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Introduction to Spec UV–Vis
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Introduction, Theory, Background
The Nature of Light
Spectroscopy—The Interaction of Light with Matter
Transitions in the UV-Visible Region
Absorption of Light by a Chromophore
The Beer–Lambert Law
Transmission and Absorption Spectra
Light Absorption in Highly-Conjugated Double-Bond Systems
UV–Visible Spectrophotometers
Single-Beam Instruments
Double-Beam Instruments
Diode Array Spectrophotometers
Spectroscopic Studies of Acid–Base Indicators
Acid–Base Indicators
The pKa of an Acid–Base Indicator
The Isosbestic Point
Distribution Diagrams
Citations
User’s Guide
Student Exercises
Instructor Notes
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3
4
4
5
6
7
8
8
10
12
12
12
13
14
15
15
Guide.pdf
Student.pdf
(available from JCE Online)
Introduction to Spec UV–Vis
Introduction to Spec UV–Vis
Stephen W. Bigger
School of Life Sciences and Technology, Victoria University of Technology, Melbourne, 8001, Australia
Introduction, Theory, and Background
The Nature of Light
One model that accounts for some of the observed properties of light considers
light to be a wave comprised of electric and magnetic field vectors that oscillate
sinusoidally at a given frequency (1, 2). The light wave travels through space at
a constant velocity. The oscillation of the electric and magnetic fields induce
oscillating magnetic and electric fields (1–4) at right angles. The oscillating electric and magnetic field vectors are thus said to be self-inductive, which accounts
for the observation that light or electromagnetic radiation propagates indefinitely in the universe.
If light is considered to be an electromagnetic wave then its velocity, frequency,
and wavelength are related by the simple formula:
c = νλ
(1)
where c is the velocity of light (2.998 × 108 m s–1), ν is the frequency (Hz or s–1),
and λ is the wavelength (m) (1, 2, 5). The frequency is the number of oscillations
made by the wave every second and the wavelength is the distance between two
adjacent wave crests or troughs (1, 2). The velocity of light is a constant.
The visible and ultraviolet (UV) regions of the spectrum are collectively referred to as the UV–visible spectral region (6, 7). This region constitutes only a
small part of the entire electromagnetic spectrum (1). Wavelengths in the UV–
visible region are usually expressed in units of nanometers (1 nm = 10–9 m).
The visible region extends from ca. 800 nm (red region) to ca. 400 nm (blue
region) and the UV region extends from ca. 400 nm to 200 nm (1, 2, 8, 9). The
color of light is determined by its wavelength, and hence the frequency. The
wavelength and frequency are related to one another by equation 1. For example, light that has a wavelength of 750 nm appears red and has a corresponding frequency of 3.997 × 1014 Hz; light that has a wavelength of 430 nm is
violet and has a frequency of 6.972 × 1014 Hz (1).
It is sometimes convenient to treat light as though it were comprised of individual particles, or photons (2). In 1900, Max Planck related the energy, E, of a
photon to its frequency, ν :
E = hν
(2)
where h is Planck’s constant and is numerically equal to 6.626 × 10-34 J s (1, 5).
Upon combining equations 1 and 2 the following expression can be derived for
the energy of a photon of light as a function of its wavelength (1, 2, 5):
E = hc/λ
(3)
Thus the energy of a photon of light is inversely proportional to its wavelength.
Red light is associated with the low-energy end of the visible spectrum and blue
light is associated with the high-energy end (2). Ultraviolet light has an even
higher energy per photon than blue light.
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Introduction to Spec UV–Vis
An alternative means of specifying a region of the electromagnetic spectrum is
by the use of wavenumbers (1, 2, 5). The wavenumber, ν , is the number of
wavelengths of electromagnetic radiation per cm and is directly proportional to
the energy of the light (1, 8, 9):
ν = 1/λ = ν/c
(4)
where ν has units of cm–1, λ is expressed in cm, and c is expressed in cm s–1.
Wavenumbers are most commonly used to characterize electromagnetic radiation in the infrared (IR) region of the spectrum (1).
The power of a beam of light is defined as the amount of energy delivered per
unit time per unit area (1, 2). In terms of the wave model of light, the power of
the beam is related to the amplitude of the oscillation (3). In the case of the
particle model of light, the power can be thought of as the number of photons
that pass per unit time though a unit of area (i.e. a photon flux). In the latter
model, each photon of monochromatic light possesses the same, discreet amount
of energy and so the power of a beam of light will be measured in units of W m-2.
