The volume of water in the Pacific Ocean is approximately 7 * 10 ^ 8 cubic km. Imagine that a glass

The volume of water in the Pacific Ocean is approximately 7 * 10 ^ 8 cubic km. Imagine that a glass of water is poured into the ocean and all the water in the ocean is well mixed. How many water molecules from those in the glass will return to the glass when scooped up again from the ocean? The volume of the glass is 200 ml.

The volume of water in a glass Vws (in cubic meters): 200 ml = 0.0002 m³.
The mass of water in a glass Mws = 0.0002 m³ * 1000 kg / m³ = 0.2 kg.
The volume of water in the ocean Vocean (in cubic meters): 7 * 10 ^ 8 km³ = 7 * 10 ^ 17 m³.
One mole of water is 0.018 kg, which contains Na = 6.022 * 10²³ molecules / mole. Na is Avogadro’s number.
0.2 kg of water will contain N molecules:
N = Na * (Mws / m), m is the mass of one mole of water.
The number of molecules in a glass is equal to Avogadro’s number multiplied by the number of moles:
N = 6.022 * 10²³ * (0.2 kg / 0.018 kg) = 66.9111 * 10²³.

The concentration of molecules from a glass in the ocean after mixing will be
n = N / Vocean = (66.9111 * 10²³) / (7 * 10 ^ 17 m³) = 9558728.571 molecules / m³.
The number of molecules that “returned” to the glass:

N1 = n * Vvc = 9558728.571 molecules / m³ * 0.0002 m³ = 1911 molecules.

Answer: 1911 molecules.