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130 3 Comprehensive Insights into UV-VIS Spectrophotometry
3.10.3.3 Limitations from Beer–Lambert’s Law
Beer–Lambert’s law establishes a direct relationship between the absorbance (A) of a
given analyte, its concentration (c), and the path length (b) of the sample. This
relationship is typically linear, but certain conditions can lead to non-linear
deviations from the law. The most significant deviations from Beer–Lambert’s law
can be categorized into three primary groups. While Beer–Lambert’s law is a
fundamental principle in UV-VIS spectroscopy and is widely used for quantitative
analysis, it has some limitations and assumptions that may affect its applicability in
certa in situations:
3.10.3.3.1 Real Deviations
Beer and Lambert laws describe the absorption characteristics of solutions that have
relatively low concentrations (<10 mM) of solute and/or analyte dissolved in
it. When analyte concentration in a given solution is higher (>10 mM), then the
analyte begins to behave differently owing to the interactions with surrounding
solvent molecules or other solute molecules present in solution and hydrogen
bonding also plays a significant role in this regard.
3.10.3.3.2 Chemical Deviations
Chemical deviations from Beer–Lambert’s law are attributed to the presence of
specific chemical species in the sample under analysis. These deviations result
from various factors, including association, dissociation, polymerization, complex
formation, and interactions of the analyte with the solvent, leading to the formation
of products with differing absorption properties. The following examples illustrate
instances of chemical deviations from Beer–Lambert’ s law:
1. The phenomenon of resonance transformation occurs in phenol red, causing its
medium to shift from the acidic form (yellow) to the basic form (red), as shown in
3.12. This resonance effect leads to changes in the electron distribution of the
Fig.
bonds within the phenol molecule as the pH of the solvent changes from acidic to
basic. UV-visible spectroscopy, being an electron-related phenomenon, results in
alterations in the absorption spectrum of the sample as the pH of the solvent
changes. The acidic and basic forms of phenol red, along with their respective UV
spectra at different pH levels, serve as examples of chemical deviations from
Beer–Lambert’s law in UV-visible spectroscopy.
2. In a concentrated solution of benzoic acid, the pH is lower, and a higher
proportion of the acid exists in the unionized form compared to a dilute solution.
The absorption wavelength of the unionized benzoic acid is 273 nm, whereas for
the ionized form of benzoic acid, the absorption wavelength is 268 nm. The
increase in wavelength for the unionized form of benzoic acid at higher
concentrations results in a positive deviation from Beer’s law. Conversely, the
lower absorption wavelength (268 nm) at low concentrations of benzoic acid
leads to a negative deviation from Beer’s law.
3. Methylene blue at the concentration of 10
660 nm, but at concentration above 10
5
M exists as monomer with λ
4
M exists as dimer with λ
of 600 nm.
max
max
of
3.10 Absorbance Laws 131
Fig. 3.12 Effect of pH on the absorbance spectrum of a pH indicator. The figure illustrates the
structural transformation of a pH indicator between its acidic (yellow) and basic (red) forms. The
absorbance spectrum below shows how the indicator’s absorbance varies with pH. At lower pH
values, the yellow acid form dominates, with a peak at a lower wavelength (highlighted by the
yellow arrow). As pH increases, the equilibrium shifts toward the red base form, which exhibits a
s
absorbance peak at a higher wavelength (red arrow). This spectral shift is useful for
trong
determining pH in spectrophotometric applications
132 3 Comprehensive Insights into UV-VIS Spectrophotometry
4. In unbuffered solution of potassium dichromate, the dissociation of dichromate
ions is observed by lowering the pH.
5. Insufficient time for the completion of reaction (incomplete reaction) also
produces deviation from Beer’s law. For example, determination of iron using
thioglycolic acid before completion of reaction.
3.10.3.3.3 Instrumental Deviations
The accuracy of measurements can be affected by the quality and calibration of the
spectrophotometer used. Instrumental factors, such as stray light, detector
limitations, and wavelength accuracy, can introduce errors.