Skoog et al. (1) point out that the terms power and intensity are often used
synonymously, which is not strictly correct since the latter is defined as the
power per unit solid angle. Indeed, in some textbooks (10, 11) the term intensity
seems to have been defined incorrectly in this way.
Spectroscopy—The Interaction of Light with Matter
Prior to the 1950s, the structure of a chemical substance was usually deduced
from information derived from qualitative tests such as the characteristic reactions of functional groups and various other chemical reactions that were designed as structural probes. Most of these tests have been replaced by instrumental methods that involve spectroscopic analysis. Spectroscopic methods are
based on examining how an atom or molecule responds when it absorbs energy
from an applied source of electromagnetic radiation (5, 12). Examples include:
UV-visible spectroscopy, infrared (IR) spectroscopy, and nuclear magnetic resonance (NMR) spectroscopy (1, 5, 6). Mass spectrometry (MS) is often included in
this list but this method does not strictly involve obtaining structural information about a molecule directly by measuring the absorption and/or emission of a
beam of electromagnetic radiation.
If an atom or molecule is exposed to a source of electromagnetic radiation it
will, under certain conditions, absorb energy from that source; this causes it to
change from a low-energy state to a state of higher energy (1, 8). The particular
energies absorbed or emitted by an atom or molecule provide information about
its structure and the systematic recording of these energies constitutes the basis of spectroscopic studies. There is a link between the sort of electromagnetic
radiation that is absorbed or emitted by an atom or molecule, and the type of
rearrangement or excitation that occurs within it as a result. Some of the major
spectroscopic regions together with the corresponding types of atomic or molecular excitations that are induced by these regions are summarized in Table␣ 1.
Table 1. The major spectroscopic regions and the corresponding type of atomic or molecular
excitations induced
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Spectroscopic Region
Approx. Wavelength Range
Excitation
UV-visible
700 nm to 200 nm
electronic
Infrared
1 × 10–4 m to 700 nm
vibrational
Microwave
0.1 m to 1 mm
rotational
Radio frequency
> 0.1 m
nuclear spin states
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Introduction to Spec UV–Vis
Absorption spectrophotometers are instruments that are used to measure the
amount of electromagnetic radiation that is absorbed by a sample (1, 2). The
sample is placed in a compartment through which a beam of radiation passes. A
detector measures the amount of absorption of the electromagnetic radiation
by the sample as the frequency (wavelength) of the incident radiation is varied.
The detector is used to compare the radiant power of the beam before it is passed
through the sample (i.e. the incident power) with its radiant power after it has
passed through the sample (i.e. the transmitted power) (1, 6).
When a frequency is reached at which the sample absorbs radiation, the detector senses a decrease in the transmitted power. The graphical representation of
the absorption pattern of an atom or molecule is called an absorption spectrum
(1, 6) and this is very characteristic of the particular species. Valuable information about the structure of an atom or molecule can be obtained from the careful interpretation of its spectrum.
Transitions in the UV-Visible Region
The absorption of electromagnetic radiation from the UV-visible region of the
spectrum causes electronic excitation to occur in atoms and molecules (1, 5, 7,
13). This means that the amount of energy embodied in a UV-visible photon is
sufficient to cause an electron in an atom or molecule to undergo a transition
from its usual ground state to an excited state that is usually the orbital of next
highest energy.
In the case of molecules, excitation by UV-visible light usually involves the promotion of electrons in the highest occupied molecular orbital (HOMO) to the
lowest unoccupied molecular orbital (LUMO) (7, 8, 13). Electrons involved in πbonds, and conjugated π-bonds in particular, are most susceptible to excitation
by UV-visible light. Some examples of structural moieties containing π-electron
systems are given in Table 2.
Table 2. Examples of moieties containing π-electron systems
Moiety
Structure
Alkene
>C=C<
Alkyne
–C≡C–
Carbonyl
>C=O
Diene
>C=CH-CH=C<
Imine
–N=CH–
The structural units in conjugated compounds that absorb electromagnetic radiation in the UV-visible region are called chromophores.
Absorption of Light by a Chromophore
Consider the passage of a light beam of certain wavelength, λ, through a sample
of path length b containing an absorbing species whose concentration is c (see
Fig. 1). The power of the incident beam is P0 and the power of the transmitted
beam is Pt (1, 2). In the path length element db, the power of the beam decreases by dP.
