Common Problems : a) Mixtures :
blank samples often contain multiple absorbing species.
the absorbance is the sum of all the individual absorbencies
A= A
1
+ A
2
+A
3
+ … = e
1 bc + e
2 bc + e
3 bc …
- substances in both the blank and sample which absorb can be
“blanked out” in both double and single beam spectrometers.

But, If the blank absorbance is high, P o will decrease too much, the response will be slow and the results inaccurate
Large blank absorbance l scan of substance
If blank absorbance too high:
dilute the sample
use a different l where the analyte absorbs more relative to the interference.
- use a different method of separation

b)
Instrumental Deviations from Beer’s Law
:
stray light (already discussed).
polychromatic light (more then a single l
)
 since all instruments have a finite band pass, a range of l ’s
 are sent through the sample.
e may be different for each l
Deviation’s from Beer’s law at high concentration

Illustration of Deviation from Beer’s law:
Let us say that exactly 2 wavelengths of light were entering the sample l
= 254 nm l
= 255 nm e e
254
255
=10,000
= 5,000 let P o
= 1 at both l ’s
What happens to the Beer’s law plot as c increases?
A = A
254
+ A
255
At the individual l ’s:
A = log P o
/P (total) = log (P o
254 + P o
255 )/(P 254 + P 255 )
A
254
= e
254 bc = log P o
254 /P 254
10 e bc = P o
254 /P 254
P 254 = P o
/10 e bc = P o
10 e bc
For both together:
A = log (P o
254 + P o
255 )/(P o
254 10 e
254 bc + P o
255 10 e
255 bc )

Since P o
254 = P o
255 =1:
A = 2.0/(P o
254 10 e
254 bc + P o
255 10 e
255 bc )
A = 2.0/(10 -10,000x1.0xc
+ 10 -5000x1.0xc
)
C
10 -6 M
10 -5 M
10 -4 M
10 -3 M
A (actual) A(expected)
0.0075
0.074
0.068
5.3
0.0075
0.075
0.75
7.5
8
7
6
5
4
3
2
1
0
Negative Deviation
2 10
-4
4 10
-4
6 10
-4
Concentration (M)
8 10
-4
1 10
-3
The results are the same for more l ’s of light. The situation is worse for greater differences in e ’s (side of absorption peak, broad bandpass)
Always need to do calibration curve! Can not assume linearity outside the range of linearity curve!

b)
Chemical Deviations from Beer’s Law
:
Molar absorptivity change in solutions more concentrated than 0.01M
 due to molecular interactions
 Beer’s law assumes species are independent

 electrolytes may also cause this problem e is also affected by the index of refraction
association, dissociation, precipitation or reaction of analyte
 c in Beer’s law is the concentration of the absorbing species
 commonly use the analytical concentration
– concentration of all forms of the species. phenolphthalein:
HIn
Red, l
=600nm
K a
H + + In colorless
If solution is buffered, then pH is constant and [HIn] is related to absorbance.

But, if unbuffered solution, equilibrium will shift depending on total analyte concentration
K a example: if K a
= 10 -4
HIn
H + + In -
C
HIn
[HIn] [In ]
10 -5 8.5x10
-7 9.2x10
-6
[HIn]/[In
0.0924
]
10 -4 3.8x10
-5 6.2x10
-5 0.613
10 -3 7.3x10
-4 2.7x10
-4 2.70
Expected
Actual
C
HIn
“Apparent” deviation since can be accounted for by chemical equilibrium

But, if unbuffered solution, equilibrium will shift depending on total analyte concentration
K a example: if K a
= 10 -4
HIn
H + + In -
Isosbestic point
At the isosbestic point in spectra :
A = e b([HIn] + [In ])

c) Non-constant b :
worse for round cuvettes
- use parallel cuvettes to help
P
0
B
2
B
1
A = log
10
P o
/P = e bc
P
2
P
1

d) Instrument noise : noise short term baseline fluctuations, which decrease the precision of the analysis
 can not measure A precisely
 the various sources of noise each cause some uncertainty in the absorbance measurement and can be treated as individual standard deviations.
1) 0%T noise:
- noise when light beam is blocked
- seldom important
- typically

0.01%T
2) Readout Precision :
- especially with a meter
- typically

0.5%T  1-3% error in concentration
3) Shot Noise:
- occurs when e transfers across a junction (like the space between cathode & anode in PMT).
- causes random fluctuations in current since individual e random times arrive at
- increases with increase current (%T). Especially bad above 95%T.

