You fill a coffee cup (250 mL volume) with seawater and hypothetically dye all t

Question

You fill a coffee cup (250 mL volume) with seawater and hypothetically dye all the water molecules in the cup pink, then pour the cup back into the ocean and it mixes homogenously. After complete mixing, you refill the cup with seawater and calculate the number of pink water molecules. How many pink water molecules do you expect to find? What assumptions did you make to calculate this?

HINT: You need to first estimate the number of water molecules in the water volume of 250 mL (for this you need to assume seawater density, e.g., 1 g/cm^3). Then, estimate the volume and thus the number of water molecules in the entire ocean water. You can estimate the concentration of pink molecules.

Explanation / Answer

atomic mass of H = 1 atomic mass of O = 16

H2O has a relative atomic mass of 1+1+16 or 18

1 mole of water weighs 18 grams

1 ml of water weighs 1 gram so 250 ml weighs 250 grams

250/18 = 13.8889 moles of water in 250 ml

6.02 x 1023 molecules per mole * 13.889 moles = 83.64 * 1023 or 8.364 * 1024 molecules of water in 250ml beaker

We dye all 8.364 x 1024 molecules in pink.

Earth has 1,260,000,000,000,000,000,000 liters of water and out of which 97% is in ocean so ocean water in liters will be,

1,260,000,000,000,000,000,000 * 0.97 = 1.2222 * 1021 liters

Each liter contains, 8.364 *4 * 1024 molecules so total ocean water molecules will be,

1.2222 * 1021 * 8.364 *4 * 1024 = 40.89 * 1045 molecules.

If the pink molecules are homogenously mixed then they are evenly distributed in 40.89 * 1045 molecules. So we will get 1 pink molecules in 4.89 * 1021 molecules.

(40.89 * 1045)/ (8.364 * 1024) = 4.89 * 1021 molecules.

In the new 250 ml water we have same 8.364 * 1024 molecules.

So, (8.364 * 1024)/(4.89 * 1021) = 1.710 * 103 molecules

We will get 1.710 * 103 molecules in the 250 ml as pink dyes molecules.

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