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path length, b
P0
Pt
solution
db
Figure 1. Absorption of light by a chromophore.
To quantitatively measure the amount of radiation absorbed (or transmitted)
by the sample, it is useful to define two dimensionless quantities that are associated with the ratio of the radiant powers of the incident and transmitted light
beams (1, 5, 6, 12, 14). These are: T, the transmittance and A, the absorbance or
optical density (OD):
T = Pt/P0
(5)
A = log10(P0/Pt)
(6)
The transmittance is often expressed as a percentage, %T, and the absorbance
and transmittance are related (12) by equation 7:
A = –log10(T) = log10(1/T)
(7)
The Beer–Lambert Law
The relationship between the concentration of an absorbing species and the
absorbance can be quantified in terms of the Beer–Lambert law (1, 5, 6). Although the application of the Beer–Lambert law is most commonly associated
with the UV–visible spectral region, it is important to note that it applies to all
other spectral regions. Furthermore, it is normally assumed to hold for both the
absorption of light by a collection of atoms (as in the case of the linear calibration region in atomic absorption spectroscopy) and the absorption of light by a
collection of molecules (as in the case of UV–visible spectrophotometry) where
the OD is sufficiently low. The Beer–Lambert law applies to the absorption of
monochromatic radiation and, in the case of UV–visible spectrophotometry, it
works very well for dilute solutions (ca. < 0.01 M) of most substances. However,
this law does fail if applied to concentrated solutions where solute molecules
influence one another because of their close proximity (2).
The Beer–Lambert law can be derived by considering the situation depicted in
Figure 1. The fractional degree of absorption of light, dP/P in the path element
db is proportional to both the concentration of the absorbing species and the
thickness of the sample (1, 2, 12). This can be expressed mathematically as
follows:
–dP/P = kc × db
(8)
where k is a constant and the negative sign denotes the decrease in the power of
the light beam upon its absorption. Integrating between the corresponding limits of (P0, Pt) and (0, b) gives:
ln(P0/Pt) = kbc.
(9)
Thus if absorbance is defined as in equation 6, then 2.303A = kbc and so the
Beer–Lambert law can be written as:
A = εbc
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(10)
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Introduction to Spec UV–Vis
where the constant ε equals k/2.303 and is known as the molar absorptivity or
extinction coefficient (1, 5, 14). Numerous derivations of the Beer–Lambert law
are given in the educational literature (15–23).
If b is expressed in units of m and c is expressed in mol m–3, then the units of ε
are m2 mol–1. The most common optical path length used in UV–visible spectrophotometry is 1 cm (2) and it is also common to express concentrations in units
of molarity (i.e. mol L–1 or M). In practice, it is often convenient in calculations
to retain the path length as 1 cm and express the concentration in units of M. In
such cases the units of ε are M–1 cm–1 (12). The conversion factor between the
two different units of ε is 1 m2 mol–1 = 10 M–1 cm–1.
From equation 10 it is clear that, for relatively dilute solutions, the extent of
any absorption of electromagnetic radiation is directly proportional to the concentration of the absorbing species, although in some cases the Beer–Lambert
law is observed to hold even at high concentrations (24). Thus, from the analytical point of view, absorbance measurements can be used to quantify the concentration of an analyte (1, 6). Indeed, the Beer–Lambert law indicates that a plot
of the absorbance versus the concentration is linear, passes through the origin
(6), and has a slope equal to the product εb. A value of the molar absorptivity of
a particular absorbing species at a given wavelength can thus be determined
experimentally from the slope of such a plot.
In the case of the sample consisting of a mixture of different absorbing species,
all of which have overlapping absorption spectra, the observed absorbance, Aobs,
at a given wavelength is the sum of the individual absorbance values (1, 5, 6):
Aobs = ΣAi = ε1bc1 + ε2bc2 + …
(11)
where Ai is the absorbance due to species i, c1, c2, … , are the respective concentrations of species 1, 2, … , and ε1, ε2, … , are the respective extinction coefficients of these species.
Transmission and Absorption Spectra
A UV–visible spectrophotometer can be used to record the transmittance or
absorbance of a sample at different wavelengths. Most modern spectrophotometers are fully automated and can scan through a given range of wavelengths
while continuously recording the transmittance or absorbance of the sample (2,
5, 25). The data collected during a scan is normally displayed as a plot or spectrum either on a chart recorder or on the visual display unit (VDU) of a computer that controls the spectrophotometer (2). Of course a paper copy of the
spectrum can be produced if a computer is used to record the spectrum.
