Analytical Chemistry Summary

Would you please summarise (main points, definition, factors, components, calculations, formula, each important each paragraph, graphics ………
etc)CH 1, 5, 6, 7, 8 and 9 from the textbook (not instructor’s manual) , homework

What is Analytical Chemistry?
 Analytical Chemistry is what analytical Chemists do!
 “The study of methods determining the composition
of substances”
 Two areas of analytical methods
1) Qualitative analysis (what?)
Is that measured property indicates presence of
analyte in the mixture
2) Quantitative analysis (how much?)
The magnitude of measured property is proportional
to the concentration of analyte in the mixture
How do we measure stuff?
 This course tile is “ Instrumental Analysis” so
How do we analyze stuff?
 The chemical system
First we need something to analyze, can be anything:
water, gas, liquid, food, blood etc.
 The signal generator
Second we need a signal to interacts with the chemical system to
produce an analytical signal. It is a stimulus
Can be electromagnetic, a lamp, electrical, DC/AC signal source etc.
How do we measure stuff? cont.
 The analytical signal
Produced by the interaction of the signal with the
chemical system: ENCODING
Analytical Signal
EMR, electrons, etc.
opposite decoding
Data Domains
The various modes of encoding analytical information are called data domains and
can be electrical or non-electrical domains
Non-electrical domains
Electrical domains
Physical (light intensity, color)
Chemical (pH)
Scale Position (length)
Number (objects)
Analog: continuously variable magnitude (current, voltage, charge)
Digital: discrete values (count, serial, parallel, number)
How do we measure stuff? cont.
 e.g.
 In photometric instruments, the stimulus is a
tungsten lamp and the analytical information is
attenuated light beam.
 In mass spectrometer instrument, the stimulus is an
ion source and the analytical information is M/Z
 In FID detector, the stimulus is flame and the
analytical information is ion concentration vs. time
 In atomic emission spectrometer, the stimulus is
inductively coupled plasma and the analytical
information is UV or visible radiation
Decoding the Analytical Signal
 How do we decipher the information encoded
in the analytical signal?
1) Disperse the analytical signal (selectivity)
2) Convert an electrical signal
3) Process the electrical signal
4) Output the resultant signal
Decoding the Analytical Signal, cont.
1) Dispersive element
 Enables the selective measurement of the
analytical signal, e.g.

Monochromator (optical)
Magnetic field (mass spectrometer)
Chromatographic column (separation)
2) Convert
 Transducer
Converts the analytical signal to electrical signal,

Photomultiplier tube (PMT), photons to electrons
Electrodes (chemical potential to electrical potential)
Dispersive element
A monochromator is an optical
device that transmits a
mechanically selectable narrow
band of wavelength of light or
other radiation chosen from a
wider range of wavelengths
available at the input. The name is
from the Greek roots mono-,
single, and chroma, color, and the
Latin suffix -ator, denoting an
Photomultiplier tubes
Photomultiplier tubes (
(photomultipliers or PMTs for
short), members of the class of
vacuum tubes, and more
specifically phototubes, are
extremely sensitive detectors of
light in the ultraviolet, visible,
and near IR ranges of the
electromagnetic spectrum. These
detectors multiply the current
produced by incident light by as
much as 100 million times
Decoding the Analytical Signal, cont.
3) Signal Processor
e.g. amplification, current to voltage, AC to DC, math
(log, FT) etc.
4) Output Transducer
Convert the signal to human understandable signal
e.g., Most often a computer.
The General Instrument
Analytical Signal
Dispersive element
Convert (transducer)
Signal processor
output transducer
Calibration of Instrumental Methods
The presence of many chemical substances can often be found by
their response to some external signal. The magnitude of this
response is proportional to the amount of substance present.
Because electronic equipment is often necessary to generate the
external signal and/or to detect the chemical response, these
methods of quantitative analysis are called instrumental
methods. Instrumental methods are indirect, so the detecting
instrument requires calibration to measure the response initially
from a sample with a known concentration of analyte. This is
necessary to relate the response, which is often electrical, to the
quantity of chemical substance. Standard solutions, containing
known amounts of analyte, are first studied to calibrate the
measuring instrument.
Calibration of Instrumental Methods, cont.
External Standards

Prepared separately from the sample. A series of standards
(known concentrations) are prepared and the instrument
response signals are recorded. Data can be plot using the
least squares method
Y = mx +b

