Quantitative Instrumental Analysis

Often times, a researcher will want to know the identity of the
components of a sample mixture. For example, Jane Smith might want to know
what kind of pollutants are in her well water. Analytical instruments such
as GC-MS, AAS, or HPLC can provide a lot of information about the
contents of such a sample. They can tell us what is in a mixture and how
much is there. Determining the identities of components is referred to as
**qualitative analysis**. Determining the amounts of those compounds
is cal led **quantitative analysis**. This page looks at the methods
used to do quantitative analysis.

We will refer to the components of a sample that we are interested in
as the **target analytes**. To begin analysis, we first must use an
extraction technique in order to get the target analytes into an
appropriate solvent. From here on, we will refer to this solution as the
sample, but keep in mind that it is really the extract from the sample.

The concentrations of target analytes in the sample are usually low. For that reason, we must either select instruments sensitive enough to detect and quantify them, or concentrate the sample to detectable levels. Once this is accomplished, we can be gin our analysis.

All sample analysis instruments have some means of detecting the
presence of analytes. Analytes enter a **detector** and generate an
electronic signal called a **response**. The response can have other
names depending on the instrument or the type of signal generated by its
detector. Other names include absorbance, intensity, abundance, etc. The
data system of the instrument (usually a computer) has some way of storing
and displaying that response.

Usually, the response is displayed on a graph where the x-axis is time
(retention time) and the y-axis is a measure of the intensity of the
response. In chromatography, this graph is called a **chromatogram**.
During the course of a sample evaluatio n (or "run"), the graph is
constantly updated to produce a line. When the run begins, there are no
analytes in the detector, the response is zero, and the line produced on
the chromatogram is called the **baseline**.

As the analyte enters the detector, the response intensity increases,
usually very rapidly. The line on the graph shoots upward until the
maximum response occurs. As the analyte is swept out of the detector, the
line returns to the baseline until ano ther analyte enters the detector.
The chromatogram will show a **peak**. (See Figure 1.) The size of the
peak is proportional to the concentration of the analyte. If we measure
the peak, we can evaluate the concentration of the analyte.

**Figure 1:** Typical chromatogram.

There are several measurements used to determine the size of the peak. They include height, width and area. However, height and width are effected by how fast the analyte moves through the detector. An analyte that is moved slowly will produce a short, broad peak. If we speed up the process, the analyte will produce a tall, thin peak. Therefore, the preferred measurement is the area of the peak. We can determine that area by treating the peak like a triangle, and using some geometry and algebra. However, most data systems can determine the area more precisely for us using complex computer algorithms.

Before we can quantitate our analyte, we must know something about the
relationship between peak area and concentration. The simplest method is
to determine a **response factor**. The response factor (RF) is the
proportionality constant for the analyte. Each analyte will have a
unique RF under given instrumental conditions. (Our job is to keep those
conditions constant). Equation 1 shows us that RF is simply the
concentration (C) divided by the area (A).

If we a prepare a sample of a known concentration (called a
**standard**) and evaluate it, we can measure the peak area and
determine the RF. This process is referred to as a **calibration**.
(The standards used for calibrating an instrument are simply referred to
as **calibration standards** sometimes abbreviated as "cal stds.")
Once we know the RF for our target analyte we can determine the
concentration of that analyte in our sample by running it on the
instrument and getting the peak area. Concentration is simply

This method works fairly well provided the concentration in our cal std
is close to the concentration in our sample. If the two differ
greatly, then we lose accuracy. However, since we don't yet
know what the concentration is in the sample (why else would we do this?),
then we don't know what concentration cal std to use. We can solve this
problem and increase our accuracy by constructing a **calibration
curve**.

A calibration curve is simply a graph where concentration is plotted along the x-axis and area is plotted along the y-axis. (Response, absorbance, intensity, peak height, etc.) can also be used depending on the instrument. The user will make several cal stds at different concentrations. After running each one on the instrument and getting an area, the points are then plotted on the graph. (See Figure 2.) The points are then connected with a line. That line represents the calibration curve. Note that every different analyte will produce a different calibration curve. We must construct a calibration curve for each analyte we are interested in.

**Figure 2**: Typical calibration curve.

Figure 2 is an example of a calibration curve for a hypothetical compound X. It was created by running 5 different calibration standards (5, 10, 15, 20, 25 m g/mL). Each concentration gave a peak area (5000, 10000, 15000, 20000, 25000). Peak area was then plotted against the concentrations.

Once we have constructed our curve, we can analyze our sample. We simply determine the peak area for the analyte in our sample, and then draw a line on the graph at that area (note the red arrows). When the calibration curve is reached, we drop a lin e down to the x-axis. That will give us the concentration of the analyte in our sample.

Note that the calibration curve in Figure 2 is first order linear. Not
all analytes will give a linear response for all ranges of concentrations.
AAS typically uses non-linear calibration curves. However, most analytes
are linear for certain ranges. This range of concentrations is referred to
as the **linear dynamic range**. If we analyze our sample in the linear
dynamic range, we can calculate a regression line equation and use it to
solve for concentration rather than using our pencil and ruler. If the
sample concentration is outside of that range, we can we either dilute it
or concentrate it further by evaporating some of the solvent.

Keep in mind that there are many other techniques for quantitative instrumental analysis. This is one method.

Last update: May 8, 1998