Answer: 8652.36857143 x [tex]10^{4}[/tex] molecules
Explanation:
We need a lot of assumptions in this case.
1. We don't know the mass of water that was present in Archimedes' bath tub that day.
2. Since it recycles, we don't know the total mass of water present on earth.
Assuming the total mass of water on earth is 1.4 × [tex]10^{18}[/tex] tonnes;
converting tonnes to kgs -->>  1.4 × [tex]10^{21}[/tex]kg
Since only 2.5% of this is fresh, (the rest is saline and ocean-based)
-->> 2.5% of 1.4 × [tex]10^{21}[/tex]kg = 0.035  × [tex]10^{21}[/tex]kg
An average bath tub holds about 80 gallons of water.
80 gallons to kgs = 302.8329 kg
Using Avogadro's number,
we have about 6 × [tex]10^{23}[/tex] molecules in 18g of water;
1kg of water would contain about 3.3 × [tex]10^{25}[/tex] molecules.
An average water can holds about 355mL of fluid.
Therefore the number of molecules in the can is [tex]10^{25}[/tex].
The number of bathtub molecules present in the can is;
302.8329 x [tex]10^{25}[/tex] / 0.035 x [tex]10^{21}[/tex]
= 8652.36857143 x [tex]10^{4}[/tex] molecules