For determining the unknown from least squares methods
Cunknown = (Y-b)/m
Where: Y = is the response value for the unknown
b = the y intercept
m = the slope
 Do not account for the interference in the matrix
Calibration Curve
DL =
Detection limit
limit of quantitation
limit of linearity
Calibration of Instrumental Methods, cont.
2) Standard Addition Method (Spiking)
Useful for analyzing complex samples (matrix effect)
 Prepare a set of volumetric flasks all the same volume
 Add successive increments (volumes) of the standard

one increment in each flask (different amounts)
Add a single measured volume of the sample (unknown)
into each flask
Dilute the flasks to the volume using DI water
Measure the instrument response signals of the sample
and all the standards plus sample.
Fit a least squares line to the data
Calibration of instrumental methods, cont.
 For determining the unknown concentrations from
standard addition least square method use the
Cx = (b Cs)/m Vx
Cx = -(Vs)oCs)/ Vx
Cs = concentration of standard solution
b = the y intercept
m = the slope
Vx = volume of the sample used
(Vs)o = X intercept
Cx = conc. of sample
Example Standard Addition
Ten-milliliter aliquots of a natural water sample were pipetted into 50.00
mL volumetric flasks. Exactly 0.00, 5.00, 10.00, 15.00, and 20.00 mL of a
standard solution containing 11.1 ppm of Fe3+ were added to each,
followed by an excess of thiocyanate ion to give the red complex
Fe(SCN)2+. After dilution to volume, the instrument response for each of
the five solutions, measured with spectrophotometer was found to be
0.240, 0.437, 0.621, 0.809, and 1.009, respectively. Following the steps
discussed in the standard-addition method. What was the concentration
of Fe3+ in the water sample? Calculate it using the two methods discussed
in slide 17. Data in the next slide.
Example Standard Addition, cont.
Volume of standard
solution, mL*
Volume of
sample, mL
Thiocyanate added
Total volume,
Standard Addition Method, cont.
This graph is an example of a standard
addition plot used to determine the
concentration of Fe3+ in an unknown
sample by atomic absorption
spectroscopy. The point at zero
concentration added iron is the
reading of the unknown, the other
points are the readings after adding
increasing amounts (‘spikes’) of
standard solution. The absolute value
of the x-intercept is the concentration
of iron in the unknown
y = 0.0382x + 0.2412
R² = 0.9998
Vol. Standard added
Standard Addition Method, cont.
Cx = (b Cs)/m Vx
Cx = -(Vs)oCs)/ Vx
eq. 1
eq. 2
Using eq.1
Cx = (0.2412 * 11.1 mg/L)/0.0382 * 10 mL = 7.0 ppm
Using eq.2
Cx = 6.15 * 11.1 mg/L/10 mL = 6.9 ppm
Calibration of Instrumental Methods, cont.
3) Internal standard method
“Is a substance that is added in a constant amount
to all samples, blanks, and calibration standards in
an analysis.”
 The internal standard should provide a signal that
is similar to the analyte signal in most ways but
sufficiently different so that the two signals are
 Can compensate for random and systematic errors
See Figure 1-12 text
Calibration of Instrumental Methods, cont.
 Prepare a calibration stock solution of the analyte of

