate molar absorptivities of the individual components at the selected wavelengths. Then,
the calculated molar absorptivities are used to calculate concentrations of species in unknown
samples.
Experience with rapid-scanning spectrophotometers has shown that some of these
instruments tend to drift with time and cause problems with the use of absorbances as described
above. This problem can be solved using first-derivative spectroscopy.
The solid curve in Fig. 1B is the first-derivative spectrum of the same mixture of the
EDTA complexes of Co(II), Cu(II), and Ni(II). The other plots represent derivative spectra of the
individual complexes. Careful examination of the shape of the derivative spectrum of the mixture
at selected wavelength regions shows that the shape reflects features of the individual spectra.
Accordingly, it is possible to select regions of the spectrum that emphasize spectral features of
each individual component relative to the others.
The arrows at the top of the figure represent wavelengths near points of maximum
differences among the individual components. Derivatives at these wavelengths should permit
the resolution of the three complex ions from one another.
D. Standards and unknowns
Each group will obtain spectra for ten different solutions of known concentrations.
Seven of these solutions will be treated as standards, three solutions will be used as pretend “unknowns.”
Of the seven solutions used as standards, three will contain only one metal ion,
permitting you to record and visualize the absorption spectra for the individual complex ions. The
remaining four standards will contain different concentrations of the metal ions. Molar
absorptivities obtained using the seven standard solutions will be used to calculate the metal ion
concentrations in the pretend unknown solutions.
E. Data processing
Different approaches could be used to solve the simultaneous equations involving
absorbance and derivative data. A matrix algebraic method implemented using a spreadsheet
program will be used in this experiment.
III. ABSORBANCE/CONCENTRATION RELATIONSHIPS
The first step to understanding the procedures used here is to understand the
absorbance/concentration relationships for mixtures monitored at several wavelengths. We shall
begin with the relationship for one component at one wavelength and proceed from there to three
components at several wavelengths.
A. One component/One wavelength
According to Beer’s law, the absorbance at a wavelength,λ for a given concentration, C,
of a species is given by:
A λ = ε λbC + α λ
(2a)
where Aλ and ελ are the absorbance and molar absorptivity, respectively, at each wavelength,λ, b
is the path length (usually in cm), C is the concentration of the absorbing species, and αλ is the
intercept at wavelength, λ. Because the molar absorptivity, ελ, is constant at each wavelength
and the path length, b, is constant for all wavelengths, Eq. 2a can be simplified to:
A λ = β λC + α λ
(2b)
2
The symbol, βλ = ελb, is called the proportionality constant herein. The proportionality constant,
βλ, is the sensitivity of the method, i.e. the change in absorbance per unit of change in
concentration.
B. Three components/one wavelength
This experiment involves the resolution of three components. Assuming that
absorbances of the three components are additive, the absorbance at a wavelength, λ, can be
represented as follows:
A λ = β λ,1C1 + β λ,2C2 + β λ,3C3 + α λ
(2c)
where Aλ is the absorbance at wavelength, λ, βλ,1, βλ,2, and βλ,3 are the proportionality constants
for the three components at wavelength, λ, and C1, C2, and C3 are concentrations of the three
components and αλ is the intercept at wavelength, λ.
A similar relationship can be written for derivative data by simply replacing the path
length, molar absorptivity, and concentration. α and β terms with suitable symbols, e.g. α’ and β’.
For three components, the relationship would be:
 dA 

 = β'λ,1 C1 + β'λ,2 C2 + β'λ,3 C3 + α'λ
 dλ  λ
(2d)
C. Three components/multiple wavelengths
In this experiment you will measure the absorbances of each sample at five different
wavelengths, λ1 through λ5. We could write equations similar to Eqns. 2c and 2d for each
wavelength to obtain a total of five equations. If we set λ1 = 1 and λ5 = 5, the absorbance
equations for wavelengths 1 and 5 would be:
A 1 = β1,1C1 + β1,2C2 + β1,3C3 + α1
(2e)
A 5 = β5,1C1 + β5,2C2 + β5,3 C3 + α 5
(2f)
and
There would be three additional absorbance equations for wavelengths 2, 3, and 4 and five
analogous derivative equations. The concepts are straight forward and the notation needed to
keep track of all the players is messy. Accordingly, we shall forego the other eight equations.