A transmission spectrum is a plot of the transmittance (or %T) of the sample
versus the wavelength, and an absorption spectrum is a plot of the absorbance
versus the wavelength (1, 2). Clearly, since transmittance and absorbance are
mathematically related, the absorption spectrum can be readily derived from
the transmission spectrum and vice-versa.
Figure 2 is a schematic diagram that shows the relationship between a transmission spectrum and an absorption spectrum. In the case of UV–visible spectrophotometry it is, perhaps, more common to record and work with absorption
spectra, as the absorbance is a quantity that is directly proportional to the concentration of the absorbing species (2, 5, 6, 12, 25). Also, it is quite common to
find wavelengths expressed in units of nm when UV–visible spectra are displayed (6).
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100
λ = λmax
80
60
40
0.4
T = 60%
Absorbance
Absorbance (A)
Transmittance (T%)
Introduction to Spec UV–Vis
T = 40%
A = 0.398
∆A1
λ ≠ λmax
∆A2
A = 0.220
0.2
0
λ1
λ2
Wavelength
Figure 2. Schematic diagram showing the relationship between a transmission spectrum and an
absorption spectrum.
∆c
Concentration
Figure 3. Schematic plot of A versus concentration at two different wavelengths: a. λ = λmax and
b. λ ≠ λmax. The diagram demonstrates the difference in the sensitivity of UV-visible spectrophotometry at different wavelengths.
The wavelength of maximum absorbance, λmax, is the wavelength at which the
absorbance reaches its maximum value, Amax (i.e. minimum transmittance) (7).
For a fixed concentration and path length, the absorbance and extinction coefficient are proportional to one another. This means that the maximum extinction
coefficient, εmax, coincides with Amax which, in turn, occurs at λmax. For quantitative analytical work, it is therefore preferable to perform absorption measurements at λmax because the technique is most sensitive under such conditions (1, 6). In particular, since dA/dc = εb, then for a constant path length b, the
observed change in absorbance for a given change in concentration will be a
maximum when ε = εmax, which occurs at λmax. This is shown in Figure 3.
Light Absorption in Highly-Conjugated Double-Bond Systems
Systems of highly conjugated double bonds (CDBs) can be considered to be the
chromophores that are responsible for the observed color of certain compounds
(7). For example, lycopene is a pigment that contributes to the red color of tomatoes and paprika and it contains in its chemical structure a system of eleven
CDBs (13, 26). These absorb the blue-green region of visible light (λmax = 505
nm) causing this compound to appear red. Valuable information about π-electron systems can be learned from both the value of λmax and the intensity of the
absorption peak.
As the number of CDBs increases:
•
the number of groups capable of absorbing electromagnetic radiation increases;
•
εmax increases;
•
the energy gap between the HOMO and the LUMO decreases;
•
absorption shifts to longer wavelengths (7, 13).
A shift of the absorption peak towards longer wavelengths is known as a
bathochromic shift; a shift towards shorter wavelengths is called a hypsochromic shift (2, 27). A striking example of a system that exhibits a bathochromic
shift with an accompanying increased absorbance is the conjugated polyene structures formed by the dehydrochlorination of polyvinyl chloride during its thermal degradation (28).
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Introduction to Spec UV–Vis
UV-Visible Spectrophotometers
General as well as detailed descriptions of UV-visible spectrophotometers and
their components are given throughout the educational literature (29–33). There
are two basic types of UV-visible spectrophotometer, namely single-beam and
double-beam instruments. These are discussed separately below.
Single-Beam Instruments
Figure 4 is a schematic diagram of a single-beam UV-visible spectrophotometer
(5, 6, 25) that shows the main functional elements (34) of the instrument. These
are the radiation source, disperser, sample cell, signal processor, and readout
device.
hν
P0
current
Pt
i0 or it
white
radiation
source
disperser
slit
sample
or
reference
photodetector
λ
V0 or Vt
current-to-voltage
converter
T
READOUT
voltage
Figure 4. Schematic diagram showing the functional elements of a single-beam spectrophotometer.