Prepare a stock solution of the internal standard
Use the stock solution of the calibration standard to
prepare a set of calibration standards with different
concentrations by adding the proper increments to the
Add the proper amount of the internal standard to each
flask to prepare the desired concentration of the internal
standard. It should be the same concentration in each
the blank, the sample and the calibration standards.
In the following example note the improvement in
calibration curve when the internal standard is used
Calibration of Instrumental Methods, cont.
 Make a plot of the ratio of the analyte signal to the
internal-standard signal as a function of the
analyte concentration of the standards.
 The ratio of the samples is then used to obtain
their analyte concentrations from a calibration
 The figure in slide 28 shows the calibration curve
for Na, signal intensity vs. concentration.
 The lower curve shows I Na/I Li vs Na conc. Note
the improvement in calibration
In summary
Internal Standards
 A constant amount of the internal standard is
added to all samples. That same amount of the
internal standard is also included in each of the
calibration standards.
 The ratio of the peak area (or height) of the target
compound in the sample to the peak area (or
height) of the internal standard in the sample is
compared to a similar ratio derived for each
calibration standard.
In summary, cont.
 This ratio is termed the response factor (RF) or
relative response factor (RRF), indicating that the
target compound response is calculated relative to
that of the internal standard.
Response Factor Equation
RF = ((Ax)(Cis))/((Ais)(Cx))
Ax= Area of the compound
Cx= Concentration of the compound
Ais= Area of the internal standard
Cis= Concentration of the internal standard
Internal Standard Method Fig. 1-12 text
Performance Characteristics: Figures of Merit
How to choose an analytical method? How good is
 How reproducible? – Precision
 How close to true value? – Accuracy/Bias
 How small a difference can be measured? – Sensitivity
 What range of amounts? – Dynamic Range
 How much interference? – Selectivity
 The minimum signal detected- Detection limit
Performance Characteristics: Figures of Merit, cont.
1) Precision
Can be measured in various terms (about 7
 As standard deviation, S
 As relative standard deviation: RSD = S/xavg
 Coefficient of variation (cv) = (S/xavg) 100%
 Standard error of the mean, Sm = S/√N
N = number of samples
Performance Characteristics: Figures of Merit, cont.
2) Accuracy/Bias
 Determinate errors (operator, method, instrumental)
 Bias = Xavg – Xtrue
 Xtrue can be determined by analyzing one or more
standard reference material
 % error = 100 x (Xavg – Xtrue )/Xtrue
Performance Characteristics: Figures of Merit, cont.
3) Sensitivity
Standard deviation of measurements
Slope of calibration curve
“The ability of the instrument to
discriminate between small differences
in analyte concentration”
Calibration sensitivity:
S = mc + signalblank
Slope determines the sensitivity
Larger slope of calibration curve m,
more sensitive measurement
Performance Characteristics: Figures of Merit, cont.
4) Detection limit
 Signal must be bigger than random noise of blank
 Minimum signal: Signal min = Av. Signal blank + ksblank
 From statistics (student’s t), k = 3.14 at 98% confidence
 Also, from 20 to 30 blank measurements
Cm = (Signal min – avg signalblank)/m
Cm = conc. detection limit
m = slope
Performance Characteristics: Figures of Merit, cont.
5) Dynamic range
Starts from lowest concentration at
which quantitative measurement
can be made (LOQ) to the
concentration at which the curve
departs for linearity about 5%(LOL).
LOQ = 10 (sbl)
Where sbl = standard deviation of
limit of quantitation
limit of linearity
Performance Characteristics: Figures of Merit, cont.
6) Selectivity:
 No analytical method is completely free from interference

by contaminants. Best method is more sensitive to analyte
than interfering species (interferant).
Matrix with species A&B: Signal = mAcA + mBcB + Signal
Selectivity coefficient for A with respect to B: kB,A = mB/mA
k’s vary between zero (no selectivity) and large number
(very selective).
mA & mB are calibration sensitivities (slide 32)
 Read example 1-2 (Text)
Signal and Noise
 Noise, what is it?
 “Any “unwanted” part of the analytical signal
 There is always some noise in a signal
 Warning
 There is always hidden costs associated with S/N

Decrease resolution (selectivity)
Increase measurement time
New sources of noise
Signal-to-noise ratio (S/N)
“is a measure used to quantify how
much a signal has been corrupted
by noise. It is defined as the ratio of
signal power to the noise power
corrupting the signal. A ratio higher
than 1:1 indicates more signal than
Signal and Noise
 Calculating S/N
Standard deviation of signals
Noise Sources in Instrumental Analysis
1) Chemical
 Uncontrollable factors affecting the
chemistry of the system

Temp or pressure affecting equilibrium

Humidity that causes the change in the
moisture content of the sample

Lab fumes

Noise Sources in Instrumental Analysis, cont.
2) Instrumental
a) Flicker noise
Flicker noise is a type of electronic noise often referred
to as 1/ƒ noise.
 It occurs in almost all electronic devices and results
from a variety of effects, such as impurities in a
conductive channel, generation and recombination
noise in a transistor due to base current, and so on.
 It is always related to a direct current. Its origin is not
well known.
 In electronic devices, it is a low-frequency
phenomenon, as the higher frequencies increases the
level of noise decreases.
Flicker Noise
Frequency of signal
More noise sources
b) Environmental Noise
Radio, power line, TV satellite
More Instrumental Noise sources
c) Johnson (thermal ) noise
Voltage fluctuation due to random electron motion in resistive
d) Shot noise
Current fluctuation due to random electron motion across a
junction (evacuated space between cathode and anode)
Signal/Noise Enhancement
a) Hardware Devices
 Grounding and shielding
 Analog filtering (circuit filtering)
 Modulation
Where the analytical signal encoded at a frequency
where 1/f is negligible i.e. high frequency. This is
why low “f” signals from transducers are converted
to high “f”. Often accomplished by the use of
devices called Choppers
Signal/Noise Enhancement, cont.
b) Software methods
 Many of the devices discussed before are being
replaced by computer software methods