Notes: The proportionality constants, β and β’, have units of M-1 or mM-1 depending on whether
concentrations are expressed as M or mM.
IV. SOLVING FOR CONCENTRATION
If we had numerical values for the proportionality constants, βλ and βλ’ and the intercepts,
αλ and αλ’, then we could solve five simultaneous equations for three unknown concentrations,
C1, C2, and C3. Standard solutions with known concentrations will be used to obtain the
calibration constants.
A variety of methods can be used to solve multiple simultaneous equations. One of the
most effective methods involves the use of matrix algebra or determinant methods. That is the
approach used in this experiment.
Two spreadsheet programs, one to calculate smoothed derivatives and to organize data
and one for the matrix-based calculations will be used to process data. These programs
(SMOOTHED DERIVATIVE_31.XLS and MULTI-COMPONENT WORKSHEET.XLS) are
described later.
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V. EXPERIMENTAL
A. Instrumentation
Spectral data for absorbance vs. wavelength will be collected by the computer using a
rapid-scanning spectrophotometer with a charge-coupled device (CCD) detector. Operating
instructions will be provided in the laboratory. Absorbances will be recorded at several hundred
wavelengths for each sample. These multiwavelength data will be copied and pasted into a
spreadsheet program described later for processing.
B. Solutions
All solutions must be prepared in distilled water. A stock EDTA solution and standard
solutions of the metal ions in 0.10 M EDTA will be provided. It will be necessary for you to
prepare diluted standards in 0.1 M EDTA.
1. Solutions provided
The following solutions will be provided:
a. EDTA (0.1 mol/L @ pH = 7). Dissolve 74.4 g of the disodium salt of EDTA
(Na2H2Y•2H2O) in about 1600 mL of water and adjust the pH to 7.0 using 6 M sodium hydroxide.
(The EDTA dissolves slowly; this solution should be prepared in advance to save time and
ensure complete dissolution). After the EDTA is completely dissolved, dilute to 2.0 L with water
and check to ensure that the pH is 7.0; readjust the pH to 7.0 if necessary.
b. Stock solutions of metal ions. Three stock solutions containing 0.05 mol/L Co(II),
0.0125 mol/L Cu(II), and 0.08 mol/L Ni(II) in 0.1 mol/L EDTA solution will be provided. Record
the exact concentrations of these stock solutions. Recommended starting materials (and
molecular masses) used to prepare these solutions are CoSO4•7H2O (281.1), CuCl2•2H2O
(170.5) and NiSO4•6H2O (262.9). The cobalt sulfate dissolves slowly and accordingly should be
prepared at least 24 h in advance.
Note: Hydrogen ion, H+, is released as the metal ions react with H2EDTA2-. The hydrogen ion
released can react with H2EDTA2- to form H4EDTA that is insoluble. If any of the stock solutions
contain insoluble crystals, the crystals are probably H4EDTA. Although these crystals will not
cause any problems, you should try to avoid getting them into your standard solutions.
2. Solutions you must prepare
a. Standard solutions. Diluted standard solutions to be prepared are summarized in
Table 1. All groups in each laboratory will share one set of standards; handle the standards
carefully! Although, all groups in each laboratory are welcome to share a single set of data for the
standards, I recommend that you collect at least two sets of data for standards and that you store
them on separate disks. Each group is responsible for obtaining an electronic record of the
spectra on a floppy disk.
Rinse ten 100-mL volumetric flasks with distilled water followed by a small volume of 0.1
M EDTA. Label individual flasks as S1, S2, S3, ... U3 as in Table 1. Add the indicated volume of
each standard solution to each 100-mL volumetric flask, dilute to volume with 0.10 mol/L EDTA
and MIX THOROUGHLY.
Each lab section will need approximately 150 mL of each stock solution (30 mL for
rinsing a buret and 115 mL for dilutions). Record the concentrations of the stock solutions and
use these values to calculate concentrations of solutions in Table 1. (The MULTICOMPONENT.XLS program is designed to do these calculations automatically after correct entry
of volumes and concentrations of standards.)
Note: Solutions A-C contain only one ion each; these solutions are used to obtain the spectra for
the EDTA complexes of the individual metal ions.
