Final answer:
Food coloring in water spreads evenly through diffusion, which is the process by which molecules move from a region of higher concentration to one of lower concentration until evenly distributed.
Step-by-step explanation:
When a drop of food coloring is placed in a container of clear water, the colored dye molecules spread evenly throughout the water. This process is known as diffusion. Diffusion is the movement of molecules from an area of higher concentration to an area of lower concentration until they are evenly distributed. Initially, the drop of food coloring creates a region of high concentration in the water. Over time, due to molecular motion which is random and the absence of barriers to their movement, the dye molecules spread out until there is no longer a concentration gradient, resulting in an even color throughout the water.