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When you put food coloring in cold water, it takes longer for the molecules to mix with the water. But when you drop food coloring in hot water, diffusion occurs must faster, and easier. Diffusion is the intermixing of two different types of particles. Since at high temperature the molecules posses more kinetic energy,the rate of their motion increases and diffusion occurs faster.

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Take 2 beaker,some water ,potassium permagnate,one tripod stand,one burner Take one beaker with water and put a piece of potassium permagnate but do not stir or disturb it take another beaker and heat the water in it We can observe that in the first beaker the potassium permagnate(solute )took more time to dissolve whereas in the second beaker the solute diffused at greater speed This is because the heat which is applied increses the kinetic energy of the particles i.e the movement of particles increases and this helps to increase the rate of diffusion
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