Experiment 10
Absorption Spectroscopy
and
The Beer-Lambert Law
Purpose:
The purpose of this experiment is to learn the use of the Spectronic 20 spectrophotometer to
investigate the absorption of visible light by an aqueous solution of a transition metal ion (Cu2+,
Co2+, or Ni2+) by determining the wavelength of maximum absorption and demonstrating the
relationship between absorbance at this wavelength and solution concentration as defined by the
Beer-Lambert Law.
Background:
Spectroscopy is the study of objects based on the spectrum of color they emit or reflect.
Scientists spend much time studying the interactions between matter and energy. Because there
are several forms of energy and a large supply of matter, these studies have provided many
measurements and much knowledge about the universe and its behavior. A study of
electromagnetic energy with matter provides valuable and important information about
molecular structure and properties. In fact, some of the most convincing evidence about atomic
and molecular structure, and the origin and makeup of the universe have been obtained this way.
Light is electromagnetic radiant energy. Depending upon the point of view, light can be
thought of as having either wave properties or particle properties. The argument as to whether
light behaves as waves or particles persisted for centuries. Wave–particle duality is a theory
that proposes that all matter exhibits the properties of not only particles, which have mass, but
also waves, which transfer energy. A central concept of quantum mechanics, this duality
addresses the inability of classical concepts like "particle" and "wave" to fully describe the
behavior of quantum-scale objects. The idea of duality originated in a debate over the nature
of light and matter that dates back to the 17th century, when Christiaan Huygens and Isaac
Newton proposed competing theories of light: light was thought either to consist of waves
(Huygens) or of particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de
Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds
that all particles also have a wave nature (and vice versa).
According to the wave theory, electromagnetic radiation is composed of both electric and
magnetic fields whose waves vibrate in mutually perpendicular planes. It is the electric field of
light interacting with the electrons of matter which produces observable properties of a
substance.
Two fundamental characteristics are associated with any wave – the wavelength and the
frequency. The wavelength,  (Greek letter, lambda), is measured from the crest of a wave to the
-
adjacent crest (see figure 1). Wavelengths range from very small (measured in nanometers, 110
9
m) to quite large, several meters. The frequency is the number of waves passing a point in unit
time and is designated  (Greek letter, nu). Frequency can be expressed in cycles (or vibrations)
per second. Wavelength and frequency are inversely proportional to each other; the shorter the
wavelength, the more waves pass a point in a given time and thus the higher the frequency.
Similarly, the longer the wavelength, the lower the frequency.
Figure 1:
Wavelength and frequency are related by the speed of light (c = 2.9981010 cm/sec).
c = λν
Another important relationship is that between these quantities and the energy of light.
E = hν
or the equivalent
Where: h is Planck’s constant (6.62610
-34
E = hc / λ
Joulesec)
The greater the energy of the radiation, the shorter its wavelength and the higher its
frequency; the smaller the enrgy of radiation, the longer its wqavelength and the lower its
frequency.
Relationship of Light Absorbed or Transmitted and Observed Color
Light from the sun is composed of a continuum of energies and thus, of a continuum of
wavelengths and frequencies. Most of the electromagnetic radiation continuum is invisible to
humans; the portion we perceive is referred to as visible light. Wavelengths of visible light
-5
-5
extend from about 800 nm (8.010 cm) to about 400 nm (4.010 cm). Figure 2 shows the
entire wavelength range of the electromagnetic spectrum arbitrarily divided into regions called
bands and the portion occupied by visible light.
Figure 2: Electromagnetic Spectrum
High
Frequency ()
Low
High
Energy (E)
Low
Short
Wavelength ()
Long
It is against the high energy Ultraviolet (UV) radiation that sun screen lotions are formulated
to protect our skin in the outdoors. Our skin perceives the low energy infrared (IR) radiation only
as heat. The lamps placed over food in cafeterias emit most of their energy in the red part of the
Infrared region, keeping the food warm.
If little or none of the visible light striking our eyes is not absorbed prior to striking the eye,
the color appears white. If this band of visible light is separated into narrow bands of
wavelengths by a prism, we perceive the component colors. Isaac Newton divided the visible
spectrum into seven color bands ranging in sequence starting with the shortest wavelengths (left
to right in figure 2 above): violet, indigo, blue, green, yellow, orange, red.
