Question

Legend has it that, many centuries ago,Archimedes jumped out of his bathtub and ran across town nakedscreaming "Eureka!" after he solved an especially difficultproblem. Though you may not have thought of things this way before,when you drink a glass of water, the water that you are drinkingcontains some water molecules that were in Archimedes' bathwaterthat day, because water doesn't get created or destroyed on a largescale. It follows the water cycle, which includes rain,evaporation, flowing of rivers into the ocean, and so on. In themore than two thousand years since his discovery, the watermolecules from Archimedes' bathwater have been through this cycleenough times that they are probably about evenly distributedthroughout all the water on the earth. When you buy a can of soda,about how many molecules from that famous bathtub of Archimedes arethere in that can?

Answer 1

Answer: 8652.36857143 x $10^{4}$ 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 × $10^{18}$ tonnes;

converting tonnes to kgs -->>  1.4 × $10^{21}$kg

Since only 2.5% of this is fresh, (the rest is saline and ocean-based)

-->> 2.5% of 1.4 × $10^{21}$kg = 0.035  × $10^{21}$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 × $10^{23}$ molecules in 18g of water;

1kg of water would contain about 3.3 × $10^{25}$ molecules.

An average water can holds about 355mL of fluid.

Therefore the number of molecules in the can is $10^{25}$.

The number of bathtub molecules present in the can is;

302.8329 x $10^{25}$ / 0.035 x $10^{21}$

= 8652.36857143 x $10^{4}$ molecules