Ensemble averaging
 Needs a repeatable signal (time domain method)
 Sum digitally stored replicate signals
 S/N increases as (n)1/2 , n is number of measurements
 To mass a 10 mg object on an analytical balance (σ = 0.1
for n = 1,
S/N = Signal average/stand. deviation =10/0.1= 100.
In general (S/N)n = (n)1/2 (S/N)n=1
for n = 4,
(S/N)4 = (4)1/2 (100) = 200
Ensemble Averaging
Signal Averaging a Spectrum
 S/N increases with n1/2
 Need good synchronization for each replicate scan
Signal/Noise Enhancement, cont.
 Boxcar Averaging
 For smoothing irregularities and enhancing S/N in
wave form. Take the mean of points 1,2 &3, repeat
for 4, 5 &6 and cont.
Signal/Noise Enhancement, cont.
 Savitsky-Galay Smoothing
 A weighted moving average to a series of data. For
three points smoothing
Fourier transform spectroscopy
 measurement technique whereby spectra are collected based on
measurements of a radiative source, using time-domain or spacedomain measurements of the EMR or other type of radiation
 Rather than allowing only one wavelength at a time to pass
through to the detector, this technique lets through a beam
containing many different wavelengths of light at once, and
measures the total beam intensity. Next, the beam is modified to
contain a different combination of wavelengths, giving a second
data point. This process is repeated many times. Afterwards, a
computer takes all this data and works backwards to infer how
much light there is at each wavelength.
 To be more specific, between the light source and the detector,
there is a certain configuration of mirrors that allows some
wavelengths to pass through but blocks others (due to wave
interference). The beam is modified for each new data point by
moving one of the mirrors; this changes the set of wavelengths
that can pass through.
Fourier transform spectroscopy, cont.
The Fourier transform
spectrometer is just a
Michelson interferometer
but one of the two fully
reflecting mirrors is
movable, allowing a variable
delay (in the travel-time of
the light) to be included in
one of the beams
An “interferogram” from a Fourier
transform spectrometer. This is the
“raw data” which can be Fourier
transformed into an actual
spectrum. The peak at the center is
the ZPD position (“Zero Path
Difference”): Here, all the light
passes through the interferometer
because its two arms have equal
Fourier transform spectroscopy, cont.
Fourier Analysis
 In Fourier analysis, a curve is decomposed into series
of sines and cosines \
Y= ao sin(0ωx) + bo cos(0ωx) + b1 sin (1ωx) + b1 cos (1ωx)
+ a2 sin (2ωx) + b2 cos (2ωx) +…
ω = 2pi/(x2 – x1)
 Example
Here the curve spans from
x1 = 0 to x2 = 10
 Constructive
interference occurs if
they are in phase
Molecular and Atomic
Spectrometry is the study of
electromagnetic radiation (EMR) and its
To begin to understand the theory and
instrumental application of spectrometry
requires an understanding of the
interaction of EMR (i.e. light) with matter
What is nature of light?
Are their different types of light?
–How are they the same?
–How are they different?
How does light propagate?
What is Light?
Light is a form of energy
Light travels through space at extremely
high velocities
– The speed of light (c) ~ 3 x 1010 cm/sec or
186,000 miles per second
Light is classified as electromagnetic
radiation (EMR)
Characteristics of Light
Light behaves like a wave.
– That is, it can be modeled or characterized
with wave like properties.
Light also behaves like a particle.
– The photon and photoelectric effect.
Today, we envision light as a selfcontained packet of energy, a photon,
which has both wave and particle like
EMR Wave Characteristics
Wavelength (l) is the distance from one wave crest to
the next.
Amplitude is the vertical distance from the midline of a
wave to the peak or trough.
Frequency (v) is the number of waves that pass through
a particular point in 1 second (Hz = 1 cycle/s)
Wave Properties of
Electromagnetic Radiation
EMR has both electric (E) and magnetic
(H) components that propagate at right
angles to each other.
The Electromagnetic Spectrum
Intro. to Spectrometric Methods
The study of the interaction of electromagnetic radiation
(EMR) with matter.
So, just what is EMR?
– An oscillating electric and magnetic field which travels through space
– A discrete series of “particles” that possess a specific energy but have no
Wave Properties of EMR
The product of λ and ν is constant
