Introduction
“What do Chemists really do?” is a question that is often asked of those who have chosen chemistry as a
career. Sometimes the questions come from simply curious and sometimes from would-be wizards and
alchemists. There is no simpler answer than “Chemistry is molecules and chemists study the properties,
occurrence, appearance and disappearance of molecules. Chemists make new molecules, detect the
presence of new molecules and measure how much of a given molecule type is present.” Analytical
chemistry is the study of chemical and physical systems important to chemical measurement and
especially quantitative measurement. As chemistry matures, the chemical systems become more complex
and even more challenging to study. Often the concerted action of several kinds of molecules can be
much different than their individual, isolated behavior. The more complex the chemical system, the more
complex the response, and the better the analytical tools must be.
It is important that the student learns that measurement is not “analysis” even if the word analysis is
incorrectly used to describe the unit operation carried out. The natural progression of a well-designed
experiment in analysis follows the sequence:
Experimental Design.
In this stage, the measurement task is defined, the errors that can be expected
from the measurement techniques are examined and compared to the measurement demand made by the
question whose answer is sought. Put in simple terms, if one wanted to measure the volume of a
container using the Ideal Gas Law, PV=nRT, then spending a great deal of time refining temperature
control while neglecting pressure control would be a mistake. Why? Because the T is Kelvin and at room
temperature one degree would be 1/300 or .3%. One would need to control the pressure that well before
devoting more time to temperature control strategies.
Sample and Sampling.
“Garbage in is garbage out!” is a phrase borrowed from the computer
programmers but applies to measurements. Care must be taken to assure that the sample is representative
of the system of interest. A bad or contaminated sample can give very precise measurement results
unrelated to the question being asked.
Measurement.
The measurement system must be calibrated using standards and validated by trial with
known, “real” samples. The people doing the measurements must also have their skills compared to
determine if there is any bias in the individual techniques reflected in the individual results.
Analysis.
This is the stage at which the molecular information is extracted from the measured results.
That can be as simple as: “There is 22 ppm benzene present in your soda water.” Or the process can
involve a much more complex response such as the gas phase composition above a burning rubber
sample or a sample of shale containing shale oil. The question may be one of “Pattern Recognition”
where the answer might be: “Yes, this sample of petrolatum is from the production lot in question.” or “
Well, it appears to be an alcohol!” It may be necessary to find ways to remove background signals from
the response of the samples to the analytical method or even background signals that are added by the
measurement method. The general name for such operations is “deconvolution”. OR, the task could be to
predict the complex behavior of the material in question. Example? Coal burns to leave ash. The wt% ash
depends on the silicate content of the coal rank being burned and varies across ranks. IT is possible to
estimate the ash content from the infrared reflectance spectrum of a sample of coal IF one uses the best
analysis techniques.
The examples chosen in this tutorial are drawn from the armory of tools all called Factor Analysis.
Combined with the experiments given as examples, the student is led through the basic concepts of
Factor Analysis and specific examples of deconvolution or actual spectra from “real” instruments,
prediction of retention in real chromatography, and chemical-class recognition. The goal is to help begin
the development of a sense of chemical intuition as to what Factor Analysis can provide. The “geometric
approach” is aimed at that goal with the underlying linear algebra illustrated but not presented with full
and detailed rigor at this stage. It is important that one first understands the concept and where Factor
Analytical methods can be best applied. “ No amount of algebra covers up for a bad premise!” is
especially true here.
Factor Analysis Tutorial
Matlab Tutorial
Experiment 1
Experiment 2
Experiment 3
Experiment 4