Exploring Chemical Analysis
Fourth Edition
18
Let There Be Light
歐亞書局
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Let there be light and there was light.

Spectrophotometry-the use of electromagnetic
radiation to measure chemical concentrations
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18-1 Properties of Light

Light can be described both as waves and as particles.

Light waves consist of perpendicular, oscillating electric and
magnetic fields.

Wavelength, λ.

Frequency, ν, is the number of oscillations per second.

One oscillation per second is also called 1 hertz (Hz).

Relation between frequency and wavelength: λν=c
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Figure 18-1
Figure 18-1 Plane-polarized electromagnetic radiation.
Ordinary, unpolarized light
has electric and magnetic field
components in all planes.
Polarized light processes in
one plane.
Example: Relating Wavelength and Frequency
 What is the wavelength of radiation in your
microwave oven, whose frequency is 2.45 GHz?
SOLUTION:
C=nl
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Light can also be thought of as particles called photons.
The energy, E (measured in joules, J), of a photon is
proportional to its frequency：
h: Planck’s constant ( = 6.626×10-34 J‧s).
~
n
: (=1/λ) is called the wavenumber 波數.
能量
~~ 正比於波數 頻率
~~ 反比於波長
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 High energy
Figure 18-2
low energy 
Figure 18-2 Electromagnetic spectrum, showing representative molecular processes
that occur when radiation in each region is absorbed.
The visible spectrum spans the wavelength range 380 to 780 nanometers (1 nm= 10－9P.395
m).
vibration
 low energy
high energy 
Figure 24-3 in Skoog’s analytical Chemistry, 8th edition
能量
~~ 正比於波數 頻率
~~ 反比於波長
Example: Photon Energies
By how many joules is the energy of a molecule increased when it absorbs
(a) visible light with a wavelength of 500 nm
(b) infrared radiation with a wavenumber of 1 251 cm-1?
SOLUTION:
(a)
(b)
The lowest energy state of a molecule is called the ground state.
Figure 18-3
When a molecule absorbs a photon
 its energy increases
 the molecule is promoted to an excited state.
吸收能量
釋放能量
• Absorption of light increases the energy of a molecule.
• Emission of light decreases its energy.
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18-2 Absorption of Light
A spectrophotometer
measures
transmission of light.
Figure
18-4
Figure 18-4 Schematic representation of a single-beam
spectrophotometric experiment.
Light with a very narrow
range of wavelength is said
to be monochromatic.
In Figure 18-4, light passes through a
monochromator (單色器,單光器) , a
device that selects a narrow band of
wavelengths.
只有一個波長之光線的,單色光的
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Transmittance 穿透率
Transmittance, T, is the fraction of incident light that
passes through a sample.
P0 ≧ P
0≦T<1
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Absorbance
吸光率
The most useful quantity for chemical
analysis is absorbance, A:
When no light is absorbed, P = P0 and A = 0.
 The sample does not absorb the light.
P0 ≧ P
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Figure 24-7 in Skoog’s analytical Chemistry, 8th edition
Example: Absorbance and Transmittance
• What absorbance corresponds to 99% transmittance?
• What absorbance corresponds to 0.10% transmittance?
SOLUTION:
Transmittance 穿透率 ↗
 Absorbance 吸光率↘
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Absorbance is proportional to the concentration of
light-absorbing molecules in the sample.
Figure 18-5 shows that the absorbance of KMnO4 is proportional to
concentration over four orders of magnitude (fro 0.6μM to 3 mM).
Peak absorbance at 555 nm is
proportional to concentration
from 0.6μM to 3 mM.
Beer’s Law