Radiation Source
The radiation source produces all wavelengths in the spectral region of interest. Usually, a deuterium lamp or hydrogen lamp is used as a source of UV light
and a tungsten filament lamp produces light in the visible spectral region (1, 5,
6, 25). The internal optics of the instrument may be arranged so that switching
between these two sources can occur when required (25), but this arrangement
is more common in double-beam spectrophotometers. A tungsten-halogen lamp
is used as a single source in some less-expensive instruments (1, 25). These
lamps produce emission in the visible region with some emission in the near
UV region (1).
Disperser
Light of a particular wavelength is selected from the source by some type of
disperser (5). In modern instruments the disperser is commonly a grating monochromator (5). In older instruments, light from the source is refracted through a
prism (6) in order to select a given wavelength. The use of prisms as devices for
wavelength selection is no longer preferred due to the greater expense and lower
wavelength resolution compared with grating devices.
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Sample Cell
The light beam (power, P0 and wavelength, λ) emerging from the disperser is
passed through a cell that contains the sample (2, 5). If some of the incident
light beam is absorbed by the sample, the beam will emerge from the cell with
reduced power, Pt (2).
Detector
A device such as a photomultiplier (PM) tube or a photocell is used to measure
the power, P, of the light beam (1, 5, 6). Such devices produce an electric current,
i, that is proportional to the power of the beam (1, 35). A detector response
corresponding to P0 can be achieved simply by removing the sample from the
light path. However, a more reliable reading of P0 is made by replacing the
sample with a reference solution that includes all species in the test system
except the sample (2, 5). The use of a reference accounts for the small loss in
light transmission due to the cell, solvent, etc., which otherwise could erroneously be attributed to absorption by the sample. A detector response corresponding to Pt is achieved by placing the sample in the light path (2, 5).
Signal Processor
The current produced by the detector is passed through a current-to-voltage
(CV) converter (34, 35). The latter is essentially a fixed resistor that produces a
potential difference or voltage, V across its terminals. In accordance with Ohm’s
law, the potential difference is proportional to the current and so the potential
difference can be used as the input signal to an analog-to-digital converter (ADC).
An ADC (35, 36) is a device that converts an input voltage to binary numbers, n,
that are proportional to the voltage (see Fig. 4). The digital information produced by the ADC can be passed to a suitable device for display (1).
Readout Device
There are at least three ways of displaying the signal produced within a spectrophotometer depending on the extent to which the output signal from the
detector is processed.
•
The current produced by the detector can be displayed directly by a galvanometer or moving coil meter (35) as a needle deflection on a calibrated scale.
•
The voltage produced by the CV converter (35) can be displayed using a voltmeter that has a suitably calibrated scale.
•
The processed data from the ADC can be handled digitally and displayed by a
readout device such as a liquid crystal display (LCD) or light-emitting diode
(LED) display (1, 35).
The following proportionalities apply at the different stages in a single-beam
instrument: i ∝ P (detector), V ∝ i (CV converter), n ∝ V (ADC) and so n ∝ P (35).
Thus each of the quantities i, V, and n is proportional to the power, P, of the light
beam.
The use of single-beam instruments is most appropriate in situations where
multiple measurements at a single wavelength are required. If it is necessary
to make measurements at many different wavelengths, then the use of a singlebeam instrument can prove to be quite tedious as the response of the detector
corresponding to P0 must be recorded at each new wavelength (2). The sample
and reference solutions must be interchanged in order to do this.
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Introduction to Spec UV–Vis
Double-Beam Instruments
Figure 5 is a schematic diagram of a double-beam UV-visible spectrophotometer (2, 10, 12, 25) showing the main functional elements (34) that are essentially the same as those of the single-beam instrument. The functional elements
of a double-beam spectrophotometer are discussed separately below and particular attention is given to the important differences between single-beam and
double-beam instruments.
hν
white
radiation
source
disperser
microprocessor
slit
current
P
it
sample
photodetector
i0
P0
n0
A = log10(n0 /nt)
READOUT
hν
analog-to-digital
converter
V0
nt
Vt
number
voltage
current-to-voltage
converter
Figure 5. Schematic diagram showing the functional elements of a double-beam spectrophotometer.
Radiation Source
The radiation source in a double-beam instrument is the same as that used in a
single-beam instrument and is commonly a deuterium lamp/tungsten filament
lamp system (5, 25).
Disperser
Similarly to single-beam instruments, the dispersion of light into its component wavelengths in a modern double-beam instrument (5) is commonly achieved
using a grating monochromator. In a double-beam instrument a drive mechanism enables the wavelengths produced by the disperser to be scanned between
limits that are set by the user (2).