When light impinges on a substance, one or more combination of things can happen to the
light. The light can be scattered, reflected, transmitted, or absorbed by the substance. The
absorbed light energy causes such changes as atomic and molecular rotation, vibrations, and
electron transitions to higher energy levels. As a result of this absorption, our eyes or specially
designed instruments may sense phenomena such as heat, fluorence, phosphorescence, or color.
Modern instrumentation can record these phenomena to a very high degree of precision.
The simplest cases are those where all incident light directed at a substance is either absorbed
or transmitted. If a substance absorbs all wavelengths in the visible range, none of the light is
reflected back to our eyes and the substance appears black. If the substance absorbs none of the
incident visible light, it appears white (all light reflected) or colorless (all light transmitted).
Colorless substances usually absorb in the UV or IR regions of the spectrum, on either side of the
visible range.
If a substance absorbs light principally in one wavelength range (generally, a number of
wavelengths on both sides of the principal absorpton are also absorbed, so a broad absorption
band results), the color perceived will be a mixture of all the wavelengths which are not
absorbed. For example, the indigo dye in blue jeans has its maximum absorbance in the 500 –
650 nm range. Because this asorbance is in the red-to-green region, the wavelengths which are
not absorbed are in the 400-500 nm range, thus, the color observed would be blue-violet. An
aqueous solution that appears yellow, a narrow range around 550 nm, means that wavelengths on
either side of yellow, primarily blues, greens and reds, are being absorbed. A green solution
would be expected to transmit green wavelengths, while blocking blues, yellows, and reds. Table
1 is a summary of the relationship between the wavelengths of colors observed and colors
absorbed.
Table 1:
Wavelength
Absorbed (nm)
410
430
480
500
530
560
580
610
680
720
Color
Absorbed
violet
blue-violet
blue
blue-green
green
yellow-green
yellow
orange
red
red-purple
Color
Observed
yellow-green
yellow
orange
red
purple
violet
blue-violet
blue
blue-green
green
Complimentary Colors:
A more fundamental grouping than Newton’s are the systems of 3 primary colors and their
secondary complimentary colors. Complementary colors are pairs of colors which, when
combined in the right proportions, produce white or black. When placed next to each other, they
create the strongest contrast and reinforce each other. They are widely used in art and design and
especially in video monitors, such as television screens. In painting, which uses subtractive
colors, the traditional primary–secondary complementary color pairs, described since at least the
early 18th century, were red–green, yellow–violet, and blue–orange. The more accurate RGB
(red, green, blue) color model, invented in the 19th century and fully developed in the 20th
century, uses additive color combinations of red, green, and blue light against a black
background to make the colors seen on video screens. In the RGB color model, the light of two
complementary colors, such as red and cyan, combined at full intensity, will make white light,
since two complementary colors contain light with the full range of the spectrum. If any of these
three colors is absorbed from white light, the complementary color is observed. The proper
combination and intensities of the three primary colors create every conceivable color and shade.
Table 2 below is a summary of the primary-secondary complimentary colors used in the RGB
model.
Table 2: Complimentary Colors
Complimentary Colors and Wavelengths of Maximum Absorption (nm)
Primary
Red
Green
Blue
690
520
480



Secondary
Cyan (Green-Blue)
488
Magenta (Red-Blue)
(non-spectral)
Yellow (Red-Green)
580
Spectroscopy:
Spectroscopy is a basic analytical technique and research tool that utilizes the interaction
bertween matter and electromagnetic energy. A spectrometer is an instrument that separates
electromagnetic radiation according into wavelengths, passes these separated wavelength bands
through a sample, and detects the intensity of the transmitted light. In analyzing a new sample, a
chemist first determines the sample's absorbance spectrum. The absorbance spectrum is a plot of
absorbance vs wavelength and shows how the absorbance of light depends upon the wavelength
of the light.
The absorption spectrum is characterized by the wavelength of maximum absorption
(λmax) at which the absorbance is the greatest (see figure 3 below. The value of λmax is important
for several reasons. It is used in order to obtain the highest sensitivity and to minimize deviations
from Beer's Law (see development below). It is characteristic of each unique compound
providing information on the electronic structure of the compound.