Since has a unit of 1/s and has a unit of length, their product, c,
is the velocity of light.
In vacuum, all EMR travels at the velocity of :
2.99792458 x 108 m/s
“The speed of light”
Velocity of propagation in m/s in
other media
λi . νi = velocity of propagation in the media
EMR Wave Characteristics
The frequency of a wave is dictated (or fixed) by
its source, it doesn’t change as the wave passes
through different mediums.
The speed of a wave (u), however, can change
as the medium through which it travels changes
umedium = lv = c/n
Where n = refractive index
Velocity in vacuum
nvacuum = 1
nair = 1.0003 (vair = 0.9997c)
nglass ~1.5 (vgas ~ 0.67c)
Since v is fixed, as l decreases, u must also
Particle Properties of EMR
The energy of a photon depends on its
frequency (v)
Ephoton = hv
h = Planck’s constant
h = 6.63 x 10-27 erg sec or 6.63 x 10-34 Js
Relationship between Wave and
Particle Properties of EMR
Example: What is the energy of a 500 nm
 = c/l = (3 x 108 m s-1)/(5.0 x 10-7 m)
 = 6 x 1014 s-1
E = h =(6.626 x 10-34 J•s)(6 x 1014 s-1) = 4 x 10-19 J
Photoelectric Effect
• Monochromatic
radiation impinges on a
cathode coated with an
alkali metal.
• Electrons are ejected
from the atom and travel
to the positively charged
• The DC amplifier and
readout register the
current created in the
Propagation velocity
Some Radiation Phenomena
Wave description explains certain EMR
– transmission
– reflection and refraction
– Diffraction, the apparent bending of waves around small
obstacles and the spreading out of waves past small openings
– interference
– scattering
– Polarization, the polarization is perpendicular to the wave’s
direction of travel
Propagation of Direction
In two different media reflection always occurs
Reflection ↑ with ↑ of the difference in ni of two media
Normal Incidence ormal
I = Beam (light) intensity
From low density medium to high, bending is towards the normal
Refractive Index
At specified frequency i
ni : in liquids 1.3-1.8
in solids 1.3-2.5
Velocity in
Velocity in the medium
uniformity in all directions
Rayleigh Scattering
Rayleigh scattering (named after the British
physicist Lord Rayleigh is the elastic scattering of
light or other EMR radiation by particles much
smaller than the wavelength of the light, which
may be individual atoms or molecules. It can occur
when light travels through transparent solids and
liquids, but is most prominently seen in gases.
Rayleigh scattering is a function of the electric
polarizability of the particles.
Rayleigh scattering of sunlight in the atmosphere
causes diffuse sky radiation, which is the reason
for the blue color of the sky and the yellow tone of
the sun itself.
When slit is close to lambda the diffraction is
How Light Interacts with Matter.
Atoms are the basic
blocks of matter.
They consist of heavy
particles (called protons
and neutrons) in the
nucleus, surrounded by
lighter particles called
How Light Interacts with Matter.
An electron will interact with a photon.
An electron that absorbs a photon will
gain energy.
An electron that loses energy must emit a
The total energy (electron plus photon)
remains constant during this process.
Characteristics of Absorption
Absorption is defined as the process by
which EMR is transferred, in the form of
energy, to the medium (s, l, or g) through
which it is traveling
Involves discrete energy transfers
Frequency and wavelength selective
Ephoton = hv = c/l
Characteristics of Absorption
Involves transitions from ground state
energy levels to “excited” states
– The reverse process is called emission
For absorption to occur, the energy of the
photon must exactly match an energy level
in the atom (or molecule) it contacts
– Ephoton = Eelectronic transition
We distinguish two types of absorption
– Atomic
– Molecular
How Light Interacts with Matter.
Electrons bound to
atoms have discrete
energies (i.e. not all
energies are allowed).
Thus, only photons of
certain energy can
interact with the
electrons in a given
How Light Interacts with Matter.
Consider hydrogen, the
simplest atom.
Hydrogen has a specific
line spectrum.
Each atom has its own
specific line spectrum
(atomic fingerprint).
Energy Transitions and Photons
The energy of photon that can interact with a transition jump
depends on the energy difference between the electronic
Unique Atomic Signatures
Each atom has a specific set of energy levels, and thus a
