SPECTROCHEMICAL METHODS

Electromagnetic Radiation

Electronic Vector

Magnetic Vector at 90 deg

Characteristics

Wavelength (l) crest to crest distance 10

^{-9}NM ==> 100 KmSpeed (c) speed of light

vacuum 3.00 x 10^{8} m/sec

slower in all other media - slowed by electronic interactions

h = Refractive index = __speed in vac __> 1

speed in medium

function of wavelength

light of different energy moves at different rates in medium other than vacuum.

*sigma* wave number = waves/cm = cm^{-1 }=
1/ *Lambda* in vacuum

Frequency ( *sigma* ) = waves passing fixed
point/sec.

period (p) time per wave crest *nu* = 1/p

all are related *nu* = __c __

*L**ambda
*

E = h*nu* = hc/8
= hc*sigma*

Intensity and power

P = energy/sec/area

I = energy/sec/unit solid area (steridians)

Properties of Waves

** **

Constructive (in phase) Interference

Destructive (out of phase) Interference

**Electromagnetic spectrum **

Gamma rays | X rays | VacUV | UV | VIS | NIR | IR | FAR IR | : WAVE | RADIO |

0.01D | 0.10D | 10 nm | 200 nm | 340 nm | 800 nm | 2.5 : | 25 : | .04 cm | 25 cm |

0.10D | 100D | 200 nm | 400nm | 800 nm | 2.5 : | 25 : | .04 cm | 25 cm | 1000Km |

Interaction of matter and Electromagnetic Radiation

All can interact with matter in a wide variety of ways.

Most interaction depends on size of particle relative to wavelength.

Particles < 1/2 *Lambda* are
transparent.

Electronic vector Interactions

X-rays - - ionize atoms eject inner shell e^{- }

UV-VIS - energy charges in valence e^{-}

IR - molecular vibrations

microwave - molecular rotations

Magnetic vector Interactions ( in magnetic field)

microwave - electron spin changes

radio wave - nuclear spin changes

**Spectroscopy** - 1 or more courses required to cover in any detail

Open peephole on what is there to be known.

Show energy levels in diagrammatic form

_____3s ____ 3p ____ 3d

E ____ 2s ____ 2p

____1s describe transitions

Emission occurs when e^{- }state drops. Studied for atoms.

Absorption occurs when photon of exactly the energy of the transition strikes the atoms. Studied for molecules (hard to exited enough to emit.)

Molecular spectroscopy uses molecular rather than atomic orbitals in diagram. S , P , N

CAChe can calculate them and show relative energies.

Quantitative aspects of Absorption

Beer's Law Beer-Lambert Law (Harry Gray's version)

Log relationship between

distance light travels in an absorbing medium

and concentration

if each thin segment (dx) absorbs some fraction of all of incident light (P_{x})

dP = -k P_{x }C dx

k= cross section area of absorbing region of molecule (0rbital or conjugated system)

P_{X} = Probability of transition occurring (0 => 1 )

C = Concentration

-dP/P_{x} = kC dx

Integrate over entire path length b

log(P_{0}/P) = k/2.303 Cb = , bC or (abC)

__P __= Transmittance (T)

P_{o}

log __1 __= -log T = A Absorbance - A is dimensionless

T

A = abc C in gm/l

A= e bc C in moles/l

bC = cm*mol/1000cm^{3 }= mol/1000cm^{2}

a units cm^{2}/gm
e unit = cm^{2}/mol

Limitations

Light must be monochromatic

Parallel

Enter at a right angle.

Extensions - Multicomponent Systems

A _{1} = , _{1}bC_{1} + , _{2}bC_{2} + , _{3}bC_{3} +.....

Total abs. = sum of absorbencies of individual absorbing species.

Measure at several wavelengths solve simultaneous equations. Calc. conc. of all species.

HP instrument 6 or 7 component mixture solves 125 simultaneous eq. Each wavelength in region.

Best possible accuracy.

**Deviations from Beers Law** - Accuracy

Instrumental

1. Non-monochromatic light

value of , or a not constant across bandwidth of spectrometer.

Negative deviation at high conc.

Beers Law

Negative Deviation

Concentration error and lower sensitivity.

Need more standards.

Wide slits give lower A values - Value measured on ST320 or Spec 20 will be less than for HP diode array which may be less than PE 330

Stray light

a) Reflections

b) Higher orders

c) slit diffraction

Chemical Deviations

Equilibria - acid base pH control

Activity coef.

Temperature

Solvent effects

Diagnostic Tool for Deviations

Plot A vs path length.

Beers Law - straight line

Stray Light - negative deviation

Instrumentation for Optical Spectroscopy.

Spectrometer - Record light through sample at given wavelength.