Sample and Reference Cells
The light beam emerging from the disperser is split into two beams of equal
intensity. These beams are passed simultaneously through the reference and
sample cells (5) and emerge with powers P0 and Pt respectively (see Fig. 5). The
optics of the instrument are arranged so that each of the emerging beams is
directed onto the detector via a chopper that alternately passes each beam onto
the detector (2, 25). The electronics controlling the detector are synchronized to
the chopping frequency so that separate detector response signals that originate from the reference and sample can be isolated. The main advantage of
chopping between the sample and reference beams is that the power of each
beam can be measured using the same detector. Such an arrangement:
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Introduction to Spec UV–Vis
•
Reduces costs.
•
Practically eliminates the need to ensure the output stability of the source remains constant during the measurement of P and P0 (1).
•
Eliminates the difficulty of having to match the spectral response characteristics of the detectors if two separate detectors were to be used.
For simplicity, the signals that are created in a double-beam instrument due to
the sample and reference can be considered and treated separately as indicated
in Figure 5.
Detector
The range of detector systems that are used in dual-beam spectrophotometers
(1, 2, 5, 6) is essentially the same as those used in single-beam instruments.
Signal Processor
In principle, the signal processing that occurs in a double-beam instrument is
the same as that outlined previously for a single-beam instrument. However, in
the case of a double-beam instrument the signals from the reference and sample
are handled simultaneously (2, 6), whereas in a single-beam instrument they
are handled separately (see Figure 5).
The following proportionalities apply at the different stages of signal processing in a double-beam instrument: i0 ∝ P0, it ∝ Pt (detector); V0 ∝ i0, Vt ∝ it (CV
converter); n0 ∝ V0, nt ∝ Vt (ADC) and so n0 ∝ P0 and nt ∝ Pt (35). At any one of
these stages the constant of proportionality between the variables is the same
for both the sample and reference signals and so the absorbance can be readily
calculated from any of the following equalities:
A = log10(i0/it) = log10(V0/Vt) = log10(n0/nt)
(12)
Thus double-beam instruments can measure the absorbance (or transmittance)
continuously as the wavelength of the incident light is scanned (1, 5) and this
feature makes these instruments particularly suitable for recording spectra.
Readout Device
There are a number of readout devices that are used in double-beam instruments. For example, the voltages V0 and Vt generated at the CV converter (35)
stage in the instrument can be manipulated electronically to produce either a
voltage, VT, that is proportional to the voltage ratio Vt/V0 or a voltage, VA, that is
proportional to the logarithm of 1/VT. The voltages VT or VA could be used as the
input signals to drive the vertical pen deflection on a chart recorder or x–y
recorder (35) and will produce pen deflections proportional to the transmittance and absorbance, respectively. A calibration of the transmittance or absorbance axis can be achieved in such an arrangement by recording the pen deflection obtained for situations corresponding to T% = 100 (i.e. A = 0; reference
solution in sample beam) and T% = 0 (i.e. A = ∞; sample beam prevented from
reaching the detector).
If a chart recorder (35) is used, the wavelength axis of the spectrum can be
calibrated by determining the starting wavelength and relating the selected
chart speed to the constant rate at which the wavelength drive mechanism
scans through the wavelengths. If an x–y recorder (35) is used, a voltage that is
proportional to the position of the wavelength drive mechanism can be generated
and used to drive the x-deflection of the pen, thereby establishing the wavelength axis of the spectrum.
In modern spectrophotometers, digital information in the form of the numbers
n0 and nt that are created by an ADC device is transferred to a microprocessor
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Introduction to Spec UV–Vis
that calculates either the transmittance or absorbance. The position of the wavelength drive mechanism can be controlled with a computer by means of a calibrated stepper motor (37). The computer can continuously change the position
of the stepper motor (and hence the wavelength) and store this information
along with the corresponding transmittance or absorbance that is processed
concurrently. In such cases, the VDU of the computer (35) is used as a readout
device on which the spectrum is plotted by the computer software. Methods for
interfacing UV-visible spectrophotometers to microcomputers have been discussed in the educational literature (38, 39).
