Transcript Chapter 13 – UV-VIS AND NEAR IR ABSORPTION

Chapter 13 – UV-VIS AND
NEAR IR ABSORPTION
SPECTROSCOPIES
First part of this chapter applicable to
other absorption spectroscopies e.g. IR
and AA even though it is covered in this
section.
Beer’s Law – Ideal Behavior
• Decrease in power is
proportional to power
going through cell and
distance traveled:

dP
= kCdx
P
• Rearrange and integrate
over the length of the cell:
where e = molar absorptivity
and is the collection of other
terms.
• %T = P/Pox100
 ln
P
= kcb
Po
Po
log
= ebc
P
Chapter 13 - 2
Absorbance
• Another term called absorbance is
generally used in place of either of these
and is defined as A = log(Po/P);
• Beer's law equation becomes: A = ebC.
• Beer’s Law predicts linear behavior
between concentration and absorbance
but not between amount power coming out
of sample.
Chapter 13 - 3
Losses During Absorption
• Real sample cells have losses
due to reflection and scattering;
• Minimized by using a reference
cell. with the same spectral
characteristics.
• Measured absorbance is A =
log Psolvent/Psolution and is
assumed to be approximately
equal to the correct
absorbance in the absence of
these effects i.e. log Po/P.
Chapter 13 - 4
Real Limitations
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Linearity is observed in the low
concentration ranges(<0.01), but
may not be at higher
concentrations.
This deviation at higher
concentrations is due to
intermolecular interactions.
As the concentration increases, the
strength of interaction increases
and causes deviations from
linearity.
The absorptivity not really constant
and independent of concentration
but e is related to the refractive
index (h ) of the solution by the
expression:
At low concentrations the refractive
index is essentially constant-so e
constant and linearity is observed.
Willard, Merritt, Dean and Settle, Instrumental
Methods of Analysis, p. 68
Chapter 13 - 5
e  e true 

( + 2 ) 2
CHEMICAL DEVIATIONS
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Apparent deviations in Beer's law sometimes
occur from various chemical effects, such as
dissociation, association, complex formation,
polymerization or other equilibrium.
E.g. K2Cr2O7 solutions exist as a dichromate,
chromate equilibrium:
–
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At lmax of 350 (and 450) nm and 372 nm
respectively.
There is a strong dependence of position of this
equilibrium on relative pH.
Absorbance at one of these wavelengths for a given
initial concentration of [K2Cr2O7] strongly depends
upon the pH.
When plotting absorbance as a function of [K2Cr2O7],
the plot will not be linear since dilutions will affect the
equilibrium and thus the relative amounts of the two.
Isobestic points where the absorption coefficient
is the same for the two species. This point can be
used to determine concentrations of analytes with
no danger from non-linearity associated with the
analyte being in different forms.
Chapter 13 - 6
Willard, Merritt, Dean and Settle,
Instrumental Methods of Analysis, p. 70
INSTRUMENTAL DEVIATIONS
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Factors affecting resolution and sensitivity:
Polychromatic radiation: Non-linear behavior is observed
when band width of incident radiation is larger than the
bandwidth of the absorbing band.
E.g. Assume there are two wavelengths incident upon the
sample and occur at significantly different parts of the
absorption band.
the absorption coefficients for the two were not the same.
the total radiant power = PA,o + PB,o = Po.
radiation out of the sample would be P = PA + PB.
measured absorbance will be:
 P A,o + PB,o 

A measured = log
+
PB 
 PA
Beer's law for each is: PA,o/PA = 10eAbc and PB,o/PB = 10eBbc.