Figure 3:
Absorbance
 max
Wavelength
All spectrometers have the following fundamental parts: a source or radiant energy, a prism
or grating to isolate radiant energy to narrow wavelength regions, a device for holding the
sample, and a detector for measuring light intensity. Sophisticated instruments include automatic
recorders, digital readouts, computer interfaces, and arrays of detectors that allow the user to
analyze a wider range of wavelengths.
By far the most common device for measuring transmittance or absorbance of ordinary
samples in the visible light-near ultraviolet range is the Spectronic 20, a long time (50 yrs+)
instrument known for its durability and reliablity. A block diagram of how the “Spec 20”
operates is shown in figure 4 below.
Figure 4:
Monochromator
Full spectrum visible light
Source Lamp
Sampl
Detector
The output from the detector is a variable voltage, dependent on how much light passes
through the sample and then impinges on the detector (usually a photomulitpier tube). This
output is then routed to either an analog meter or digital display, depending on the model of
the Spectronic 20. The readings given by the meter or display can be either read in
absorbance (A) or percent transmittance (%T).
The Beer_Lambert Law:
The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–
Lambert–Bouguer law (named after August Beer, Johann Heinrich Lambert, and Pierre
Bouguer) defines the mathematics relating the absorption of light to the properties of the material
through which the light is traveling. The derivation of the equations used with the law involves
two principle variables.
Transmissivity:
The amount of light absorbed as it is transmitted through the substance. It is defined as the
ratio of the light intensity leaving the sample to the intensity entering the sample:
T =
I
Io
Spectrometers measure the percent (%T) transmittance of light passing through the sample.
 I 
%T =    100
 Io 
Absorbance:
Absorbance is the amount of light absorbed expressed in logarithmic terms. It is defined as
the negative logarithm (base 10) of the Transmittance.
 I
A = - log10 T = - log10  
 Io 
The law states that there is a logarithmic dependence between the transmissivity of the light
through the sample and the product of the “absorption coefficient ()” of the substance and the
distance (l) the light travels through the material. The absorption coefficient is a measure of the
rate of decrease in the intensity of electromagnetic radiation (as light) as it passes through a given
substance. The absorption coefficient can, in turn, be rewritten as a product of the molar
absorptivity ( ε) and the molar concentration (c) of the absorbing species. Molar absorptivity
(also called the molar absorption coefficient or molar extinction coefficient) is a wavelengthdependent intrinsic property of the species and is a measurement of how strongly a chemical
species absorbs light at a given wavelength. Incorporating these terms into the expression for
absorbance results in the following:
 I
A = - log10 T = - log10   =   l =   c  l
 Io 
Where: A
T
I
Io

is the measured absorbance ( absoption units, technically unitless)
is the amount of light absorbed passing through sample (transmittance)
is the intensity of the radiation leaving the sample
is the intensity of the incident radiation
is the absorption coefficient
l is the path length of the sample cell
 Epsilon is-1 the -1wavelength-dependent molar absorptivity with units
of L mol cm
c is the analyte concentration (Molarity) with units of mol/L
Absorbance vs. Solute Concentration:
The amount of light absorbed by a sample is related to the concentration, thus, the density, of the
absorbing species. The more concentrated (more dense) a sample is, the greater the amount of
light absorbed. As can be seen in figure 5 below, a plot of a series of known concentration values
versus the measured absorbance from a Spec 20 spectrophotometer results in a linear curve. Such
a curve can be used as a calibration curve, which can then be used in the determination of the
concentrations of unknown samples of the substance.
Figure 5:
.
Example Problem
What is the concentration of an unknown solution whose absorbance value was measured
at 0.46.
The solution to this problem can be obtained from either the regression equation printed
in the upper left hand corner of the plot or directly from the graph.
From the regression equation:
Y = 4.0890  X + 0.004
4.0890  X = Y - 0.004 = 0.46 - 0.004 = 0.456
0.456
X =
= 0.111 mol / L
4.0890
From the calibration chart:
a.
b.
c.
d.