unique set of photon wavelengths with which it can interact.
Energy Level Diagram
Absorption and emission
for the sodium atom in the
gas phase
Illustrates discrete energy
ΔEtransition = E1 – E0 = hv = hc/l
Particle Description of light
Movement of e to higher
energy state
Energy States of Chemical
Molecular Absorption
More complex than atomic absorption
because many more potential transitions
– Electronic energy levels
– Vibrational energy levels
– Rotational energy levels
Emolecule = Eelectronic + Evibrational + Erotational
– Eelectronic > Evibrational > Erotational
Result – complex spectra
Energy States of Chemical Species,
Femtosecond10 -15
Emission Spectrum of a Brine Sample (oxyhydrogen flame)
Continuum Spectra
Wide range of wavelengths
Black body continuum radiation
Black body continuum radiation is the result of excitations of the
electrons of atoms and molecules by thermal collisions. Because of
thermal motion of the atoms or molecules the photons emitted due
to transition between levels separated by an energy hv, will have
some spread, (line width). If the photon is absorbed and re-emitted
many times in the volume along the path to the emitting surface the
line broadens, and if it happens enough times the lines will merge to
form a continuum.
The standard way to construct a “block body” is a cavity with an
absorbing surface, kept at constant temperature, with a small hole
for the radiation to emerge. This assures that the emerging photons
will have had many absorptions and emissions before exiting.
Since the energy transitions in molecules are between rotational and
vibrational levels, there are many closely spaced lines in the
emissions spectrum to start with.
Effect of Chemical State
Absorption spectra vary widely in
appearance. Some are numerous
sharp peaks, whereas others consist
of smooth continuous curves.
Generally influenced by:
a) Complexity
b) Physical State
c) Environment of absorbing species
Relaxation Processes
Relaxation Processes, cont.
Stokes shift
Stokes shift is the difference (in wavelength or
frequency units) between positions of the band maxima
of the absorption and emission spectra (fluorescence
and Raman being two examples) of the same electronic
transition. It is named after Irish physicist George G.
When a system (be it a molecule or atom) absorbs a
photon, it gains energy and enters an excited state. One
way for the system to relax is to emit a photon, thus
losing its energy (another method would be the loss of
heat energy). When the emitted photon has less energy
than the absorbed photon, this energy difference is the
Stokes shift. If the emitted photon has more energy, the
energy difference is called an anti-Stokes shift; this
extra energy comes from dissipation of thermal
phonons in a crystal lattice, cooling the crystal in the
process. Yttrium oxysulfide doped with gadolinium
oxysulfide is a common industrial anti-Stokes pigment,
absorbing in the near-infrared and emitting in the
visible portion of the spectrum.
Partial Energy Levels Associated
With Few of the States of a Molecule
Excitation Methods
Major Classes of Spectrochemical
1) Emission
Pe = kc
Atomic emission
2) Luminescence
Pl = kc
3) Scattering
Psc = kc
Raman, turbidity & particle size
4) Absorption
-logP/P0 = kc
Atomic and molecular
(Absorption) Spectrophotometry
n General Stuff:
•Qualitative: Spectrum (a plot of A vs. l) is
characteristic of a specific species
•Quantitative: Absorbance at a particular l can be
related to the amount of absorbing species
Definitions and units
l : monochromatic wavelength (cm)
Po : incident radiant power (erg cm -2 s -1 )
P : transmitted radiant power (erg cm -2 s
b : absorption path length (cm)
Beer’s Law
or the Beer-Lambert Law
Pierre Bouguer discovered that light transmission
decreases with the thickness of a transparent sample in
1729. This law was later rediscovered by Lambert, a
mathematician, and then by Beer, who published in 1852
what is now known as the Beer-Lambert-Bouguer law. Beer’s
1852 paper is the one that is often cited in older textbooks.
Bouguer’s contribution is rarely mentioned and the law is
known as either “Beer’s law” or “the Beer-Lambert law”.
Consider a beam of light
with an (initial) radiant
intensity Po
The light passes through a
solution of concentration (c)
The thickness of the
solution is “b” cm.
The intensity of the light
after passage through the
solution (where absorption
occurs) is P
Concentration (c)