4) Flicker Noise:
- noise from the lamp due to intensity changes
- important at high transmittances.
5) Cell positioning uncertainty :
- not really noise, but affects precision
- minor imperfections, scratches or dirt change %T
- may be the major cause of imprecision
Category Characterized by
Case I
S
T
= k
1
Case II
S k T T
T

2
2 
Typical Sources
Limited Readout resolution
Heat detector Johnson noise
Likely to be Important in
Inexpensive photometers and spectrophotometers having small meter scales
IR and near-IR spectrophotometers and photometers
Dark current and amplifier noise Regions where source intensity and detector are low
Photon detector shot noise High-quality UV-visible spectrophotometers
Case III
S
T
= k
3
T
Cell positioning uncertainties
Source flicker
High-quality UV-visible and IR spectrophotometers
Inexpensive photometers and spectrophotometers

Taken together, these noise sources indicate that the intermediate absorbance and transmittance ranges should be used.
- at low %T, 0%T, noise and readout precision are important
- at high %T, shot and flicker noise are large.
Keep A in range of 0.1 – 1.5 absorbance units (80 -3%T)

:
A) Molar Absorptivities ( e
) in UV-Vis Range : e
= 8.7 x 10 19 PA
P
– transition probability (ranges from 0.1 to 1, for likely transitions)
A – cross-section area of target molecule (cm 2 )
-
-
~10 -15 cm 2 for typical organics e max
= 10 4 to 10 5 L/mol-cm e
< 10 3 – low intensity (P 
0.01)
Name but-1-en-3-yne cyclohex-2-enone
Structure l max
219
225 e
7,600
10,300 toluene 206 7,000
3,4-dimethylpent-3-en-2-one 246 5,300

CH
3
CH
2
CH
2
- For Compounds with Multiple Chromophores:
 If greater then one single bond apart
e are additive
l constant
CH
=CHCH
2
2
CH=CH
CH
2
2
CH=CH
2 l max
= 184 e max
= ~10,000 l max
=185 e max
= ~20,000
H
2
C=CHCH=CH
2
 If conjugated
- shifts to higher l ’s (red shift) l max
=217 e max
= ~21,000

Example 6: The equilibrium constant for the conjugate acid-base pair
HIn + H
2
K = 8.00x10
-5
O H
3
O + e
= 8.04x10
3
+ In e
= 0.755x10
3
Calculate the absorbance at 430 nm for an indicator concentration of 3.00x10
-4 M

:
B) Absorbing Species in UV/Vis:
1) Electronic transitions involving organic compounds, inorganic compounds, complexes, etc.
Basic process:
M + h n  M *
10 -8 – 10 -9 s
M*

M + heat
( or fluorescence, light, or phosphorescence ) or
10 -8
M*
– 10 -9 s

N
( new species, photochemical reaction )
Note : excited state (M*) is generally short and heat produced not generally measurable.
Thus, get minimal disturbance of systems (assuming no photochemical reaction)

2) Absorption occurs with bonding electrons.
E( l
) required differs with type of bonding electron.
- UV-Vis absorption gives some information on bonding electrons (functional groups in a compound.
- Most organic spectra are complex
 electronic and vibration transitions superimposed
 absorption bands usually broad
 detailed theoretical analysis not possible, but semi-quantitative or qualitative analysis of types of bonds is possible.
 effects of solvent & molecular details complicate comparison

- Single bonds usually too high excitation energy for most instruments (

185 nm )
 vacuum UV
 most compounds of atmosphere absorb in this range, so difficult to work with.
 usually concerned with functional groups with relatively low excitation energies (190
 l
850 nm).
Types of electron transitions: i) s
, p
, n electrons
Sigma ( s
) – single bond electron
Low energy bonding orbital High energy anti-bonding orbital

Pi ( p
) – double bond electron
Low energy bonding orbital High energy anti-bonding orbital
Non-bonding electrons ( n ): don’t take part in any bonds, neutral energy level.
Example: Formaldehyde



 s  s
* transition in vacuum UV n
 s
* saturated compounds with non-bonding electrons l
~ 150-250 nm e
~ 100-3000 ( not strong) n
 p
*, p  p
* requires unsaturated functional groups (eq. double bonds) most commonly used, energy good range for UV/Vis l
~ 200 - 700 nm n
 p
* : e
~ 10-100 p  p
*: e
~ 1000
– 10,000

Absorption Characteristics of Some Common Chromophores
Chromophore Example Solvent l max
(nm)
Alkene
Alkyne
Carbonyl
C
6
H
13
HC CH
2
C
5
H
11
C C CH
3
n-Heptane
n-Heptane
n-Hexane
177
178
196
225
186
280
Carboxyl
Amido
Azo
Nitro
Nitroso
Nitrate
O
CH
3
CCH
3
O
CH
3
CH
O
CH
3
COH
O
CH
3
CNH
2
H
3
CN NCH
3
CH
3
NO
2
C
4
H
9
NO
C
2
H
5
ONO
2
n-Hexane
Ethanol
Water
Ethanol
Isooctane
Ethyl ether
Dioxane
180
293
204
214
339
280
300
665
270 e max
13,000
10,000
2,000
160
1,000
16
Type of transition p  p
* p  p
*
_
_ n  s
* n  p
*
Large
12
41 n  s n  p
* n  p
*
*
60 n  p
*
5
22
100
20
12 n  p
* n  p
*
_ n  p
* n  p
*

