If you have 2.86 gallons of pure water, how many molecules of water are ionized at any given time ?

The molar mass of water is 18 grams per mole. So in 18 grams of water, there are 6.02 x 1023 molecules.

One gallon of water is equal to 3.7854118 liters. If we assume that the water is at 4 °C (to keep things simple), the density of water is exactly 1 gram per milliliter, or 1 kilogram per liter. So 1 gallon of water at 4 °C weighs exactly 3.7854118 kilograms, or 3785.41118 grams.

If one mole of water weighs 18 grams, then there are 210.30 moles of water in a gallon. Since one mole of water is made up of 6.02 x 1023 molecules, in one gallon of water there are 1.266 x 1026 molecules.

That is: 126600000000000000000000000 molecules!

If we multiply that by the number of atoms in a single water molecule -- 3 atoms -- then we get:

379800000000000000000000000 atoms!