Shaanxi Normal University Instrumental Analysis

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Shaanxi Normal University

Instrumental Analysis

Chapter 1

Introduction to Spectrochemical Methods

This

composite

image

of

a

sunspot

group

was

collected

with

the

Dunn

solar

tele
-

scope

at

the

sacramento

Peak

Observatory

in

New

Mexico

on

March

29
.

2001
.
The

lower

portion,

consisting

of

four

frames,

was

collected

at

a

wavelength

of

393
.
4

nm,

and

the

upper

portion

was

collected

at

430
.
4

nm
.
The

lower

image

represents

calcium

ion

concertraTion,

with

the

intensity

of

the

blue

color

proportinal

to

the

amount

of

the

ion

in

the

suspot
.

The

upper

image

shows

the

presence

of

the

CH

molecule
.

Using

data

like

these
.

it

is

and

abundance

ofvirtually

any

chemical

species

in

the

observable

universe
.

Note

that

the

Earth

could

fit

into

the

large

black

core

sunspot

in

the

upper

left

of

each

of

composite

images
.

Shaanxi Normal University

Instrumental Analysis

1
A

PROPERTIES

OF

ELECTROMAGNETIC

RADIATION

Electromagnetic

radiation

is

a

form

of

energy

that

is

transmitted

through

space

at

enormous

velocities
.

1
A
-
2

The

Particle

Nature

of

light
:

Photons

Wave

nature

of

a

beam

of

single
-
frequency

electromagnetic

radiation
.

In

(a)
.

a

plane
-
polarized

wave

is

shown

propagating

along

the

x
-
axis
.

The

electric

field

oscillates

in

a

plane

perpendicular

to

the

magnetic

field,

If

the

radiation

were

un

polarized,

a

component

of

the

electric

field

would

be

seen

in

all

planes
.

In

(b)
.

only

the

electric

field

oscillations

are

shown
.


Shaanxi Normal University

Instrumental Analysis



V
(1
-
1)


Note

that

in

Equation

1
-
1
,

(distance/time)

=

(waves/time)

(

distance/wave)
.

1
10
1
8
10
00
.
3
10
00
.
3








s
cm
ms
c

(1
-
2)

1
4
2000
/
10
00
.
5
1





cm
m
cm
m



Calculate

the

wavenumber

of

a

beam

of

infrared

radiation

with

a

wavelength

of

5
.
00

m

EXAMPLE 1
-
1


Shaanxi Normal University

Instrumental Analysis

Figure

1
-
2

Change

in

wavelength

as

radiation

passes

from

air

into

a

dense

glass

and

back

to

air
.

Note

that

the

wavelength

shortens

by

nearly

200

nm
.

or

more

than

30
%
.

as

it

passes

into

glass
:

a

reverse

change

occurs

as

the

radiation

again

enters

air
.

Shaanxi Normal University

Instrumental Analysis

1
A
-
2

The

Particle

Nature

of

light
:

Photons





hc
hc
h
E



Where

h

is

Planck's

constant

Js
34
10
63
.
6


EXAMPLE

1
-
2


Calculate

the

energy

in

joules

of

one

photon

of

the

radiation

described

in

Example

1
-
1


J
m
c
s
m
c
s
J
hc
E
20
1
10
34
10
98
.
3
2000
10
00
.
3
10
63
.
6













Shaanxi Normal University

Instrumental Analysis

1
B

INTERACTION

OF

RADIATION

AND

MATTER


The

visible

region

of

the

spectrum

extends

from

about

400

nm

to

700

nm
.

Shaanxi Normal University

Instrumental Analysis

1
B
-
1

The

Electromagnetic

Spectrum


Emission

or

chemiluminescence

processes
.

In

(a),

the

sample

is

excited

by

the

application

of

thermal

electrical
.

or

chemical

energy
.

These

processes

do

not

involve

radiant

energy

and

are

hence

called

nonradiative

processes
.

In

the

energy
-
level

diagram(b)
.

the

dashed

lines

with

upward
-
pointing

arrows

symbolize

these

nonradiative

excitation

processes,

while

the

solid

lines

with

downward

pointing

arrows

indicate

that

the

analyte

loses

its

energy

by

emission

of

a

photon
.

In(c),

the

resulting

spectrum

is

shown

as

a

measurement

of

the

radiant

power

emitted

PE

as

a

function

of

wavelength


Shaanxi Normal University

Instrumental Analysis

Absorption

methods
.

Radiation

of

incident

radiant

power

Po

can

be

absorbed

by

the

analyte,

resulting

in

a

transmitted

beam

of

lower

radiant

power

P
.

For

absorption

to

occur,

the

energy

of

the

incident

beam

must

correspond

to

one

of

the

energy

differences

shown

in

(b)
.

The

resulting

absorption

spectrum

is

shown

in

(c)
.

Shaanxi Normal University

Instrumental Analysis

1
C

RADIATION

ABSORPTION

1
C
-
1

The

Absorption

Process

o
p
p
T
/

(1
-
4)

%
100
%
tan



o
P
P
T
ce
transmit
Percent
monochromatic

radiation


refers

to

radiation

of

a

single

color
;

that

is,

a

single

wavelength

or

frequency
.

In

practice,

it

is

virtually

impossible

to

produce

a

single

color

of

light


Shaanxi Normal University

Instrumental Analysis

The

absorbance

A

of

a

solution

is

related

to

the

transmittance

in

a

logarithmic

manner
.


p
p
T
A
o
log
log



(1
-
5)

Shaanxi Normal University

Instrumental Analysis

Measuring Transmittance and Absorbance


For example. about 8.5% of a beam of yellow light is lost
by reflection when it passes through a glass cell.


