THERE are faults with this because of the inverted lid will impart impurities unless it is inert like glass
You'd probably pay about as much for the electric/gas for the stove to heat the water as it would cost to just pick up a gallon while you're at the store.
rain is distilled
careful on which surfaces it lands on
Given all the crap in the atmosphere today, especially in urban areas, I would NOT consider rain water distilled or clean!!! Those days are long gone.
pollution has a lot to answer for