P A,o + PB,o

Substitute: A = log



e
bc

e
bc
A
B
+ PB,o  10
 P A,o  10

Not linear.except when eA = eB.
Chapter 13 - 7
Stray Light
• Must account for the effect of
stray light on the measured
absorbance. The measured
absorbance is
where Ps = radiant power of the
stray light.
• Negative deviations in the Beer's
law plot observed since are the
result since the measured
absorbance will be smaller than it
should be.
Chapter 13 - 8
Am
 Po + Ps 

 log 
 P + Ps 
Photometric errors
• errors in the measurement of the transmittance; can
have a dramatic affect on the estimation of
concentration.
• Normal Error Analysis starting with Beer's law equation:
• C = A/eb = .1
log T
0.424 ln T
I
log o = 
=
• C = f(T). eb
I
eb
eb
2

C


• General error equation is s2 =    s2
C
T
 T 
• Take the derivative of both sides to get: CT =  0.434
ebT
2
2
• Substituting we get: s2 =  0.434   s2 =  C   s2
C
sC
=
 ebT 
sT
T ln T
T
 T ln T 
or
C
• Conclusion: Optimum transmittance.
• sT related to type of noise.
Chapter 13 - 9
T
Transmittance Errors
Chapter 13 - 10
Chapter 14 Applications of
UV-Vis
USING UV-VIS
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Organic and inorganic
species absorb radiation in this
energy range causing
electronic transitions.
• Common orbitals involved
present in molecule given from
quantum mechanics.
• Electrons in high energy
orbitals in excited state;
usually caused by absorption
of a photon.
• Electrons occasionally can be
promoted to triplet state.
E.g. formaldehyde absorbs in the
UV region.
Instrumental Analysis, Christian, O’Reilly, p. 162
Chapter 14 - 12
Electronic Transitioins
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Transfer of electron from occupied state to an
unoccupied state occurs when photon
absorbed: M + hu  M*.
Vibrational and Rotational states also exist;
energy of absorber (ground and excited
states) given by: Etotal = Eel + Erot + Evib
Electronic transition can be to one of these
levels.
Relaxation can occur possibly through excited
vibrational and electronic states or it can relax
by collision with another molecule to produce
heat. Not useful!
For a given electronic level a relatively wide
range of photon energies possible due to the
number of closely spaced energy levels. Can
promote the transition of the electron from
some ground state to some other excited state
(often observed as broad absorption band).
Instrumental Analysis, Christian, O’Reilly, p.
164
Chapter 14 - 13
ORGANIC COMPOUNDS
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Energy separation between excited and ground state of valence electrons in UV-Vis
range.
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Single bonds: restricted to the vac-UV(l<180 nm).
Functional groups commonly studied.
MO treatment: Absorbers:
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
bonding electrons-those participating in bond formation; absorption associated with more
than one atom.
non-bonding or unshared electrons: Absorber is single atom.
MO = delocalized areas in which bonding electrons move due to overlap of AOs.
Equal number of bonding and antibonding MOs.
Electrons tend to occupy the low energy states. Called ground states and correspond to
bonding electrons.
Typical ground states are s, p states
sn orbitals (not involved in the bonding)
E.g. The formaldehyde molecule has each of these orbitals.
• When photon hits sample, electron absorbs photon to undergo electronic transition to
an antibonding state.
• Transition described by two orbitals involved. E.g. n  s*, s  s*, etc.;
• The energy of each transition is equal to the energy separation between the individual
orbitals.
Chapter 14 - 14
Electronic Transitions
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s  s* = vacuum-UV (l < 200 nm);
N2 and O2 strongly absorb so that vacuum must be used
to obtain spectra. Studies of absorption in this energy
range are thus not performed very often-harder to do.
n  s* = best observed with saturated compounds with
nonbonding electrons.
The energy requirements depend primarily on the kind of
atom to which it is bound.
l max shifts to shorter wavelength (higher energy) in polar