Shaanxi Normal University

Instrumental Analysis

To compensate for these effects.

solution
solvent
o
P
P
P
P
A
log
log


(1
-
6)

Beer's Law

abc
P
P
A
o


)
/
log(
(1
-
7)

Here,

a

is

a

proportionality

constant

called

the

absorptivity
.

Because

absorbance

is

a

unitless

quantity,

the

absorptivity

must

have

units
.


Shaanxi Normal University

Instrumental Analysis

bc
A


(1
-
8)

the

proportionality

constant

is

called

the

molar

absorptivity

and

is

given

the

special

symbol
.

ε
.


Deriving Beer’s Law

Attenuation with initial power Po by a solution containing c mol/L of
absorbing solute and a path length of b cm (P < Po).

Shaanxi Normal University

Instrumental Analysis

Using Beer's Law

EXAMPLE 1
-
3


A

7
.
25

10
-
5

M

solution

of

potassium

permanganate

has

a

transmittance

of

44
.
1
%

when

measured

in

a

2
.
10
-
cm

cell

at

a

wavelength

of

525

nm
.

Calculate


(a)

the

absorbance

of

this

solution
;

(b)

the

molar

absorptivity

of

KMnO
4

(a)

A

=

-
log

T

=

-
log

0
.
441

=

-
(
-
0
.
3554
)

=

0
.
355


(b)

From

Equation

1
-
8
,

1
1
3
1
5
L
10
23
.
2
)
10
25
.
7
10
.
2
/(
3554
.
0
/
A










cm
mol
molL
cm
bc
ε
Shaanxi Normal University

Instrumental Analysis

Why is a

Red Solution Red?

Shaanxi Normal University

Instrumental Analysis

Color

of

a

solution
.

White

light

from

a

lamp

or

the

sun

strikes

the

solution

of

Fe(SCN)
2
+
.

The

fairly

broad

absorption

s
pectrum

shows

a

maximum

absorbance

in

the

460

to

500
-
nm

range
.

The

complementary

red

color

is

transmitted
.


Shaanxi Normal University

Instrumental Analysis

Molecular Absorption


Shaanxi Normal University

Instrumental Analysis

Infrared

Absorption,

Infrared

radiation



Generally

is

not

sufficiently

energetic

to

cause

electronic

transitions,

but

it

can

induce

transitions

in

the

vibrational

and

rotational

states

associated

with

the

ground

electronic

state

of

the

molecule
.

Four

of

these

transitions

are

depicted

in

the

lower

left

part

of

Figure

1
-
12


1

to

λ
4
)
.


Shaanxi Normal University

Instrumental Analysis

Shaanxi Normal University

Instrumental Analysis

Absorption of Ultraviolet and Visible Radiation

Shaanxi Normal University

Instrumental Analysis

Typical

ultraviolet

absorption

spectra
.

The

compound

is

1
.
2
.
4
.
5
-
tetrazine,

In

(a)
.

the

spectrum

is

shown

in

the

gas

phase
.

where

many

lines

due

to

electronic
.

vibrational
.

and

rotational

transitions

are

seen
.

In

a

nonpolar

solvent

(b)
.

the

electronic

transitions

can

be

observed,

but

the

vibrational

and

rotational

structure

has

been

lost
.

In

a

polar

solvent

(c)
.

the

strong

intermolecular

forces

have

caused

the

electronic

peaks

to

blend

together

to

give

only

a

single

smooth

absorption

peak
.

(From

S
.

F
.

Mason
.

J
.

Chem
.

Soc,

1959
,

1265
.
)


Shaanxi Normal University

Instrumental Analysis

1C
-
3 Limits to Beer's Law

Real Limitations to Beer's Law


Beer's

law

describes

the

absorption

behavior

only

of

dilute

solutions

and

in

this

sense

is

a

limiting

law
.

At

concentrations

exceeding

about

0
.
01

M
.

the

average

distances

between

ions

or

molecules

of

the

absorbing

species

are

diminished

to

the

point

where

each

particle

affects

the

charge

distribution,

and

thus

the

extent

of

absorption

of

its

neighbors
.


Shaanxi Normal University

Instrumental Analysis

Chemical Deviations


Deviations

from

Beer's

law

appear

when

the

absorbing

species

undergoes

association
.

dissociation
.

or

reaction

with

the

solvent

to

give

products

that

absorb

differently

from

the

analyte
.


Instrumental Deviations: Polychromatic Radiation


Beer's

law

strictly

applies

only

when

measurements

are

made

with

monochromatic

radiation
.

In

practice,

polychromatic

sources

that

have

a

continuous

distribution

of

wavelengths

are

used

in

conjunction

with

a

grating

or

with

a

filter

to

isolate

a

nearly

symmetric

band

of

wavelengths

around

the

wavelength

to

be

employed
.


Shaanxi Normal University

Instrumental Analysis

Shaanxi Normal University

Instrumental Analysis

1
1
1
λ
0
λ
T
λ
I
I
log
bc
ε
log
A











bc
ε
0
λ
λ
1
λ
1
1
10
I
I



bc
ε
0
λ
λ
λ2
1
2
10
I
I














λ2
λ1
0
λ
0
λ
λ
I
I
I
I
A
2
1
-

=










bc
ελ
-
2
0
bc
ε
-
1
0
2
0
1
0
2
λ1
10

I
10
I
I
I









bc
ε
0
λ
bc
ε
0
λ
0
λ
0
λ
λ
λ2
2
λ1
1
2
1
10
I
10
I
log
I
I
log
A








Shaanxi Normal University

Instrumental Analysis