3.10.3.3.4 Due to Polychromatic Radiation
Beer–Lambert’s law is strictly adhered to when a source of monochromatic light is
available. In practice, a monochromator or filter is commonly employed to generate a
monochromatic light beam from a source of polychromatic light. Deviations from
Beer–Lambert’s law are minimal when the molar absorptivity of the analyte remains
relatively constant at the selected wavelength on the spectrometer. However, if the
molar absorptivity of the analyte varies at the chosen wavelength, the absorbance of
the analyte may not follow Beer–Lambert’s law. Figure
3.13 demonstrates that
deviations in absorbance across different wavelengths are minimal when
measurements are taken at the wavelength corresponding to λ
absorption measurements are typically made at specific wavelengths. Figure
. This is why
max
3.13
illustrates the disparities in deviations from Beer–Lambert’s law when values are
obtained at λ
of absorbance (band A) compared to other wavelengths of absor-
max
bance (band B).
3.10.3.3.5 Due to the Presence of Scattered Radiation
Scattered radiation pertains to radiation emitted by the device that falls outside the
specified selected wavelength band. Generally, the wavelength of scattered radiation
differs from that of the selected wavelength band. It has been noted that radiation
from a monochromator is occasionally contaminated with a small amount of
scattered radia tion. Typically, scattered radiation arises from the reflection and
scattering of light by surfaces like gratings, mirrors, filters, lenses, and windows.
When the analyte absorbs light at the wavelength of the scattered radiation, a
deviation from Beer–Lambert’s law is observed, similar to the deviation caused by
polychromatic radiation.
3.10.3.
Beer–Lambert
e to Mismatched Cuvettes
3.6 Du
’s law cannot be applied when the cuvettes containing the analyte and
blank solutions have varying path lengths or dissimilar optical characteristics. In
such instances, when plotting absorbance against concentration, the resulting curve
will exhibit an intercept “k,” and the equation can be de fined as:
3.10 Absorbance Laws 133
Fig. 3.13 Influence of wavelength selection on absorbance and calibration curves. (a) The
absorbance spectrum shows two bands: Band A (red) and Band B (blue). Band A is positioned at
the peak of the spectrum, where absorbance changes minimally with wavelength. Band B, on the
other hand, is located on the slope of the curve, where small wavelength variations lead to
significant changes in absorbance. (b) The concentration vs. absorbance graph demonstrates the
impact of wavelength selection on calibration curves. Band A follows a linear relationship, making
it suitable for accurate quantitative analysis. However, Band B exhibits deviation from linearity due
to wavelength sensitivity, leading to potential errors in concentration measurements. This figure
highlights the importance of selecting an optimal wavelength (preferably at the peak) to ensure
precise spectrophotometric analysis
A = εbc þ k
• Linearity assumption:
Beer–Lambert’s law assumes that the relationship between
absorbance and concentration is linear over a wide range of concentrations.
However, this linearity may not hold true for very high or very low
concentrations, especiall y if the analyte’s behavior deviates from the law due to
complex chemical interactions or nonlinear responses.
134 3 Comprehensive Insights into UV-VIS Spectrophotometry
• Single analyte assumption: The law assumes that the absorption is solely due to
the analyte of interest and does not account for the presence of other substances in
the sample that may also absorb at the same wavelength. This can lead to
inaccurate results in complex mixtures.
• Constant molar absorptivity: Beer–Lambert’s law assumes that the molar absorptivity (ε) of the analyte remains constant at a specific wavelength. In reality, ε may
vary with changes in temperature, pH, solvent, and the chemical environment,
which can affect the accuracy of concentration calculations.
• Monochromatic light: The law assumes the use of monochromatic (single wave-
length) light. In practice, spectrophotometers use a range of wavelengths, and the
law is applied over a narrow spectral range. The broader the spectral range, the
more challenging it becomes to apply Beer–Lambert’s law accurately.
• Path length variability: Variations in the path length (L ) of the cuvette can
introduce errors in concentration calculations. The assumption of a fixed path
length may not always hold, especially if the cuvette is not properly aligned or if
the sample is not uniformly distributed in the cuvette.
• Solvent effects: Changes in the solvent’s refractive index can impact the accuracy
of concentration measurements. The law assumes a constant refractive index,
which may not be the case in practice.