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Table 1. Volumes of solutions used to prepare diluted standard solutions.a
Volume of each standard solution (mL)
Solution descriptorsb
Co(II)
Cu(II)
Ni(II)
A-S1
0
20
0
B-S2
20
0
0
C-S3
0
0
20
D-S4
5
5
5
E-S5
10
10
10
F-S6
20
20
20
G-S7
5
10
5
H-U1
20
20
10
I-U2
10
20
20
J-U3
5
10
5
a
Use 50-mL burets to add desired volumes of the standard solutions to 100-mL volumetric flasks
and dilute to volume with 0.1 M EDTA.
b
Save spectra as SolnA, SolnB, SolnC, etc. to ensure that they are stored in order collected.
c
Symbols S1, S2, S3, U1, U2, U3, etc. refer to designations in Tables 1-1 to 1-5 in the multicomponent spreadsheet program discussed later.
Solutions A-G in Table 1 are to be used as standards. Solutions H, I, and J are to be
used as dummy unknowns. These dummy unknowns will permit you to evaluate magnitudes of
errors expected for the different ions.
b. Preparation for measurement step. Twelve 100-mL beakers will be loaned to each
group. Mark one beaker as “Blank” for 0.10 M EDTA and other beakers with appropriate letters
from Table 1 as well as each unknown. Rinse appropriate beakers with a small volume of each
standard and unknown and add sufficient solution to give a solution height of about 4 cm in the
beaker. (Different groups will use these standards; handle them carefully).
C. Measurement step
A rapid-scanning spectrophotometer will be used to collect spectral data, i.e. absorbance
vs. concentration. This instrument records data from 350 nm to 900 nm at 1 nm intervals.
Operating instructions for the instrument will be provided in the laboratory.
Set the dark current reading as instructed and then use an aliquot of the 0.10 mol/L
EDTA solution to set the 100 % T setting of the spectrophotometer. Each group should record
one spectrum for each standard. Data will be stored first on the hard drive and then
transferred to floppy disks. Procedures for handling data on the floppy disks are discussed later.
(To ensure that data are stored in the order run, it is best to label solutions and files with letters
(A, B, C, etc.) rather than numbers).
D. Data processing
This section provides an abbreviated set of instructions. Detailed instructions for using
the two spreadsheet programs associated with this experiment are included with the
spreadsheets.
You should use three totally independent Excel worksheets to process these data. Use
one worksheet for experimental data collected in the laboratory, use a second worksheet for the
derivative program, and a third worksheet for the multi-component worksheet. The Derivative 31
and Multi-component worksheets will fail if you try to use them with different pages of the same
worksheet.
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1. Smoothed derivative worksheet
Data collected in the laboratory will have one column of wavelengths (Column A) and
several columns of absorbance depending on the number of samples that were run (e.g.
Columns B-K for ten samples).
Data for wavelength and absorbances for up to ten samples (e.g. Columns A-K) should
be copied and pasted into Sheet 1 of the “SMOOTHED DERIVATIVE_31” spreadsheet program.
Wavelength data should be pasted into Column M starting at Row 14 and absorbance data
should be pasted into columns N-W starting at Row 14 for each column.
The SMOOTHED DERIVATIVE_31 program calculates 31-point smoothed derivatives in
Columns C-L and also organizes absorbance data (Sheet 2) and derivative data (Sheet 3) into
formats suitable for pasting directly into the MULTI-COMPONENT spreadsheet program.
2. Using the MULTI-COMPONENT program for standards and dummy unknowns
Both absorbance and first-derivative data should be processed using the MULTICOMPONENT program. The following procedure is described for absorbance data; a similar
procedure is used for derivative data.
This procedure assumes that both the SMOOTHED DERIVATIVE_31 and MULTICOMPONENT WORKSHEET programs are open in totally independent Excel worksheets.
a. Switch to the MULTI-COMPONENT program and click on Sheet 2. Enter volumes from
Table 1 above into Table 2-1 and concentrations of the stock standards into Table 2-2.