Diode Array Spectrophotometers
Modern diode array spectrophotometers (5, 8) use as their detectors a series of
photodiodes that are positioned side-by-side on a silicon crystal. Each diode
records simultaneously a narrow band of the spectrum and so the entire spectrum can be recorded very quickly. The main advantage of such a detection
system is that it has no moving parts, in contrast to the wavelength drive mechanism of a double-beam spectrophotometer. However, since only a limited number of photodiodes can be placed on a single silicon crystal, the resolution of the
detector is compromised to some extent (8).
Spectroscopic Studies of Acid–Base Indicators
Acid–Base Indicators
Acid–base indicators are weak acids or, sometimes, weak bases that are highly
colored compounds. The color of an indicator in acidic solution is markedly different than its color in basic solution (40, 41). In solution, the undissociated and
dissociated forms of an indicator exist in equilibrium and can be represented by
the general equation:
IndH
Ind– + H+
(13)
where IndH represents the undissociated or protonated indicator and Ind– is
its conjugate base (40). The color change that an indicator undergoes during a
titration occurs as a result of the different colors of the IndH and Ind– species
(42).
The Spec UV–Vis software has five indicator solutions whose spectral characteristics can be studied: thymol blue, methyl orange, bromophenol blue,
bromothymol blue, and phenol red. With the exception of methyl orange, each of
these indicators has a structure based on that of phenolsulfonephthalein (i.e.
phenol red). This structure exists as two isomeric forms that are interconverted
via an intramolecular proton transfer (see Fig. 6a). In the case of the phenolsulfonephthalein indicators, the IndH species absorbs at a shorter wavelength than
the Ind– species. In contrast to the other indicators which undergo a single color
change across a certain pH range, thymol blue exhibits two such color changes
due to its ability to form (in addition to the IndH and Ind– species) a species
that can be represented as IndH2+. All three of these species absorb in the visible region of the spectrum.
Figure 6b shows the structure of methyl orange to be the sodium salt of a moiety that contains an azo group (–N=N–). This structure is closely related to that
of the food dye p-dimethylaminoazobenzene (butter yellow) (7, 13, 43, 44). The
protonated form of methyl orange is formed when a lone pair of electrons on one
of the nitrogen atoms of the azo group reacts with a H+ ion to produce a zwitterion (2). Table 3 lists the structural details that pertain to Figure 6a, as well as
the operative pH range, color change, and pKa values (44–46) of the indicators.
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O
OH
a
R2
R3
R2
R4
R3
R5
R4
R5
R1
R1
C
C
OH
OH
O
=
S=
O
b
R7
R6
SO3H R7
R6
O
N≡N
(CH3)2 N
SO3- Na+
Figure 6. Chemical structure of a: isomeric forms of indicators based on phenolsulfonephthalein and b: methyl orange indicator.
Table 3. Structural details, operative pH range, color change and pKa values of some acid–
base indicators.
R1a
R2
R3
R4
R5
R6
R7
pH Range
Colorb
pKac
Phenol Red
H
H
H
H
H
H
H
6.4–8.4
Y–R
7.90–8.00
Bromophenol Blue
H
Br
Br
H
Br
Br
H
3.0–4.6
Y–B
4.10–4.20
H
i-Pr
H
1.2–2.8
R–Y
1.65
8.0–9.6
Y–B
8.90
6.0–7.6
Y–B
7.00–7.30
3.2–4.4
R–Y
3.46–3.70
Indicator
Thymol Blued
Bromothymol Blue
Mee
Me
H i-Pre Me
Br i-Pr
H
i-Pr
Methyl Orange
Br
Me
a. See Figure 6a for the chemical structures to which R1–R7 apply.
b. R = red; Y = yellow; B = blue.
c. pH and pKa ranges are maximum ranges (44–49 ).
d. Thymol blue has two color transitions in the visible region: the acid and base forms.