• Polyatomic ions and complexes: Beer–Lambert’s law assumes that the analyte
exists in a simple, unaltered form. In cases where the analyte forms polyatomic
ions or complexes, the law may not be directly applicable.
Despite these limitations, Beer–Lambert’s law remains a valuable tool for quan-
titative analysis in many applications. To mitigate potential issues, scientists often
perform calibration experiments to establish the validity of the law within the desired
concentration range and employ correction techniques when necessary. Additionally, modern spectrophotometers equipped with advanced features and software can
help address some of these limitations.
3.11 Instrument Calibration in UV-VIS Spectroscopy
Instrument calibration is a crucial step in UV-VIS spectroscopy, ensuring the
accuracy and reliability of the spectroscopic data obtained. Calibration involves
comparing the instrument’s measurements against known standards to correct for
any systematic errors and establish a reliable baseline. Proper calibration enhances
the quality of analytical results and ensures that the data obtained can be trusted for
quantitative analysis, identification, and characterization of compounds. By regularly calibrating the spectrophotometer, researchers can ensure the integrity of their
data, enhance the validity of their findings, and support consistent analytical performance over time. Proper calibration practices not only improve the quality of
quantitative analyses but also contribute to the overall credibility of scientific
research and applications.
3.12 Terms Used in UV-VIS Spectroscopy 135
3.11.1 Key Aspects of Instrument Calibration
• Baseline correction: Calibration helps establish a baseline or reference spectrum,
which is essential for accurate absorbance measurements. A proper baseline
ensures that the signal obtained is due solely to the analyte and not influenced
by the solvent or other factors.
• Wavelength accuracy: Ensuring that the wave length readings are accurate is
critical for identifying
and quantifyi
ng compounds. Calibration checks using
standard materials with known absorbance maxima can help confirm that the
instrument is measuring the correct wavelengths.
• Absorbance calibration: The instrument’s absorbance scale must be calibrated to
ensure that the values obtained correlate with actual concentrations of analytes.
This is often done using calibration standards with known concentrations to
generate a calibration curve.
• Validation of the spectrophotometer: Regular calibration and validation
that the
spectrophotometer is functioning correctly. This includes checking the
ensure
light source stability, detector response, and any drift in the absorbance readings
over time.
3.11.2 Calibration Procedure
• Preparation of calibration standards: Select appropriate calibration standards
that closely resemble the analyte of interest in terms of molecular structure and
absorbance properties. Prepare a series of dilutions to create a range of
concentrations.
• Measurement of stand ards: Measure the absorbance of each standard at the
desired wavelength. Record the absorbance values for each concentration to
create a calibration dataset.
• Creating a calibration curve: Plot a graph of absorbance (y-axis) versus concen-
tration (x-axis). A linear relationship is expected in accordance with the Beer–
Lambert law. Calculate the slope, intercept, and correlation coefficient (R
evaluate the quality of the calibration.
• Routine calibration checks: Regularly check the calibration using quality control
samples and known standards. This ensures ongoing accuracy and reliability in
the spectroscopic measurements.
• Documentation:
Maintain
detailed records of calibration procedures, standards
used, calibration curves, and any adjustments made to the instrument. This
documentation is essential for quality assurance and regulatory compliance.
2
) to
3.12 Terms Used in UV-VIS Spectroscopy
In UV-VIS spectrophotometry, two main terms namely chromophore and
auxochrome are used. The detailed descriptions of these two terms are as follows:
136 3 Comprehensive Insights into UV-VIS Spectrophotometry
3.12.1 Chromophore
Chromophore is derived from the Greek word “Chromophorus,” which means the
color carrier. It can be defined as the part of a molecule that is covalently bonded to
unsaturated groups and is responsible for imparting color after absorbing light in the
UV or visible (VIS) region. Alternatively, it can be defined as a functional group
containing multiple bonds capable of absorbing radiation above 200 nm. In broader
terms, it can also be defined as any structural feature present in a molecule that is
responsible for absorbing electromagnetic radiation (EMR) and imparting color to
the compound. For example, in nitro compounds, the yellow color is produced due to
the presence of the NO2 group, making NO2 a chromophore. Typical examples of
chromophores include NO2, N=O, C=C, C=N, C N, C=O, C=S, etc. White
light is composed of various colors (radiations). When a specific compound is placed
in the path of white light, it absorbs some specific colors from the white light while
transmitting the remaining colors. The precise color of the compound that it reflects
depends on the wavelength it absorbs from the white light. For instance, if a
compound absorbs blue light (435–480 nm) from white light, it will transmit yellow
light. As a result, the compound will appear yellow to the human eye. The transmitted or reflected color from the compound is known as the complementary color of the
absorbed color. Table
from each region of white light.