solvents such as H2O.
.p  p* and n  p* = the energies experimentally more
accessible than the other transitions Þ more commonly
studied.
.p bond  multiply bonded functional groups are involved.
The molar absorptivity for the p  p* transition is 100 to
1000 times larger than the absorptivity for the n  p*
transition.
.lmax is affected by the polarity of the solvent in each case.
n  p* shifted to shorter l (blue shift; hypsochromic
shift) with increases in polarity. Believed to be due to
increased solvation of the lone pair in the polar solvents.
p  p* shifted to longer l (red shift; bathochromic shift);
attractive polarization lowers both energy levels but has a
greater effect on the excited state. Shifts are relatively
small in magnitude compared to the blue shifts.
Chapter 14 - 15
Red shift in polar solvent (lmax increases)
Undergraduate Instrumental Analysis,
Robinson, p. 177.
Blue shift in solvent with H available to bond with
lone pair (lmax decreases)
Undergraduate Instrumental Analysis,
Robinson, p. 178.
Chromophores
• Certain structural groups tend to cause color or at least make the
molecule likely to absorb radiation in compounds (called
chromaphores).
E.g. Functional groups since they absorb radiation at wavelengths that
are characteristic of their particular group.
Chapter 14 - 16
Affect of Conjugation on lmax
• The MO treatment of p electrons allows for the delocalization of
electron density. When they are conjugated, further delocalization
occurs, lowers energy between orbitals and causes a shift in lmax to
longer l
• Multiple functional groups that are conjugated show the same trend.
Skoog & Leary
Chapter 14 - 17
ABSORPTION BY INORGANIC
SYSTEMS
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Absorption of these compounds is generally similar to those for organic compounds.
Most ions and complexes are colored (visible); the bands are broad and strongly
affected by its environment.
E.g. aquated Cu(II) = pale blue whereas when it is complexed with NH3 it is a darker
blue.
Crystal Field Theory: In the absence of an external electrical or magnetic field, the
energies of the 5d orbitals are identical. When a complex forms between the metal
ion and water (or some other ligand), the d-orbitals are no longer degenerate (not the
same energy). Therefore, absorption of radiation of energy involves a transition from
one of the lower energy to one of the higher energy d-orbitals.
Skoog & Leary
Chapter 14 - 18
CHARGE TRANSFER
ABSORPTION
• Most important from an analytical point of view
since the absorption coefficients are very large.
• Observed by complexes with one of the
components having electron-donor
characteristics and another component with
electron-acceptor characteristics.
• When absorption occurs, an electron from a
donor group is transferred to an acceptor,
• E.g. When the iron (III) thiocyanate ion complex
absorbs radiation, an electron from SCN orbital
is transferred to an excited state of iron.
Chapter 14 - 19
APPLICATIONS
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Mixtures:Determining the concentration of
mixtures the components of which absorb in the
same spectral regions is possible.
Strategy of the analysis. Total absorption at
some wavelength of a two component mixture:
Atotal,l1 = AM,l1 + AN,l1.
Each should obey Beer's law at this wavelength as
long as concentration is sufficiently low. The
contribution from each would then be:
AM,l1 = eM,l1bCM and AN,l1 = eN,l1bCN. and
Atotal,l1 = eM,l1bCM + eN,l1bCN.
Similarly at some other wavelength we would
have,
Atotal,l2 = eM,l2bCM + eN,l2bCN.
.eb can be determined for each using standard
solutions.
Take absorbance readings of mixture at the two
ls.
Substitute into above so that there are two
equations with two unknowns.
Chapter 14 - 20
Mixtures
E.g. Simultaneous determination of Ti and V. Determine the % of each
if 1.000 g of a steel was dissolved and diluted to 50.00 mL;
spectrophotometric analysis produced an absorbance of 0.172 at
400 nm and 0.116 at 460 nm. Two separate solutions were also
analyzed; The first solution which contained Ti (1.00 mg/50.00 mL),
gave an absorbance of 0.269 at 400 nm and 0.134 at 460 nm. The
