Is it possible to dilute food coloring so that all that is left is water?

Answer 1

No. It won't matter how much water you add, the coloring chemical(s) will still be there if only in trace amounts such as parts per trillion.

Answer:

Using the principles of Homeopathic remedies, that is diluting the solution over and over again, we find an interesting result. Lets start with a drop of food colouring. Assume it has a weight of 1/10th gram. Being generous assume it has a density and molecular weight similar to water that's about 1/20 of a mole or (6.02 x 1023)/20 molecules of colouring agent. Put the drop in a liter of water, mix it and withdraw a drop of the solution. It will contain 3 x1018 molecules. Repeat this process over and over putting a drop in, mixing and removing a drop of the new solution. Each removed drop contains the folowing number of molecules:

Solution 2: 3 x1014 molecules in the drop

Solution 3: 3 x1012 molecules in the drop

Solution 4: 3 x108 molecules in the drop

Solution 5: 3 x104 molecules in the drop

Solution 6: 3 molecules in the drop

Now here's the problem. When we mix these three molecules into the next liter we have almost no chance (1 in 3000) of getting even one molecule in the drop we take out. To all intents and purposes the colouring agent is gone.