Locate absorbance value (4.6) on the Yaxis
Move horizontally to right to the intersection with the calibration curve
Move vertically down to the X-axis
Interpolate the concentration value  ~ 0.111 mol/L
The Experiment:
The Spectronic 20 spectrophotometer will be used to determine the wavelength of visible
light absorbed by substances in solution. Before measurements of wavelength can be made, the
instrument must be calibrated with a reference blank (distilled water). The first part of the
experiment involves the determination of the wavelength of maximum absorption. During this
exercise, the absorbance of a stock solution will be measured at increasing wavelengths from
about 380 nm to 700 nm. Is important to note that each time the wavelength is changed the
instrument must be recalibrated.
From the plot of absorbance vs wavelength, the wavelength of maximum absorbance will be
determined. This wavelength will then be used for all subsequent measurements of the substance
solutions, regardless of concentration. As long as the wavelength does not change, it is not
necessary to recalibrate the instrument.
The stock solution will used to prepare standard solutions of known concentration. These
solutions, along with distilled water (molarity = 0.0 mol/L) will be used to prepare a calibration
curve of absorbance vs concentration. The absorbance of a solution of unknown concentration
will then be determined and its concentration determined from the calibration curve.
Pre-Lab Report & Notebook:
Download from the department data base to your hard drive or flash drive a copy of the lab
report template and the data summary table for the Hess’s Law experiment.
http://chem.gmu.edu/templates
Print the summary results tables for the Absorption Spectroscopy experiment.
Prepare the Pre-lab report according to instructor’s instructions.
Materials and Equipment:
Materials
stock solution
distilled water
Equipment
Spectronic 20 spectrophotometer
cuvettes (cells of precise dimensions)
50 ml Buret
small test tubes (labelled)
calculator
Procedure:
Sample Solutions:
Each student will be assigned one of three stock solutions. These solutions, each of which
has a unique color, are:
1. 0.200 M cobalt nitrate (red)
 Co(NO3)2
2. 0.200 M nickel nitrate (green)
 Ni(NO3)2
3. 0.200 M copper nitrate (blue)
 Cu(NO3)2
The solution that the student will use to determine the concentration of an unknown
sample will be taken from the same stock solution used to obtain the wavelength of
maximum absorption.
Cuvettes:
Cuvettes (or cells) are sample tubes of precise dimensions, made from special glass to
ensure uniform transmittance of light. Two cuvettes will be needed – one for a reference
blank (distilled water), and one for your solutions. The composition of glass may vary
from one manufacturer to another or from batch to batch. Check to see that both cuvettes
are the same brand, such as Pyrex or Kimax.
Wash and rinse cuvettes with distilled water. Rinse a cuvette with the sample solution
and then add fresh sample solution to measure the absorbance. Wipe the outside of the
cuvette with a tissue and handle the cuvette only on its top sides.
Calibration of the Spec 20 spectrophotometer:
1. Turn on the instrument and allow it warm up for about 20 minutes
2. Set the wavelength to 380 nm with the wavelength selector knob
3. With no cuvette in the instrument, set the readout display to 0% transmittance using the
left hand knob
4. Place a cuvette approximately half filled with the reference blank (distilled water) in the
instrument sample holder
5. Align the front of the cuvette with the mark on the front of the sample holder
6. Close the top of the holder and keep it closed until the sample is changed (prevents stray
light from entering the instrument).
7. Set the readout display to 100% transmittance (zero absorbance) using the right hand knob
8. Remove the reference blank. The display should read zero transmittance. If it does not,
repeat steps 3 through 6, or obtain instructors help
The absorption spectrum and the wavelength of maximum absorption:
Note: The development of the absorption spectrum requires measurement of the sample
absorbance at different wavelengths ranging from 380 nm to 700 nm.
The instrument must be recalibrated each time the wavelength is changed.
1. Obtain a 15 ml sample of your assigned stock solution of known concentration
(0.200 M).