Spectronic 20, HP Diode Array Spectrometer

Spectrophotometer - __Ratio__ of 2 beams PE 330

A. Sources of Radiation

1. Black body radiators - Tungsten lamp 2870^{o}K - 1.5 micron peak

Quartz - Iodide - 3600^{o}K more UV & VIS

2. Discharge Lamps

H_{2} or D_{2 }165 to 360 Nm.

D_{2} lasts longer and brighter than H_{2}.

B. Detectors

1. Eye - Colorimetry

No numerical Readout Most sensitive to __Green__

2. Photovoltaic Cells

No power supply needed

Portable

Response like eye

3. phototube

Photo emissive surface

Work function - photon energy

needed to eject e^{-'}s photo cathodes designed for various regions of the
spectrum.

each photon produces 1 or more e^{- }

some thermal e^{- }also produced

shot noise

dark current __function of temp.__

4. Solid State Detectors - Photodiodes and change couple devices.

Photodiodes - pn junction conduct in reverse direction due to photon flux.

Linear photodiode Arrays

512 diodes - detect 512 wavelengths at once - complete spectrum not scanned. **HP
Spectrometer**

Good visibility sensitivity

Rapid response

high linearity

C. Monochromators

1. Filters

Glass 30-50 nm band width

5-20% T at max.

2. Prisms - Dk2A

3. Gratings - parallel lines on glass

Practical considerations

A. Cells

Glass or Plastic **Vis only**

Quartz UV-VIS-NIR $60-100 each

Flat parallel windows best

Cylindrical cells must always be in the same position

(mark on spec 20 cells)

B. Solvents - must be transparent

UV cutoff

Solvent |
UV Cutoff |

Acetone |
330 |

Acetonitrile |
210 |

Benzene |
280 |

Carbon disulfide |
380 |

Chloroform |
245 |

Dichloromethane |
233 |

Ether |
220 |

Ethyl Acetate |
260 |

Hexane |
210 |

Methanol |
210 |

Water |
200 |

Errors in concentration due to errors in Transmittance

Assume error is a constant value of Transmittance (T)

A=abC A= -log T

C = - log(T)/ab

take derivative of C with respect to T

dC/dT = -0.4343/T(ab)

Want relative concentration error dC/C so divide by

C= -log(T)/ab

ab term cancels

dC/C has a minimum at T=0.368 (36.8%)

Use this equation to calculate the relative error in concentration (dC/C) for a given relative error in Transmittance (dT/T).

Problem assignment will help you explore this topic for yourself.

Applications of Spectrophotometry

Direct determination of a chromophoric compound - anything that absorbs strongly.

Absorbances range from 0 to 500,000 , wide range of sensitivities.

1. use tabulated absorbance

2. measure absorbance from a single standard

3. prepare calibration curve

Form a chromophore with non-absorbing species

1. metals react with ligands to form colored complexes - large number of analytical methods developed to use this

2. organic derivatives - 2,4-dinitrophenyl hydrozones

azo coupling (acid rain nitrate detn.)

vanillate ion in lab

1. Direct Use of Beer’s Law – Least Precise and Accurate (one point calibration) assumes blank=0.00

2. Using a Standard Curve

Known concentrations vs Abs. – Least Squares

3. Standard Addition Method

Useful if matrix of sample has background absorbance which cannot be accounted for in a blank or calibration curve.

Three approaches to Std. Add.

1. Add micro amounts of standard and ignore dilution.

2. Add standard and correct for dilution.

3. Dilute unknown and standard additions to constant volume.

Graphical treatment of std. addition

4. Spectrophotometric titration

**E. Use of Spectrophotometry to study reaction stoichiometry** - metal complexes,
enzyme substrate complexes, etc.

1. Job’s Method _ Continuous variation method. Use where ratio is close to 1:1

Total moles of two reactants constant. Plot Mole ratio vs A

2. Mole-Ratio method - use where ratio is large

Like a titration. Treat constant molar conc. of metal with varying molar amounts of ligand. (Plot A vs Moles ligand)

3. Slope Ratio Method- use where binding is weak and large excesses of reagent are required to force complete reaction.

xM + yL =====> M_{x}L_{y}

Add small amounts of metal to large excess of ligand - drives reaction to completion
even if K_{f} is small. Measure slope of graph of Abs vs conc. Slope = **e**b/x

Add small amounts of ligand with large constant excess of metal - excess metal drives reaction to completion.

Slope = **e**b/y

**(e**b/x)/(**e**b/y) = y/x

Luminescence

Fluorescence

Excited electron returns to ground state and emits a photon.

Excitation - GS to Excited Electronic State

Fluorescence - Excited Electronic State to Excited Vibrational state of electroninc GS.

E_{exc} > E_{Flu}

*Lambda* _{exc} < *Lambda* _{em}

Very sensitive and selective since 2 wavelengths involved

Non-Linearity at solutions with A> 0.03