e. Me = CH3–; i-Pr = (CH3)2CH–;
The pKa of an Acid–Base Indicator
Consider the dissociation of an indicator in accordance with equation 13, where
the analytical concentration of the indicator is c. If α is the degree of dissociation (12, 50) of the indicator (i.e. the fraction of the indicator present in its
dissociated form), then at equilibrium:
[Ind–] = [H+] = αc
(14)
[IndH] = (1 – α)c
(15)
Ignoring activity coefficients, an expression for Ka of the indicator can be written in terms of the degree of dissociation as follows (12, 50):
Ka = α2c/(1 – α) = [H+]α/(1 – α)
(16)
since [H+] = αc. Now, taking –log10 of both sides of equation 16:
pKa = pH – log10[α/(1 – α)]
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(17)
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Introduction to Spec UV–Vis
If the absorbance of the indicator solution is measured at a given wavelength, λ,
first at a low pH where the indicator is present predominantly in its undissociated form (IndH) and second at a high pH where it is present predominantly in
its dissociated form (Ind–), the following equations apply:
AIndH = ε1bc
(18)
AInd– = ε2bc
(19)
where AIndH and AInd– are the absorbances due to the IndH and Ind– species
respectively, ε1 and ε2 are the respective extinction coefficients of these species
at the wavelength λ, and b is the optical path length. At any intermediate pH
value where both the IndH and Ind– species are present the observed absorbance, A, is comprised of contributions from both of the absorbing species (see
equation 11) and thus (1, 5, 6):
A/b = ε1[IndH] + ε2[Ind–]
(20)
Equation 21 can be derived from equations 18, 19 and 20:
A = AIndH – α(AIndH – AInd–)
(21)
From equation 21:
α = (AIndH – A)/(AIndH – AInd–)
(22)
α/(1 – α) = (AIndH – A)/(A – AInd–)
(23)
Equation 24 (47, 48, 51) can be derived upon substituting equation 23 into equation 17 and rearranging:
pH = pKa + log10[(AIndH – A)/(A – AInd–)]
(24)
Thus a plot of pH versus log10[(AIndH – A)/(A – AInd–)] should be a straight line
that has a slope of unity and a vertical axis intercept equal to pKa.
The Isosbestic Point
Consider a solution of the indicator IndH at a given analytical concentration, c.
If the pH is adjusted to a sufficiently low value so that only the IndH species is
present then one may record the absorption spectrum of the pure IndH species
that will be present at concentration c. On the other hand, if the pH is adjusted
to a sufficiently high value, the absorption spectrum will be that of the Ind–
species, which will be present at the same concentration as the IndH species
was under conditions of sufficiently low pH. Now, if the absorption spectra of
the IndH and Ind– species overlap at a particular wavelength, λiso, the isosbestic
point (2, 5), then from equations 18 and 19:
ε1(λiso) = ε2(λiso) = εiso
(25)
From equations 20 and 25 the absorbance at the isosbestic point, Aiso, is given
by:
Aiso = εisob([IndH] + [Ind–])
(26)
Since the IndH and Ind– species are in equilibrium, the sum of their concentrations will always be equal to c, the analytical concentration of the indicator.
Thus the absorbance at the isosbestic point will always be the same irrespective of the relative proportions of the IndH and Ind– species (2). All spectra of
the indicator that are measured at a given concentration but at different pH
values will pass through the isosbestic point. The presence of an isosbestic point
in a series of superimposed spectra is good evidence for there being two species
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in the system present in equilibrium with each other (2, 5). It is also interesting
to note that in some systems of greater complexity one may observe more than
one isosbestic point.
Distribution Diagrams
The degree of dissociation, α, of a weak acid (12, 50) is the fraction of its analytical concentration, c, that is present in the form of the dissociated species. In the
case of an acid–base indicator, the dissociated and undissociated species may be
represented as Ind– and IndH, respectively, and so:
αInd– = [Ind–]/c
(27)
where [Ind–] is the equilibrium concentration of the dissociated (or deprotonated)
indicator. Furthermore, the fraction of the indicator present in the form of the
undissociated species can also be defined:
αIndH = [IndH]/c
(28)
where [IndH] is the equilibrium concentration of the undissociated (or protonated) indicator.
A plot of αInd– as a function of the pH is called a dissociation curve. A plot of
αIndH versus pH is called a formation curve (52, 53). A mass balance equation
for such a system can be written as follows:
αInd– + αIndH = 1
A plot of αInd– or αIndH versus
the pH is known as a distribution diagram (see Fig. 7). On
such a diagram, the dissociation curve divides a vertical line
into two parts; the lower part
is equal to αInd– and the upper
part is equal to αIndH. The converse is true in the case of a formation curve (52).
It is important to note that at
the midpoint on the dissociation (or formation) curve [Ind–]
= [IndH] and so the pH at which
this occurs is equal to the pKa
of the indicator.
Degree of Dissociation/Formation
(29)
1.0
← αInd-
αIndH →
0.5
pKa
0
14
0
pH
Figure 7. A schematic distribution diagram showing
the relationship between the formation curve (αIndH)
and the dissociation curve (αInd–).
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