How To Calculate RF

There are many methods to separate and identify different compounds. Chromatography is the science that allows you to separate the components of a mixture. The **R_f **(sometimes informally written as "rf value") is part of that.

There are many different kinds of chromatography. Here, the focus is the simplest kind of chromatography: paper chromatography or thin layer chromatography (TLC). Both use the same general procedure, which is described below.

All types of chromatography have a stationary phase and a mobile phase. The stationary phase, as you might be able to guess from the name, does not move. In paper chromatography, the stationary phase is the paper itself.

To begin the separation of compounds, the substance to be analyzed is dotted onto the bottom edge of the piece of paper. Then the paper is placed in a beaker containing the mobile phase, which is a solvent. The solvent should be under the spot where the substance for analysis is dotted. It should not submerge the analyte.

The liquid moves up the paper by capillary action. If the analyte or part of the analyte is attracted to the mobile phase, it will move with it. If it has a stronger attraction for the stationary phase, it will not move.

After the solvent has moved up the stationary phase to some extent, you have a chromatogram. This chromatogram tells you something about the separation of different components in a mixture or tells you about what substance you have. How?

If the conditions for developing a chromatogram are the same, then the distance a particular substance moves should change. This distance is measured by the retention factor formula or **R_f**.

The retention factor formula is:

\(R_f = \dfract{distance\enspace substance\enspace moves}{distance\enspace solvent\enspace moves}\)

This value should be same for a substance when the chromatogram is developed in the same way.

This is useful when you have a mixture of substances.

For example, say you have four samples: Three are standards, and one is mixture. Your job is to identify which components are in the mixture.

What are standards? Standards are a pure sample of a substance. This can be run on the chromatogram as a comparison.

The mixture can be run, after which you can determine how far different components in it run.

Say Standard #1 has a strong affinity for water (the mobile phase). This means that it will travel up the paper with the mobile phase. Standard #2 on the other hand has a strong affinity for paper. This means that it will stay with the stationary phase. Lastly, Standard #3 has an affinity for both water and paper. You predict it will move an intermediate amount.

You find that the solvent moves 5.7 cm while Standard #1 moves 0.5 cm, Standard #2 moves 4.8 cm, and Standard #3 moves 2.9 cm. What are the R_f values for each standard?

\(R_f\enspace standard_1\enspace = \dfrac{0.5}{5.7} = 0.09\)

\(R_f\enspace standard_2\enspace = \dfrac{4.8}{5.7} = 0.84\)

\(R_f\enspace standard_3\enspace = \dfrac{2.9}{5.7} = 0.51\)

Now, you know the R_f values for the standards. Next, on another piece of paper you place a dot of the mixture and allow the chromatogram to develop by placing it in water.

Once removed, you find that there are two dots that separated from the initial dot you placed. This likely means that there are only two components in your mixture. Next, you need to figure out which of the standards these two components correspond to. To do this, you measure the R_f values.

The solvent moved 4.5 cm. One component (called component 1) moved 2.2 cm, and the other moved 3.9 cm (called component 2). To see which standard these components correspond to you will need to use the retention factor formula to calculate the R_f values.

\(R_f\enspace component_1\enspace = \dfrac{2.2}{4.5} = 0.49\)

\(R_f\enspace component_2\enspace = \dfrac{3.9}{4.5} = 0.87\)

Given these R_f values, it is likely that component 1 corresponds to Standard #3 since the R_f values are very similar. Component 2 is likely Standard #2.