2. Record compound name, molecular formula, and concentration
3. Place a cuvette containing some of the stock solution into the sample holder
4. Set the wavelength to 380 nm with the wavelength selector knob
5. Calibrate the instrument
6. Change the instrument to “absorbance” mode
7. Read the absorbance of the sample at 400 nm
8. Remove the cuvette from the instrument
9. Increase the wavelength by 25 nm,
10. Calibrate the instrument
11. Reinsert the cuvette into the sample holder
12. Read and record the wavelength value and absorbance
13. Repeat steps 8 through 12 increasing the wavelength by 25 nm each time until you
have reached 700 nm
14. Identify the wavelength of maximum absorbance from your data
15. Refine the maximum wavelength value by repeating steps 8 through 12 at 10 nm
increments starting about 25 nm to the left of the presumed maximum wavelength
and ending about 25 nm to the right
Calibration Curve for Absorbance and Concentration
Note: The same assigned stock solution used above will be used to create a series of solutions
of known concentration to be used in creation of a calibration curve from which the
concentration of an unknown sample of the stock solution will be determined.
1. Attach 2 clean 50 ml burets to a buret holder attached to a ring stand
2. Rinse the first buret with stock solution making sure the stop cock operates normally
3. Rinse the second buret with distilled water
4. Add about 15 ml of the stock solution to the first buret
5. Add about 15 ml of distilled water to the second buret
6. From the stock solution buret deliver approximately 3 ml of stock solution to a
labelled test tube
Note: Do not attempt to deliver an exact volume of stock solution, but whatever
volume is delivered should be recorded to the precision of the buret (0.01 ml)
7. From the distilled water buret deliver approximately 7 ml of distilled water to the test
tube, recording the exact volume delivered
8. The total volume in the test tube should about 10 ml (to nearest 0.05 ml)
9. From the stock solution buret deliver approximately 7 ml of stock solution to another
labelled test tube, recording the exact volume delivered
10. From the distilled water buret deliver approximately 3 ml of distilled water to the new
test tube, recording the exact volume delivered
11. The total volume in the test tube should about 10 ml (to nearest 0.05 ml)
12. Add the exact volumes of stock solution and distilled water added to each test tube to
determine the exact total volume of diluted solution
Note: These two solutions, plus a sample of distilled water, and a sample of the stock
solution make up the standard solutions of known concentration to be used to
create the calibration curve.
13. Calculate the concentrations of the two diluted solutions using the dilution equation:
Volconc × Cconc = Voldil × Cdil
1L
• Cconc (mol / L)
1000 ml
1L
Voldil (ml) •
1000 ml
Volconc (ml) •
Cdil (mol / L) =
Where: Cconc
= Concentration of stock solution (mol/L)
Volconc
= Volume of stock solution (ml
Cdil
= Concentration of diluted solution
Voldil
= Volume of diluted solution (ml)
14. Set the Spec 20 to the max you determined for your assigned stock solution
15. Calibrate the instrument
16. Read the absorbance value for each of the standard solutions
17. Read the absorbance value of the unknown solution
Note: Use the same cuvette for all four measurements
Rinse the cuvette first with distilled water and then with the solution to be
measured before filling it to take the measurement
Data Processing:
Use the printed Pre-lab report as a notebook to record results in the results section of the
applicable procedure.
Follow the instructions below to populate the spreadsheet file and setup the algorithms for
the spectroscopy computations.
Summarize the measured and computed laboratory results in the printed copy of the
Spectroscopy Results Summary Table.”
If required by the instructor, transfer laboratory results to the electronic files and finalize the
report.
Spreadsheet Processing:
Enter Class Data into laboratory Database
Use a lab computer to enter experimental results into the laboratory data base (Excel
spreadsheet) using the appropriate Web-based data entry form as shown in Figs 6 & 7.
Figure 10.6: Input Screens for Absorbance Results
Retrieve Class Data
Outside of class, retrieve the class data in spreadsheet form from the Department
website
http://chem.gmu.edu/results
Save the spreadsheet on your hard drive or a flash drive with an appropriate file name.