A : absorbance
ε: molar absorptivity 莫耳吸光係數
b: the pathlength that the light travels through a substance
c : concentration
b
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Color Plate 13 shows that color intensity increase as the
concentration of the absorbing
Absorbance is
Colormolecule
Plate increases.
13
a measure of the color.
COLOR PLATE 13
Fe(phenanthrolines)32+ Standards for Spectrophotometric
Analysis (Section 18-2) Volumetric flasks containing
Fe(phenanthroline)32+ solutions with iron concentrations
ranging from 1 mg/L (left) to 10 mg/L (right).
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Example: Using Beer’s Law
The peak absorbance of 3.16×10-3 M KMnO4 at 555 nm in a
1.000-cm-pathlength cell in Figure 18-5 is 6.54.
(a)
Find the molar absorptivity and
percent transmittance of this
solution.
(b)
What would be the absorbance if
the pathlength were 0.100 cm?
(c)
What would be the absorbance in
a 1.000-cm cell if the
concentration were decreased by
a factor of 4?
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The peak absorbance of 3.16×10-3 M KMnO4 at 555 nm in a
1.000-cm-pathlength cell in Figure 18-5 is 6.54.
(a) Find the molar absorptivity and percent transmittance of
this solution.
SOLUTION:
Percent transmittance is 100T=2.88×10-5 %.
When the absorbance is 6.54, transmittance is very tiny.
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(b) What would be the absorbance if the
pathlength were 0.100 cm?
A = (2.07×10-3 M-1 cm-1) (0.1cm) (3.16×10-3 M) = 0.654
If we decrease pathlength by a factor of 10, we
decrease absorbance by a factor of 10 to 6.54/10=0.654.
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(c) What would be the absorbance in a 1.000-cm cell if
the concentration were decreased by a factor of 4?
A = (2.07×10-3 M-1 cm-1) (10cm) (3.16×10-3 M/4) = 1.64
If we decrease concentration by a factor of 4, we
decrease absorbance by a factor of 4 to 6.54/4 to
1.64.
Example: Finding Concentration from Absorbance
Gaseous ozone has a molar absorptivity of 2700 M-1cm-1
at the absorption peak near 260 nm in the spectrum at
the beginning of this chapter.
 Find the concentration of ozone (mol/L) in air if a sample
has an absorbance of 0.23 in a 10.0-cm cell. Air has
negligible absorbance at 260 nm.
SOLUTION:
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Absorption Spectra
An absorption spectrum is a graph showing how A (or ε) varies
with wavelength (or frequency or wavenumber).
280-320 nm
320-400 nm
Figure 18-6 Absorption spectrum of typical sunscreen lotion
shows absorbance versus wavelength in the ultraviolet region.
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SPF = 1/T
SPF↗
T↘
A↗
See Problem 18-12
Example: How Effective Is Sunscreen?
What fraction of ultraviolet
radiation is transmitted through the
sunscreen in Figure 18-6 at the
peak absorbance near 300 nm?
SOLUTION:

Absorption spectrum of typical sunscreen lotion
From the spectrum, the absorbance A is about 0.35 at 300 nm.
 The transmittance is T=10－A = 10－0.35 = 0.45 = 45%.
Just over half the ultraviolet radiation (55%) is
absorbed by sunscreen and does not reach your skin. P.401
White light contains all colors of the rainbows.
A substance that absorbs visible light appear colored, when white
light is transmitted through it or reflected from it.
The substance absorbs certain wavelengths of white light, and
our eyes detect wavelengths that are not absorbed.
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18-3 Practical Matters
The instrument represented in Figure 18-4 is called a single-beam
spectrophotometer because it has only one beam of light.
Figure 18-7
Sample is usually contained in
a cell called a cuvet, which has
flat, fused-silica faces.
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Common cuvets for ultraviolet and visible measurements.
Transmittance ranges for various optical materials.
Figure 25-2, Skoog
• Simple glasses are fine in the visible region.
• Fused silica or quartz is necessary in the UV region (< 380 nm).
• Halide salts (KBr, NaCl, AgCI) are often used in the IR region but have
the discadvantages of being expensive and somewhat water soluble.
 Silicate glass is completely adequate for use in the visible region
 In the UV region, fused silica or quartz must be substituted.
 In the IR region, glass, quartz, and fused silica all absorb at
wavelengths longer than about 2.5 μm.
 Optical elements for IR spectrometry are typically made from
halide salts or, in some cases, polymeric materials.
Figure 25-2, Skoog
In a single-beam spectrophotometer, we do not measure the
power of incident beam P0, directly.
Rather, the radiant power
passing through a reference
cuvet containing pure
solvent is measured and
defined as P0.
Skoog, chapter 24
P0和Pe(或P)之間的差異未必是被樣品吸
收 而是以其他方式如散射(scattering)或
反射(reflection)

P0: radiation power passing through cuvet filled with solvent

P: radiation power passing through cuvet filled sample (solvent + solute)

Transmittance = P/P0
In a single-beam spectrophotometer
(1) Measure P0 (reference: pure solvent)
(2) Measure P (sample: solvent + solute)

P0: radiation power passing through cuvet filled with solvent

P: radiation power passing through cuvet filled sample (solvent + solute)

Transmittance = P/P0
Double-beam spectrophotometer
With a double-beam system, you can
measure P and P0 simultaneously!
Good operating techniques

