How many teaspoons of water are in all the oceans?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

22 August 2021

Chris Karanja says that he heard some one claiming that there are more molecules of water in a teaspoon of the liquid than there are teaspoons of water in all the oceans on earth. He asks: “Could this be true?”

There are two facts needed to answer this question: first, how many water molecules are there in a teaspoon of the liquid, and, second, what is the total volume of all the oceans on earth? The latter is easier to answer.

According to the United States Geological Survey (USGS), the total volume of water in all the world’s oceans is about 1.386 billion cubic kilometers. Now, a cubic kilometer is the space enclosed in a 1km x 1km x 1km cube. Since 1km = 1,000m, it turns out that one cubic kilometre is equivalent to one billion cubic metres. Thus, the oceans contain about 1.386 billion-billion cubic metres.

To put that into some perspective, the largest dam in Kenya – Masinga – has a capacity of 1.56 billion cubic metres. Therefore, we need about one billion Masinga dams to fill up all the oceans on Earth!

Now one teaspoon is about 5ml. Thus, one litre (1,000mk) has 200tsp. But there are 1,000L in one cubic metre, so, there are 200,000tsp in one cubic metre. Since the oceans have 1.386 billion-billion cubic metres of water, it turns out that they have about 277,000 billion-billion teaspoons. This is the number 277 followed by 21 zeroes; in other words, 277 sextillion teaspoons.

To find out the number of molecules, we start from Avogadro’s Number, which is the number of molecules contained in one mole of a substance. Its value is approximately 600 sextillion. Now, one mole of water is about 18g, or 18ml. Thus, one teaspoon (5ml = 5g) is about one-third of a mole. This comes to about 200 sextillion molecules.

Remembering that we found about 277 sextillion teaspoons of water in the oceans, we conclude that the original statement is inaccurate. There are approximately the same number of teaspoons of water in the oceans as there are molecules in a teaspoon.

The version of this statement that I have heard claims that there are more water molecules in a glass of water than there are glasses of water in all the oceans on Earth. Looking at the above numbers, I think this one is accurate, but I leave it you the reader to verify.