All compounds containing a chromophore in their molecules generally consist of
π electrons, and many of them also have nonbonding (n) electrons. Functional
groups that contain both n and π electrons undergo three types of electronic
transitions: n → π *, π → π *, and n → σ*, in addition to σ → σ* electronic
transitions.
Saturated hydrocarbons, on the other hand, only contain σ electrons. As a result,
σ → σ* electronic transitions are involved in these compounds. These transitions
require energy that is only available in the vacuum UV region. Therefore, saturated
hydrocarbons do not exhibit absorption in the UV-VIS region (200–800 nm) and can
be used as solvents for spectral analysis throughout this region.
Similarly, saturated compounds containing heteroatoms, such as halogens, nitro-
gen, and oxygen, have nonbonding (n) electrons in addition to σ electrons. This is
3.2 contains the complementary colors that can be produced
Table 3.2 Various regions
of visible spectrum and
their corresponding colors
Region Complementary color Wavelength (nm)
Violet Yellow-green 400–435
Blue Yellow 435–480
Green-blue Orange 480–490
Blue-green Red 490–500
Green Purple 500–560
Yellow-green Violet 560–580
Yellow Blue 580–595
Orange Green-blue 595–650
Red Blue-green 650–800
3.12 Terms Used in UV-VIS Spectroscopy 137
why, in addition to σ → σ* electronic transitions, n → σ * electronic transitions are
involved. The majority of such compounds that undergo σ → σ* electronic
transitions do not exhibit absorption in the UV-VIS region. Hence, they are commonly used as solvents for spectral analysis of analytes.
Following points should also be considered to interpret UV-VIS spectrum:
1. Nonconjugated alkenes have the absorbance at less than 200 nm of wavelength.
The
refore, they are inaccessible to UV spectrophotometer. For example, if double
bonds are conjugated in a compound, λ
1,5-hexadiene has λ
(
CH
3
(
CH
2
CH
3
CH
has λ 227 nm.
)
max
is shifted toward longer wavelength.
max
2
)
= 178 nm and 2,4–hexadiene
max
=
2. Nonconjugated compound with carbonyl group gives a weak absorption band in
the 200–300 nm region. For example, acetone which has λ
O
and that cyclohexane
has λ
)
(
= 291 nm.
max
3. Conjugation of C=C and carbonyl group shifts the λ
wavelength. For example, Ethylene ) has λ
(
CH
3
λ
max
O
) (
has λ
C
CH
3
= 290 nm.
= 279 nm and crotonaldehyde has
max
CH
(
2
(
CH
O
)
C
CH
CH
3
3
of both groups to a longer
max
2
= 171 nm, acetone
max
CH
2
= 279 nm
max
O
C
CH
)
3
3.12.2 Auxochrome
The wavelength of absorption maxima for a specific molecule or compound not only
depends on the nature of the functional group present in the molecule but also on the
nature of the chromophore. There are certain functional groups, such as -SH,
-NH2, –OH, and halogens, which are not chromophores themselves (they do not
show absorption at wavelengths higher than 200 nm). However, when they are
attached to a chromophore, they enhance the absorption of the chromophore, causing
it to shift toward a longer wavelength with increased intensity. These functional
groups are known as auxochromes. Auxochromes, when attached to a particular
chromophore, alter the ability of the chromophore to absorb light and change the
intensity of light absorption. An auxochrome is, in fact, a color-enhancing group that
contains nonbonding (n) electrons that do not absorb electromagnetic radiation
themselves in the near UV region. Still, when they are attached to a chromophore,
they alter the wavelength and intensity of the chromophore’s absorption. Therefore,
they can be defined as “any group whose presence brings about the shift of an
)
absorption band toward a longer wavelength.” For example, benzene
at 255 nm, but if any group (e.g., –OH) when attached to benzene, it increases
λ
max
(
shows
138 3 Comprehensive Insights into UV-VIS Spectrophotometry
OH
the λ
such as phenol , it has λ
max
(
)
at 270 nm. In phenol, –OH group is an
max
auxochrome. Similar ly, when –NH
increases the λ
toward longer wavelength (aniline has λ
max
compared to that of –OH group which indicate that –NH
group is attached to benzene ring, then it
2
NH
2
)
(
group is more powerful
2
at 280 nm) as
max
than the –OH group.