Spectroscopy Terms Describing
Absorption (Beer’s Law)
We Defined
Transmittance (T) = P/P0 (units = %)
Absorbance (A) (units = none)
A = log (P0/P)
A = -log (T) = log (1/T)
A = abc (or εbc) transmittance
T = —-Po
P0 = 10,000
P = 5,000
T =
= 0.5
P0 10000
A = -log T = -log (0.5) = 0.3010
Beer’s Law
A = abc = ebc
Beer’s Law
A = ebc
Path Length Dependence, b
Beer’s Law
A = ebc
Path Length Dependence, b
Beer’s Law
A = ebc
Path Length Dependence, b
Beer’s Law
A = ebc
Path Length Dependence, b
Beer’s Law
A = ebc
Wavelength Dependence, a
Beer’s Law
A = ebc
Wavelength Dependence, a
Beer’s Law
A = ebc
Wavelength Dependence, a
Beer’s Law
A = ebc
Wavelength Dependence, a
Non-Absorption Losses
“Reflection and
scattering losses.”
Limitations to Beer’s Law
– At high concentrations charge distribution effects
occur causing electrostatic interactions between
absorbing species
– Analyte dissociates/associates or reacts with solvent
– ε = f(λ); most light sources are polychromatic not
monochromatic (small effect)
– Stray light – comes from reflected radiation in the
monochromator reaching the exit slit.
Chemical Limitations
A reaction is occurring as you record
Absorbance measurements
Cr2O72- + H2O
2H+ + CrO42CrO42Cr2O72A550
Instrumental Limitations – ε = f(λ)
How/Why does ε
vary with λ?
Consider a
wavelength scan for
a molecular
compound at two
different wavelength
Larger the Bandwidth – larger deviation
In reality, a
monochromator can
not isolate a single
wavelength, but
rather a small
wavelength band
Instrumental Limitations – Stray Light
How does stray light effect Absorbance
and Beer’s Law?
A = -log P/Po = log Po/P
When stray light (Ps) is present, the
absorbance observed (Aapparent) is the sum
of the real (Areal) and stray absorbance
Instrumental Limitations – Stray Light
Aapp = Areal
 Po + Ps 
+ Astray = log 
 P + Ps 
As the analyte concentration increases
([analyte]↑), the intensity of light exiting the
absorbance cell decreases (P↓)
Eventually, P < Ps Instrumental Limitations – Stray Light Result – non-linear absorption (Analyte vs. Conc.) as a function of analyte concentration – Similar to polychromatic light limitations The EMR Spectrum Different portions of the EMR spectrum and different types of spectroscopy involve different parts (quantum states) of the atom 66 Molecular Absorption Spectra in the Solution Phase In solvents the rotational and vibrational transitions are highly restricted resulting in broad band absorption spectra 67 Emission of EMR EMR is released when excited atoms or molecules return to ground state – Reverse of the absorption process – We call this process “emission” Initial excitation can occur through a number of pathways – Absorption of EMR – Electrical discharge – High temperatures (flame or arc) – Electron bombardment 68 Emission of EMR We distinguish several types of emission 1. Atomic 2. X-Ray 3. Fluorescence Involves molecules Resonance and non-resonance modes 4. Phosphorescence Non-radiative relaxation Similar to fluorescence only relaxation times are slower than fluorescence Involves metastable intermediates 69 Energy Level Diagrams and Emission 70 Fluorescence is emission of light from excited singlet states (the electron in the excited state orbital is spin paired (has the opposite spin) to the electron in the ground state orbital) – therefore, return to the ground state is spin-allowed, and the excited state lifetime is short (1 -10 ns). Phosphorescence is emission of light from excited triplet states (the electron in the excited orbital has the same spin orientation as the ground state electron) –therefore, the transition to the ground state is spin-forbidden, and the excited state lifetime is long (ms to seconds or even minutes!) Molecular chemiluminescence: emission from an excited species that formed in the course of chemical reaction. An optical instrument in the context of instrumental analysis is used to analyze the properties of light or optical materials.  General Components Intensity stays ~same over wide range of Lambdas waves can propagate without deformation Emit limited # of lines or small range bands waves can propagate without deformation. e.g. sound waves Wave deforms as propagate Regions of spectra Change intensity only slowly as function of λ Sources Limited # of lines or bands detectors Pyroelectric: ability of certain materials to generate a temporary voltage when they are heated or cooled. Pyroelectricity (from the Greek pyr, fire, and electricity) is the ability of certain materials to generate a temporary voltage when they are heated or cooled.