Other Examples of Some
Common Chromophores

ii) d/f electrons (transition metal ions)
 Lanthanide and actinide series
- electronic transition of 4f & 5f electrons
- generally sharp, well-defined bands not affected by associated ligands
 1 st and 2 nd transition metal series
- electronic transition of 3d & 4d electrons
- broad peaks
Crystal-Field Theory
- In absence of external field d -orbitals are identical
- Energies of d -orbitals in solution are not identical
- Absorption involves e transition between d orbitals
- In complex, all orbitals increase in energy where orbitals along bonding axis are destabilized

Magnitude of
D depends on:
- charge on metal ion
- position in periodic table
- ligand field strength :
I < Br < Cl < F < OH < C
2
O
4
2~ H
2
O < SCN -
< ethylenediamine < o -phenanthroline < NO
2
-
< NH
< CN -
3
D increases with increasing field strength, so wavelength decreases

iii) Charge Transfer Complexes
 Important analytically because of large e
(> 10,000)
 Absorption of radiation involves transfer of e from the donor to orbital associated with acceptor
excited state is product of pseudo oxidation/reduction process
 Many inorganic complexes of electron donor (usually organic)
& electron acceptor (usually metal)
- examples: Iron III thiocyanate
Iron II phenanthroline
(colorless) (deep red color)

C) Qualitative Analysis:
1) Limited since few resolved peaks
- unambiguous identification not usually possible.
2) Solvent can affect position and shape of curve.
- polar solvents broaden out peaks, eliminates fine structure.
Loss of fine structure for acetaldehyde when transfer to solvent from gas phase
Also need to consider absorbance of solvent.

(a) Vapor
2) Solvent can affect position and shape of curve.
- polar solvents broaden out peaks, eliminates fine structure.
Loss of fine structure for 1,2,4,5tetrazine as solvent polarity increases
(b) Hexane solution
(c) Aqueous

3) Solvent can also absorb in UV-vis spectrum.

3) Can obtain some functional group information for certain types of compounds..
weak band at 280-290 nm that is shifted to shorter l ’s with an increase in polarity (solvent) implies a carbonyl group.
 acetone: in hexane, l in water, l max max
= 279 nm (
= 264.5 nm e
= 15)
- solvent effects due to stabilization or destabilization of ground or excited states, changing the energy gap.
 since most transitions result in an excited state that is more polar than the ground state
- 260 nm with some fine structure implies an aromatic ring.
Benzene in heptane
More complex ring systems shift to higher l ’s (red shift) similar to conjugated alkenes

C) Quantitative Analysis (Beer’s Law):
1) Widely used for Quantitative Analysis Characterization
wide range of applications (organic & inorganic)
limit of detection

10 -4 to 10 -5 M (10 -6 to 10 -7 M; current)
- moderate to high selectivity
- typical accuracy of 1-3% ( can be ~0.1%)
- easy to perform, cheap
2) Strategies a) absorbing species
- detect both organic and inorganic compounds containing any of these species ( all the previous examples)

b) non- absorbing species
react with reagent that forms colored product
- can also use for absorbing species to lower limit of detection
- items to consider: l
, pH, temperature, ionic strength
- prepare standard curve (match standards and samples as much as possible) reagent
(colorless)
Non-absorbing
Species (colorless)
Complex
(red)
When all the protein is bound to Fe 3+ , no further increase in absorbance.
As Fe 3+ continues to bind protein red color and absorbance increases.

Standard Addition Method (spiking the sample)
- used for analytes in a complex matrix where interferences in the UV/Vis for the analyte will occur: i.e. blood, sediment, human serum, etc..
- Method:
(1) Prepare several identical aliquots, V x
, of the unknown sample.
(2) Add a variable volume, V s
, of a standard solution of known concentration, c s
, to each unknown aliquot.
Note: This method assumes a linear relationship between instrument response and sample concentration.

(3) Dilute each solution to an equal volume, V t
.
(4) Make instrumental measurements of each sample to get an instrument response, IR.

(5) Calculate unknown concentration, c x
, from the following equation.
m =
D y/
D x b = y-intercept
S
 kV s c s
V t
 kV x c x
V t
S
 mV s
 b
(V s
)
0
V s
C x

( S 2

S )V x c x
 bc s mV x
S =
k =
V s c s
V x c x
V t
=
=
=
=
=
Note: assumes a linear relationship between instrument response and sample concentration.

c) Analysis of Mixtures
use two different l ’s with different e ’s
A 1 = e
1
M bc
M
+ e
1
N bc
N
A 2 = e
2
M bc
M
+ e
2
N bc
N
( l
1 )
( l
2 )
Note: need to solve simultaneous equations

d) Photometric titration
can measure titration with UV-vis spectroscopy.
requires the analyte (A), titrant (T) or titration product (P) absorbs radiation

Example 7: Given:
Species
A (7.50x10
-5 M)
B (4.25x10
-5 M)
Absorbance (1.00 cm cell)
475 nm
0.155
0.702
700 nm
0.755
0.091
Calculate the concentrations of A and B in solutions that yielded an absorbance of 0.439 at 475 nm and 1.025 at 700 nm in a 2.50-cm cell.