The value is proportional to the affinity of the solute to the solvent. The solvent acts as the mobile phase along a polar paper stationary phase. Polar compounds will interact more with the paper, travelling slowly, while nonpolar compounds will interact more with the solvent, travelling more quickly.

A large  value represents a large proclivity for the mobile solvent in the experiment. Because we are using ether, a non-polar solvent, we would expect non-polar compounds to travel the farthest on our plate. Of the answer choices, alkanes are the least polar and would thus travel farthest into the mobile phase of the four functional groups. A polar functional group, like a halide, will interact more in the stationary phase, and will thus has a significantly smaller  value. 

Generally, extraction is the best means of separating two solutes based on polarity. This technique allows separation based on solubility in two different solvents, which separate based on polarity.

Extraction, however, is not offered as an answer. The next best option would be thin layer chromatography. In this process, a polar stationary phase is introduced to a nonpolar solvent. Solutes are placed on the stationary phase. The nonpolar solvent acts as the mobile phase. Nonpolar solvents interact more with the mobile solvent, travelling quickly along the polar stationary phase, while polar solutes are attracted to the stationary phase and travel more slowly. This property allows for separation based on polarity.

Ion exchange chromatography is used to separate compounds with different charges, not necessarily differing polarities. Mass spectroscopy will identify compounds based on mass, and distillation will allow for separation based on differences in boiling point and vapor pressure.

The stationary phase in chromatography is typically attracted to the more polar compounds in a solution, while the mobile phase carried the nonpolar compounds. As a result, more polar compounds will move a shorter distance, resulting in a lower R_f factor. Glucose is a very polar molecule, and would move a shorter distance compared to the other options.

In the normal phase chromatography system described, the most nonpolar compound would elute first and the most polar compound would elute last. The silica stationary phase will interact with more polar molecules, while the hexane mobile phase will carry nonpolar molecules. This would slow the progress of polar molecules as they bond to the silica, and enhance the progress of nonpolar molecules as they interact with the mobile phase.

Compound C is the most nonpolar compound because it contains only hydrogen and carbon. Compounds A and B are more polar because of the presence of oxygen, and hence the presence of polarized carbon-oxygen bonds. The alcohol group of compound B makes this compound the most polar of the three molecules by virtue of hydrogen bonding capabilities as well as the carbon-oxygen dipole. Compound B would thus elute last.