[  It consists of a gas-filled enclosure with an infrared absorbing material and a flexible diaphragm or membrane. When infrared radiation is absorbed, it heats the gas, causing it to expand. The resulting increase in pressure deforms the membrane. Light reflected off the membrane is detected by a photodiode, and motion of the membrane produces a change in the signal on the photodiode material Wavelength selectors  Fused quartz or fused silica is glass consisting of silica in amorphous (non-crystalline) form. It differs from traditional glasses in containing no other ingredients, which are typically added to glass to lower the melt temperature. Fused silica, therefore, has high working and melting temperatures.   Sodium silicate is the common name for compounds with the formula Na2(SiO2)nO. A well known member of this series is sodium metasilicate, Na2SiO3. Also known as waterglass or liquid glass, these materials are available in aqueous solution and in solid form. The pure compositions are colorless or white. Na2CO3 + SiO2 → Na2SiO3 + CO2    Most spectroscopic (the study of the interaction between matter and radiated energy) analysis require radiation (source) that consists of a limited, narrow, continuous group of λs called bands The output of a typical wavelength selector is below Limited range means better performance Types of λ selectors:  1) Filters 2) Monochromators 1) Filters a) Absorption Filters Optical filters selectively transmit light in a particular range of wavelengths, that is, colours, while blocking the remainder.   Function by absorbing selected portions of the spectrum, Less expensive.  e.g. colored glass, dye suspended in gelatin and sandwiched between glass plates 550 nm transmitted by the filter Nominal wavelength Effective bandwidth b) Interference filters in dielectric nλ’ = 2d λ = λ’ η λ= (2dη)/n Where: n = order of interference d = thickness of Dielectric layer λ = transmitted by filter λ‘ = λ in dielectric η = refractive index of dielectric (Eta) Dielectric: insulating material or a very poor conductor of electric current  Concept d is the thickness of the dielectric layer between the films. For reinforcement to occur at point 2, the distance traveled by beam reflected at point 1 must be the multiple of Lambda in the medium. The thickness of dielectric layer determines the wave length of transmitted radiation Point 1 2 1 point 2Poi  Concept, cont. nλ’ = 2d/cos θ Where n is the order of interference constant, λ’ wavelength in the medium, d is the thickness, θ is the incident angle. When θ approaches zero (cos 0 =1) nλ’ = 2d Refractive Index The wavelength in the air is λ = λ’η By substitution, the wavelength transmitted by the filter: λ = 2d η/n 2) Monochromator  A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input. Are designed for spectral scanning (vary the wavelength)  They all use slits, collimating lenses/mirrors (bring into lines and make //), dispersion elements (gratings or prisms), and exit slits (you should have seen that in Lab 1) Ƞ1= C/v1 a) Prisms Typical Prism Monochromator b) diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. Because of this, gratings are commonly used in monochromators. b) Diffraction Monochromator Echellette Grating The conditions for constructive interference nλ = d(sinθi +sinθr) Next slide Example: For θi = 30o and θr = 45o and grating ruled at 2000 line/mm nλ = d(sinθi +sinθr) = 1/2000(sinθi +sinθr) = 6.03 x 10-7 m = 603 nm 1st order = 603/2 = 301.5 nm 2nd order n = the order  1) Spectral purity The exit beam of Monochromator is usually contaminated with stray radiation (far different from the instrument setting). It is generally caused by mechanical and housing imperfections of the instrument 2) Dispersion “The ability of the monochromator to separate different wavelengths depends on its dispersion” The focal plane represents the area light is focused linear dispersion D, variation in wavelength as a function of y (distance along the focal planes, AB, slide # 26), the extent to which a spectral interval is spread D = dy/dλ D-1 = dλ/dy = dλ/f dθr , has units of nm/mm f = focal length of monochromator = d/nf ( at small angles with diffraction

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