Outline
Final Comments on Titrations/Equilibria Titration of Base with a strong acid
End-point detection Choice of indicators Titration Curve method
Start Chapter 18 Spectroscopy and Quantitative Analysis
Weak Base titrated with strong acid
Consider a 100 ml of a 0.0100 M base with 0.0500 M HCl
Kb = 1 x 10-5
Initial pH
bb CKOH ][
Buffer Region
][
][log
acid
basepKpH a
pH @ equivalence
aa CKH ][
pH after equivalenceDominated by remaining[H+]
Review of properties of EM!
c= Where
c= speed of light = 3.00 x 108 m/s = wavelength in meters = frequency in sec-1
E=h or E=hc/
h=Planks Constant = 6.62606 x 1034 J.s
The Quantitative Picture Transmittance:
T = P/P0
b(path through sample)
P0
(power in)P
(power out) Absorbance:
A = -log10 T = log10 P0/P
The Beer-Lambert Law (a.k.a. Beer’s Law):A = bc
Where the absorbance A has no units, since A = log10 P0 / P
is the molar absorbtivity with units of L mol-1 cm-1
b is the path length of the sample in cmc is the concentration of the compound in solution, expressed in mol L-1 (or
M, molarity)
How do “we” select the How do “we” select the
wavelengthwavelength
to measure the absorbance?to measure the absorbance?
Absorbance vs. Wavelength
A
420 440 460400380
Wavelength, nm
Why?Why?
1. Maximum Response for a given concentration
2. Small changes in Wavelength, result in small errors in Absorbance
Limitations to Beer’s LawLimitations to Beer’s Law
“Fundamental” “Experimental”
1. Concentration/Molecular Interactions2. Changes in Refractive Index
1. Not Using Peak wavelength
2. Colorimetric Reagent is limiting
Interaction of Light and Interaction of Light and MatterMatter
Start with Atoms Finish with Molecules
Consider Atoms - hydrogen
Energy
Very simple view of Energy statesAssuming subshells have equivalent energies
n=1
n=2
n=3n=4n=5n=6
A
Wavelength, nm
Consider molecules With molecules, many energy levels.
Interactions between other molecules and with the solvent result in an increase in the width of the spectra.
Electronic SpectrumA
bsor
banc
e
Wavelength, , generally in nanometers (nm)
0.0400 800
1.0
200
UV Visiblemaxwith certain extinction
Make solution of concentration low enough that A≤ 1
(Helps to Ensure Linear Beer’s law behavior)
UV bands are much broader than the photonic transition event. This is because vibration levels are superimposed.
The UV Absorption process• * transitions: high-energy, accessible in vacuum UV (max <150 nm). Not usually observed in molecular UV-Vis.
•n * transitions: non-bonding electrons (lone pairs), wavelength (max) in the 150-250 nm region.
•n * and * transitions: most common transitions observed in organic molecular UV-Vis, observed in compounds with lone pairs and multiple bonds with max = 200-600 nm.
Any of these require that incoming photons match in energy the gap corresponding to a transition from ground to excited state.
What are the nature of these absorptions?
Example: * transitions responsible for ethylene UV absorption at ~170 nm calculated with semi-empirical excited-states methods (Gaussian 03W):
bonding molecular orbital antibonding molecular orbital
h 170nm photon
Experimental details •What compounds show UV spectra?
•Generally think of any unsaturated compounds as good candidates. Conjugated double bonds are strong absorbers.
•The NIST databases have UV spectra for many The NIST databases have UV spectra for many compoundscompounds You will find molar absorbtivities You will find molar absorbtivities in L•cm/mol, tabulated.in L•cm/mol, tabulated.
•Transition metal complexes, inorganics
Final notes on UV/Vis Qualitatively
Not too useful Band broadening
Quantitatively Quite Useful
Beer’s Law is obeyed through long range of concentrations
Thousands of methods Most commonly used Detection Limits ~ 10-4 – 10-6 M
Final notes on UV/Vis (cont’d)
Quant (cont’d) Cheap, inexpensive, can be relatively
fast Reasonably selective
Can find colorimetric method or use color of solution
Good accuracy ~1-5%
Uncertainty in Concentration
D
xx
D
x
D
nx
km
ss iiy
ionconcentrat
2122
nx
xxD
i
ii
)( 2
iii xxnxD )( 2
Where: x = determined concentration k = number of samples m = slope n = number of Standards (data points) D = ??