Francis Rouessac - Chemical Analysis

If we expand to n components, it is easy to calculate the mass concentration of the solute i using Eq. (1.44):

(1.44)

In addition, the percentage concentration of i can be expressed using Eq. (1.45):

(1.45)

This method becomes even more precise if several injections of the solution and of the sample are carried out. In conclusion, this general and reproducible method nevertheless demands a good choice of internal standard, which should have the following characteristics:

it must be stable, pure, and not exist in the initial sample;

it must be measurable, giving a well‐resolved elution peak on the chromatogram;

its retention time must be close to that (or those) of the solute(s) to be quantified;

its concentration must be close to or above that of the analytes in order to be in the detector’s linear response range;

it must be inert with respect to the compounds in the sample.

The advantage of this method is not needing perfect reproducibility of injections, which makes manual injections possible if the device is not equipped with an automatic injector. The disadvantage, however, is the choice of internal standard, which extends the development time of the analysis. However, with mass detectors that do not require perfect resolution, coelution of the internal standard and of the solute to quantify is possible, if we can recognize peaks caused by each of the two compounds on the mass spectrum of the mixture.

This method, also called percentage normalization, is used for mixtures in which all components have been identified and have been assigned a well‐resolved peak on the chromatogram. This method uses relative response factors, as in the internal standard method. The biggest difference here is that the solute used as a reference to calculate the relative response factor is part of the mixture to quantify.

Let us suppose that we are trying to find the mass concentrations of three compounds 1, 2, 3 in a mixture ( Figure 1.14). The analysis is again carried out in two steps.

A standard solution containing the three compounds 1, 2, and 3 at known concentrations C 1, C 2, and C 3is prepared. The chromatogram corresponding to the injection of a volume V of this standard solution shows three peaks of area A 1, A 2, and A 3. These areas will be related to the masses m 1, m 2, and m 3of the compounds in volume V , by three expressions of the Eq. (1.42)type.

Figure 1.14 Analysis by internal normalization method.

One of the compounds, 3 for example, is chosen as the substance for internal normalization. This compound 3 will serve to calculate the relative response factors K 1/3and K 2/3for compounds 1 and 2 with respect to 3 . As previously deduced:

Given that m i= C i. V , then the following equations for K 1/3and K 2/3are obtained:

The next step consists in injecting a specimen of the mixture to be measured containing compounds 1, 2, and 3 . Labelling the elution peaks as and will give direct access to the percentage mass composition of the mixture represented by x 1, x 2, and x 3via three equations of the following form:

The condition of normalization is that x 1+ x 2+ x 3= 100

If the procedure is extrapolated to n components normalized to compound j (internal reference), a general expression for the response factor of a given compound i can be obtained:

(1.46)

It is also possible to determine K i/jby plotting a concentration–response curve for each of the solutes.

In a mixture containing n solutes, if designates the area of the elution peak of compound i , and if the internal reference is j , then the content of compound i will obey the following equation:

(1.47)

This method is ideal to monitor rates of advancement of a chemical reaction and, at the same time, to follow the conversion kinetics.

1 Chromatography is a separation method and also an analytical method. It is a very reliable method, with continued innovation in order to separate, purify, identify, and quantify chemical species.

2 It is based on the adsorption or partition, depending on various parameters and interactions, of chemical species between two immiscible phases, one fixed or stationary (SP) and the other mobile (MP).

3 There are many chromatographic techniques that differ in the process used, the nature of phases, physico‐chemical equilibria, the physical state, etc., and just as many classifications are possible depending on the criterion retained!

4 To each compound, we assign a distribution factor K = CS /CM as a function of its concentration in the two phases. For each type of chromatography, thermodynamic relationships apply. From K (which is not a constant), we can calculate ΔH, ΔS, and ΔG for the separation in question.

5 A document inseparable from any chromatographic analysis, the chromatogram, or elution curve, represents the graphic recording of concentration over time. It provides information on the analysed sample and on the quality of the separation in progress.