Page 241 - Essentials of physical chemistry

Basic Spectroscopy 203

groups in organic compounds that tend to absorb light in specific color ranges; they are called
chromophores. In organic compounds, chromophores tend to have double bonds with delocalized
electrons. Some inorganic compounds also have chromophore qualities, often in the visible range of
the spectrum. The Bohr model would say that the KMnO 4 transitions are within the n ¼ 3 shell
of Mn but we are beginning to see the limitations of the Bohr model here. By following the
historical development of spectroscopy and using only the simple mathematics of the Bohr model,
we cannot invoke a modern explanation of electronic spectroscopy for molecules. Here, we want to
mention this important technique that is simple in use and has wide application in this survey of
spectroscopy.
Spectrophotometry is usually carried out at a single, optimum, wavelength that is established
during calibration with solutions of known concentrations. The procedure is to use a simple 1 cm
path glass cuvette of solution to measure an unknown concentration. KMnO 4 is a strong oxidizing
agent, so a great number of schemes can be used to measure its concentration following some test
reaction. An Internet search on the use of KMnO 4 in various tests=assays should result in finding
many applications of this very useful reagent.
In order to define the type of absorbance we are discussing, we need to define the Beer–Lambert
law:

I e l [C](l)
¼ e ¼ exp e l [C mol=L] [path length (cm)]g; A e l [C](l):
T ¼ f
I 0
The IUPAC recommended term for e(l) is the ‘‘molar absorption coefficient’’ and a student should
note the spelling with a ‘‘p’’; A is ‘‘absorbance’’ spelled with a ‘‘b.’’ ‘‘T’’ is the ratio of light
‘‘transmitted through the sample compared to a blank, not the kinetic energy T ’’ and the absorbance
‘‘A’’ is the logarithm (specify the base) of T as A ¼ ln T ¼ e l [C]l. Here, ‘‘[C]’’ is the concentra-
tion in moles=liter, ‘‘l’’ is the sample cell path length in cm, and e l is the ‘‘molar absorption
coefficient’’ at a given wavelength l. The intensity ‘‘I’’ is the amount of light transmitted through
cell, solvent, and sample while ‘‘I 0 ’’ is the ‘‘blank’’ signal of light intensity measured for only the
cell and solvent. This is a simple formula that is exploited in a large number of forensic=analytical
‘‘color tests,’’ often at a single wavelength selected for maximum sensitivity.

Example
We can use the absorbance scale on the spectrum marked ‘‘curve 1’’ in Figure 9.10 to deduce the
concentration of the KMnO 4 solution. We estimate the 525 nm peak is at A ¼ 0.85, and we assume a
1 cm path so we can solve for [C] as

2455
[C](1 cm) ffi 0:85:
Mcm
A ¼ e 525 [C](l ) ¼
and then we find

0:85 4
ffi 3:46 10 M:
[C] ffi
2455
(1 cm)
Mcm
In the simple example above, we note that the molar absorption coefficient for KMnO 4 [8] is quite
large at 525 nm and that the Beer–Lambert law can be used for very dilute solutions.
Low-cost spectrophotometers are available for single wavelength measurements but a scanning
spectrometer is a more substantial piece of instrumentation that can produce a spectral curve.
The scanning option is a decided luxury compared to hand-plotting data for single-point readings.