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. Beer’s 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
Chapter

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.
Beer’s Law predicts linear behavior between concentration and absorbance but not between amount power coming out of sample.
Chapter

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.
Chapter

5. Real Limitations
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

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.
Willard, Merritt, Dean and Settle, Instrumental Methods of Analysis, p. 70
Chapter

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.
Chapter

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.
Chapter

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.
Chapter

10. Transmittance Errors
Chapter

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.
Instrumental Analysis, Christian, O’Reilly, p. 162
Chapter

13. Electronic Transitioins
Instrumental Analysis, Christian, O’Reilly, p. 164
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).
Chapter

14. ORGANIC COMPOUNDS
Energy separation between excited and ground state of valence electrons in UV-Vis range.
Single bonds: restricted to the vac-UV(l<180 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.
Chapter

15. Electronic Transitions
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.
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.
Chapter

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.
Chapter

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.
Skoog & Leary
Chapter

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.
Skoog & Leary
Chapter

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.
Chapter

20. APPLICATIONS
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

21. Mixtures
E.g. Simultaneous determination of Ti and V. Determine the % of each if g of a steel was dissolved and diluted to mL; spectrophotometric analysis produced an absorbance of at 400 nm and 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 at 400 nm and at 460 nm. The second solution contained V( 1.00 mg/50.00 mL) and gave an absorbance of at 400 nm and 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

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.
Chapter

23. Standard Addition Method
Skoog & Leary
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:.
Chapter

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!
Chapter

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.
Chapter

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.
Instrumental Methods of Analysis, Ewing, p. 69.
Chapter

27. 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

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] >> [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