The data will be presented in the “RawData” sheet in the following columnar format:
Col
Row
1
A
2
Student Name
B
C
D
E
F
G
Chem 211 Sec 205 Spectroscopy
Student ID
Lambda
Max
Metal
Conc_
stock
Vi_A
Vf_A
3
4
H
Vi_B
I
J
K
L
M
N
O
Vf_B
Abs_A
Abs_A
Abs_B
Abs_water
Abs_Unk
Conc_Unk
Column Definitions for “RawData” sheet
Col A
Col B
Col C
Col D
Col E
Col F
–
–
–
–
–
–
student name
student ID
metal
wavelength of maximum absorption
concentration of stock solution (0.2 M)
volume of stock solution in solution A
Col G
Col H
Col I
Col J
Col K
Col L
Col M
–
–
–
–
–
–
–
final volume of solution A
volume of stock solution in solution B
final volume of solution B
absorbance of stock solution
absorbance of solution A
absorbance of solution B
absorbance of distilled water
Col N – absorbance of unknown solution
Col O – actual concentration of unknown
Create a second Excel sheet and rename it “Results”
Col
Row
1
A
B
C
D
E
Chem 211 Sec 205 Spectroscopy
M
M
M
M
Student Name
water Soln A Soln B Stock Soln
2
F
Abs
Water
3
4
G
H
I
J
K
L
M
N
Abs
Soln A
Abs
Soln B
Abs
Stock
Soln
Abs
Unknown
Slope
Intercept
M
Unknown
% Error
Column Definitions for “Results” sheet
Col A
Col B
Col C
Col D
Col E
Col F
Col G
Col H
Col I
Col J
–
–
–
–
–
–
–
–
–
–
student name
molarity of distilled water (0.0)
molarity of standard solution A
molarity of standard solution B
molarity of stock solution (0.2 M)
absorbance of distilled water
absorbance of solution A
absorbance of solution B
absorbance of stock solution
absorbance of unknown
Col K
Col L
Col M
Col N
–
–
–
–
slope of calibration curve
intercept of regression line on y-axis
concentration of unknown
% Error of unknown concentration
Algorithms to insert into applicable “ResultsMgO” cells:
Select cell A3
Enter: =RawData!A3
Select cell B3
Enter: 0.0
Select cell C3
Enter: =RawData!E3*RawData!F3/RawData!G3
Select cell D3
Enter: = RawData!E3*RawData!H3/RawData!I3
Select cell E3
Enter: =RawData!E3
Select cell F3
Enter: =RawData!M3
Select cell G3
Enter: =RawData!K3
Select cell H3
Enter: =RawData!L3
Select cell I3
Enter: =RawData!J3
Select cell J3
Enter: =RawData!N3
Select cell K3
Enter: =SLOPE(F3:I3,B3:E3)
Select cell L3
Enter: =INTERCEPT(F3:I3,B3:E3)
Transfers student name from
RawData Sheet
molarity of distilled water
molarity of soln A
molarity of soln B
molarity of stock solution (0.2)
absorbance of distilled water
absorbance of solution A
absorbance of solution B
absorbance of stock solution
absorbance of unknown
slope of regression line
intercept of regression line on
on y-axis
Select cell M3
Enter: =(J3-L3)/K3
concentration of unknown
Select cell N3
Enter your algoritym for the % error of the measured unknown concentration
Transfer algorithms to all students
Select cells A3:Nx
x = row number of last student
From “Editing” box under “Home” on Menu bar select “Fill Down” to transfer
algorithms to all students
Data Tables: Absorption Spectroscopy and the Beer-Lambert Law
Part A: Determination of max, Broad Spectrum:
Assigned “Stock Solution” (name and formula):
Concentration of Stock Solution:
Wavelength
(nm)
Absorbance
Wavelength
(nm)
Absorbance
Determination of max, Narrow Spectrum:
Wavelength
(nm)
Absorbance
Wavelength
(nm)
Value for wavelength of maximum absorbance (+/- 5 nm):
Absorbance
Part B: Calibration Curve for Absorbance versus Concentration
Sample
Number
Conc
stock
soln
(Cconc)
Vol
stock
added
V(conc)
Vol
distilled
water
added
Vol
dilute
soln
(Vdil)
Conc
dilute
soln
(Cdil)
Absorbance
1 (water)
2
3
4 (stock)
Part C: Determination of an unknown solution concentration
Unknown Number
Percent Transmittance
Concentration of Unknown (M):
(Experimental)
Concentration of Unknown (M):
(Actual)
Percent Error
Note: Remember to ask the instructor for the actual concentration before you enter your
results into the laboratory computer.