In this investigation, the student is likely to observe that the drop of purple food coloring disperses more quickly in the beaker of water at 50°C than in the beaker at 20°C.
The reason for this observation can be explained by the principles of diffusion and the effects of temperature on the kinetic energy of molecules. At higher temperatures, the water molecules have greater kinetic energy, which causes them to move more rapidly. This increased motion allows the food coloring molecules to also disperse more quickly throughout the water.
Conversely, in the beaker with water at 20°C, the water molecules are moving more slowly due to the lower temperature. Therefore, the food coloring will diffuse more slowly and take longer to spread throughout the water.
In summary, the student observes that the food coloring disperses faster in the hotter water (50°C) compared to the cooler water (20°C) due to the increased kinetic energy of the water molecules at higher temperatures, which facilitates faster diffusion of the food coloring.