Concentrations for the three components in the ten samples should be calculated automatically in
Table 2-3. Click on Sheet 1, concentrations for the first seven standards should be entered
automatically in Table 1-1.
b. Switch to the SMOOTHED DERIVATIVE_31 program with wavelength and
absorbance data in Columns M-W as described above. Click on Sheet 2 and copy transposed
wavelength and absorbance data from Table 2 for the first seven standards (Cells B16-F23).
c. Switch to Sheet 1 of the MULTI-COMPONENT program and paste the wavelength and
absorbance data into Table 1-2 (Cells D18:H25).
d. Follow a similar procedure to paste transposed absorbances for Solutions U1-U3 from
Sheet 2 of the SMOOTHED DERIVATIVE_31 program to Table 1-4 on Sheet 1 of the MULTICOMPONENT program. Concentrations of the ions in these samples will be calculated
automatically in Table 1-5.
e. Enter expected and calculated values of the “unknown” concentrations in Tables 1-6
and 1-7 of the MULTI-COMPONENT program. Concentration and percentage errors will be
calculated automatically in Tables 1-8 and 1-9.
f. To use derivatives, follow steps b-e above using transposed derivative data from Sheet
3 of the SMOOTHED DERIVATIVE_31 program.
3. Procedure for unknowns
Use this procedure only if you were assigned a true unknown (in addition to dummy
unknowns described in Table 1 above). This procedure assumes that concentrations and
absorbance or derivative data for standards are in Tables 1-1 and 1-2 of the MULTICOMPONENT program. (Part 2-a, b above).
a. Paste absorbance data for one unknown in Columns N of Sheet 1 of the SMOOTHED
DERIVATIVE_31 program. (See Note below).
b. Switch to Sheet 2 for absorbance data or Sheet 3 for derivative data.
c. Copy transposed absorbance or derivative data from the first row of Table 2-2 or 3-2.
d. Switch to the MULTI-COMPONENT program and paste the data into the first row of
Table 1-4.
e.Read unknown concentrations from the first row of Table 1-5.
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Note: Absorbance data for unknowns can be pasted into any of the data columns (Columns N to
W) on Sheet 1 of the SMOOTHED DERIVATIVE_31 worksheet provided the correct data from
the transposed data tables on Sheets 2 and 3 are used. For example, data for three unknowns
could be processed simultaneously by pasting data in Columns N, O, and P and by using data
from the first three rows of the transposed data tables on Sheet 2 or 3 of the smoothed derivative
program.
VI. REPORT
In addition to the usual information, your report should include the following information.
1. Graphical data
Plot absorbance and derivative spectra (absorbance vs. wavelength and derivative vs.
wavelength) for Solution D on separate graphs using the same wavelength range for both plots.
Include these plots in your report as Figure 1 and Figure 2. Discuss differences in shapes of the
absorption and first-derivative spectra by correlating the positions of one peak, one zerocrossing, and one valley in the derivative spectrum with the corresponding position and shape of
the absorption spectrum.
2. Dummy unknowns
Include data from Tables 1-6 through 1-9 in the MULTI-COMPONENT program in your
report for both absorbance and derivative data. Calculate and report the mean values of
unsigned percentage errors (disregard signs) for results obtained using a) absorbance data and
b) derivative data.
Discuss any similarities or difference between results obtained using the two dataprocessing options.
3. Unknowns
If you were assigned a true unknown, report the concentrations (mol/L) of the three ions
in your unknown in the usual way.
VII. ACKNOWLEDGMENTS
Publication: G. Dado and J. Rosenthal, J. Chem. Ed., 67, 1990, 797-800.
Program: The EXCEL program is a modified version of one written by Dr. Michael Everly, Amy
Instrumentation Center, Chem. Dept., Purdue University.
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0.6
A
871
0.5
733
379
Absorbance
0.4
583
462
Mix
0.3
Cu
0.2
Ni
0.1
Co
0.0
350
450
550
650
750
850
950
Wavelength (nm)
0.006
B
441
548
0.004
793
Cu
0.002
Derivative (dA/dλ)
591
Mix
0.000
-0.002
Ni
Co
-0.004
400
-0.006
350
450
550
650
750
850
950
Wavelength (nm)
Figure 1. Absorption (A) and first-derivative (B) spectra of EDTA complexes of
Cu(II), Co(II), and Ni(II). Concentrations (mol/L): Cu(II) = 0.0025; Co(II) = 0.010;
Ni(II) = 0.016. Pure components: (---, ⋅⋅⋅⋅, ⋅-⋅-⋅-); Mixture:
8