second solution contained V( 1.00 mg/50.00 mL) and gave an
absorbance of 0.057 at 400 nm and 0.091 at 460 nm.
Strategy:
• Write two simultaneous equations for the absorbance of the
unknown (one for each wavelength).
• Use results from standards to determine the proportionality
constants in each equation.
• Solve simultaneous equations.
Chapter 14 - 21
PHOTOMETRIC TITRATIONS
• Absorbance measured during
titration of analyte.
• The endpoint can be
determined by extrapolation of
the lines that result from before
and after the endpoint.
• The shape of the titration
curves depends upon the molar
absorptivities of reactants,
products and titrants.
• All absorbing species must
obey Beer's law for this method
to be successful.
Chapter 14 - 22
Standard Addition Method
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Standard addition method reduces problems with
matrix; analyte added to the matrix to change the
signal; signal change enables the determination of the
original concentration of the analyte.
Another linear procedure with volume correction:
Add volume, Vx, of the unknown solution with a
concentration cx to a series of separate containers
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Add variable amounts, Vs, of a standard solution with
concentration cs of the same compound.
Dilute these to constant final volume, Vt.
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Beer's law predicts the absorbance will vary according
to .
eb V s c s
eb V x c x
A =
+
VT
VT
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A should vary linearly with Vs; the slope and intercept
should be
eb c s
eb V x c x
S = slope =
 I = intercept =
VT
VT
Ratio of intercept and slope is:.
I
I
V x cx
=
 c x = cs 
S
cs
Vx  S
.
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Chapter 14 - 23
•Skoog & Leary
STOICHIOMETRY OF COMPLEX
IONS
• Ligand to metal ratio in can be determined
from absorption measurements. Equilibrium
not affected significantly!
• Assuming reactant or product absorbs
radiation, we can
– determine the composition of complex ions in
solutions and
– determine formation constants.
• Stoichiometry: mole ratio, continuous
variation, and slope ratio methods. One
complex only!
Chapter 14 - 24
Continuous Variation Method
• Determines metal ligand
ratio
• Solutions of cation and
ligand with identical formal
concentrations are mixed
in varying volume ratios;
but VT = const.
• A plot of A vs volume ratio
(volume ratio = mole
fraction) gives maximum
absorbance when there is
a stoichiometric amount of
the two.
Chapter 14 - 25
Mole-ratio method
• Concentration of one of the components held constant
while other is varied giving a series of [L]/[M] ratios.
• The absorbance of each of these solutions is measured
and plotted against the above mole ratio.
• The ratio of ligand to metal can thus be obtained from
the plot.
Instrumental Methods of Analysis, Ewing, p. 69.
Chapter 14 - 26
MOLE RATIO METHOD (cont’d)
Determination Kf (ML only) non-linear portion of the plot. Let:
• Fm = [M] + [ML] = the total metal concentration at equilibrium and
• FL = [L] + [ML] = the total ligand concentration at equilibrium
• at any point on the curved part of the plot: A = eMb[M] + eMLb[ML]:
assuming eL = 0.
• Determine eb for both the metal and ligand.
• Metal Let FL = 0 and [ML] = 0; AM = eMbFm or eMb = AM/Fm.
• Ligand:With a large excess of ligand, [ML] >> [M] and AML =
eMLbFM or eMLb = AML/FM.
• Known equations:
• Fm = [M] + [ML];
• FL = [L] + [ML]
• A = eMb[M] + eMLb[ML]
• Determine [ML],[M],[L]
• Kf = [ML]/[M][L]
Chapter 14 - 27
SLOPE-RATIO METHOD
• Makes it possible to determine ratio of ligand to metal.
Two plots performed with large excess of either ligand or
metal.
• Absorbance vs. FM : large excess .ligand: [L] >> [M] 
– [MnLp] = FM/n
– Beer's law will be AM = eb[MnLp] = ebFm/n
– Metal Concentration varied and plotted.
• Absorbance vs. FL: large excess of metal the [M]o >>
[L] 
– [MnLp] = FL/p and AL = ebFL/p.
– Beers law : AM = eb[MnLp] = ebFL/n
– Ligand Concentration varied and plotted.
• Slopes will be eb/p and eb/n. The ratio of the slopes
gives the ratio of p/n.
Chapter 14 - 28