Cuvets should be held with a tissue to avoid
putting fingerprints on the cuvet faces and must
be kept scrupulously clean.
Do not touch the
clear face of a cuvet.
Cuvet cleaning reagent
18-4 Using Beer’s Law
Spectrophotometric analysis with visible radiation is
called colorimetric analysis.
For a compound to be analyzed by spectrophotometry, it must
absorb electromagnetic radiation, and this absorption should be
distinguishable from that of other species in the sample.
Biochemists assay proteins in the ultraviolet region at 280 nm because the
aromatic amino acids tyrosine, phenylalanine, and tryptophan have maximum
absorbance near 280 nm.
tyrosine
phenylalanine
tryptophan
Example: Measuring Benzene in Hexane
(a)
A solution prepared by dissolving 25.8 mg of benzene (C6H6,
FM 78.11) in hexane and diluting to 250.0 mL has an
absorption peak at 256 nm, with an absorbance of 0.266 in a
1.000-cm cell. Hexane does not absorb at 256 nm.
 Find the molar absorptivity of benzene at this wavelength.
SOLUTION:
Molarabsorptivity
=ε
= A/bc
= 0.266/(1.000m)(1.321×10-3 M)
= 201.3 M-1cm-1.
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(b) A sample of hexane contaminated with benzene
has an absorbance of 0.070 at 256 nm in a cell
with a 5.000-cm pathlength.
 Find the concentration of benzene.
SOLUTION:
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BOX 18-2
Designing a colorimetric reagent to detect phosphate
Pyrocatechol
violet indicator
bound to metal
is blue
Free pyrocatechol
violet indicator is
yellow
A designed ligand that binds to two Zn2+ ions
 The distance between the two Zn2+ ions is just
right to bind to the metal ion indicator pyrocatechol
Near neutral pH, phosphate binds
tightly to the two Zn2+ ions
 The pyrocatechol is displaced
and is free
The change in adsorption provides a quantitative
measure the amount of phosphate.
UV/Vis spectra obtained by additions of [Zn2(Hbpmp)]3+ solution (final concentrations: 0, 10,
20, 30, 40, and 50 mm) to the pH 7.0 aqueous
buffer (HEPES, 10 mm) containing pyrocatechol
violet (50 mm); b) UV/Vis spectra obtained by
additions of HPO42- solution (final
concentrations: 0, 25, 50, 100, 150, 200, 250,
and 500 mm) to the pH 7.0 aqueous buffer
(HEPES, 10 mm) containing [Zn2(Hbpmp)(pyrocatechol violet)]t (50 mm).
UV/Vis spectra of the [Zn2(H-bpmp)]3+ -pyrocatechol violet mixture (50 mm in
a pH 7.0 aqueous solution) in the presence of various anions (250 mm).
Using a Standard Curve to Measure Nitrite

The aquarium nitrite analysis is based on a
reaction whose colored product has an
absorbance maximum at 543 nm (Figure 18-9):
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To measure the amount of nitrite –
the nitrite analysis is based on a reaction whose colored product
has an absorbance at 543 nm.
Figure 18-9
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For quantitative analysis, we prepare a standard curve
(also called a calibration curve) in which absorbance at
543 nm is plotted against nitrite concentration in a
series of standards.
Reagents
1. Color-forming reagent
2. Standard nitrite (~0.02 M)
• standard curve
• calibration curve
Calibration curve for nitrite analysis
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Table 18-2
(1.830, 0.325)
(?, 0.278)
(0.9150, 0.164)
(0.4575, 0.082)
Calibration curve for nitrite analysis
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Procedure
1. Construct a standard curve from known nitrite
solutions.
2. Analyze duplicate samples of unknown aquarium
water that has been filtered prior to dilution to
remove suspended solids.
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Example: Preparing Nitrite Standards
How would you prepare a nitrite standard containing
approximately 2 ppm nitrite nitrogen from a
concentrated standard containing 0.018 74 M NaNO2?
SOLUTION
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Example: Using the Standard Curve
From the data in Table 18-2, find the molarity of nitrite, with
an average absorbance 0.276, in the aquarium.
SOLUTION
---- by the method of least square
代入所觀測之吸收值入直線方程式
得到濃度值
由重量濃度單位改為M
Enzyme-Based Nitrate Analysis-A Green Idea

Nitrate (NO3-) in natural waters is derived from sources
such as fertilizers and undertreated animal and human
waste.

NO3- is commonly analyzed by reducing to NO2-,
followed by colorimetric assay of NO2-.

Metallic Cd has been the most common reducing
agent for NO3-. However the use of toxic Cd should be
reduced.
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Enzyme-Based Nitrate Analysis - A Green Idea
The enzyme nitrate reductase catalyzes the reduction:
NADH is derived
from niacin
b-Nicotinamide adenine dinucleotide
colorimetric assay
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