3.12.3 Absorption and Intensity Shifts in UV-VIS Spectroscopy
Substituent groups, when attached to a basic chromophoric structure by replacing
hydrogen atoms, can significantly influence the intensity and position of the absorption bands of the chromophore. These substituent groups themselves do not absorb
UV radiation, but their presence ca n significantly modify the absorption
characteristics of the principal chromophore. These substituents, which are often
auxochromes, have the potential to either enhance or diminish the intensity and shift
the wavelengths of absorption bands (Fig.
3.14). Following are the four types of
absorption and intensity shifts:
3.12.3.1 Bathochromic Shift (Red Shift)
When the maximum absorption wavelength (λ
) of a given compound shifts
max
toward longer wavelengths, this phenomenon is referred to as a bathochromic shift
or red shift in UV-VIS spectroscopy. A bathochromic shift occurs due to the
Fig. 3.14 Schematic representation of absorption and intensity shifts (upper part of the figure) and
their relevant descriptive terms (lower part of the figure in the form of table)
3.12 Terms Used in UV-VIS Spectroscopy 139
Fig. 3.15 Effect of alkaline medium on the absorption spectrum of a nitro-phenol compound. This
figure illustrates the structural transformation of a nitro-phenol compound in an alkaline medium.
Under neutral conditions, the molecule exhibits a maximum absorption wavelength (λ
255 nm. However, upon deprotonation in an alkaline medium, the absorption maximum shifts to
265 nm, indicating a bathochromic (red) shift. This shift occurs due to the increased delocalization
of electrons upon deprotonation, which stabilizes the excited state and lowers the energy gap
between molecular orbitals. Such spectral shifts are commonly observed in acid-base equilibria
involving conjugated systems
max
) a t
presence of an auxochrome in the compound or variations in the pH of the
surrounding medium. For example, auxochrome groups such as -OH or -OCH3,
when incorporated into a compound, tend to enhance its absorption at longer
wavelengths. An illustrative example of this shift can be observed with
p-nitrophenol, which exhibits a bathochromic shift in an alkaline medium
(Fig. 3.15). In this case, the negatively charged oxygen atom within the -OH
effectively delocalizes electrons, leading to the observed red shift in the
group
absorption spectrum.
3.12.3.2 Hypsochromic Shift (Blue Shift)
When the maximum absorption wavelength (λ
) of a given compound shifts
max
toward shorter wavelengths, this change is referred to as a hypsochromic shift or
blue shift in UV-VIS spectroscopy. A hypsochromic shift occurs due to the presence
of a functional group that disrupts conjugation or as a result of changes in the pH of
the surrounding medium. For instance, aniline exhibits a hypsochromic shift in an
acidic medium, leading to a blue shift in its absorption spectrum (Fig. 3.16). In this
case,
the loss of conjugation is responsible for the observed shift toward shorter
wavelengths.
3.12.3.3 Hyperchromic Shift
When the absorption intensity (ε) of a given compound increases, this type of shift is
known as a hyperchromic shift. Hyperchromic shifts occur due to various factors,
including the introduction of an auxochrome, which ultimately leads to an increase
in the intensity of the compound’s absorption. For example, when a methyl group
(an auxochrome) is introduced into the structure of pyridine, it enhances the intensity
of pyridine’s absorp tion spectrum, increasing from 2750 to 3560 (Fig. 3.17).