Chapter 13

1
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.

2
Beers Law Ideal Behavior

• Decrease in power is proportional to power going
  through cell and distance traveled
• Rearrange and integrate over the length of the
  cell
• where e molar absorptivity and is the
  collection of other terms.
• T P/Pox100

3
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.
• Beers Law predicts linear behavior between
  concentration and absorbance but not between
  amount power coming out of sample.

4
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.

5
Real Limitations

• Linearity is observed in the low concentration
  ranges(lt0.01), 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.

6
CHEMICAL DEVIATIONS

• 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
• 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.

7
INSTRUMENTAL DEVIATIONS

• 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
• Beer's law for each is PA,o/PA 10eAbc and
  PB,o/PB 10eBbc.
• Substitute
• Not linear.except when eA eB.

8
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.

9
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 .
• C f(T).
• General error equation is
• Take the derivative of both sides to get
• Substituting we get
• or
• Conclusion Optimum transmittance.
• sT related to type of noise.

10
Transmittance Errors
11
Chapter 14 Applications of UV-Vis
12
USING UV-VIS

• 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.

13
Electronic Transitioins

• 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).

14
ORGANIC COMPOUNDS

• Energy separation between excited and ground
  state of valence electrons in UV-Vis range.
• Single bonds restricted to the vac-UV(llt180 nm).
  
• Functional groups commonly studied.
• MO treatment Absorbers
• 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.

15
Electronic Transitions

• s s vacuum-UV (l lt 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.

16
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.

17
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.

18
ABSORPTION BY INORGANIC SYSTEMS

• 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.

19
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.

20
APPLICATIONS

• MixturesDetermining 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.

21
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.

22
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.

23
Standard Addition Method

• 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
• Add variable amounts, Vs, of a standard solution
  with concentration cs of the same compound.
• Dilute these to constant final volume, Vt.
• Beer's law predicts the absorbance will vary
  according to .
• A should vary linearly with Vs the slope and
  intercept should be
• .
• Ratio of intercept and slope is.

24
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!

25
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.

26
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.

27
MOLE RATIO METHOD (contd)

• 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
  eMbM eMLbML assuming eL 0.
• Determine eb for both the metal and ligand.
• Metal Let FL 0 and ML 0 AM eMbFm or eMb
  AM/Fm.
• LigandWith a large excess of ligand, ML gtgt M
  and AML eMLbFM or eMLb AML/FM.
• Known equations
• Fm M ML
• FL L ML
• A eMbM eMLbML
• Determine ML,M,L
• Kf ML/ML

28
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 gtgt
  M ?
• MnLp FM/n
• Beer's law will be AM ebMnLp ebFm/n
• Metal Concentration varied and plotted.
• Absorbance vs. FL large excess of metal the
  Mo gtgt L ?
• MnLp FL/p and AL ebFL/p.
• Beers law AM ebMnLp 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.