# Calculate The Mass In Grams Of A Single Water Molecule?

## 2 Answers

James Harden answered
The mass of a single water molecule is 2.9907x10-23 g to five significant figures, or 2.9907 times one hundredth of a millionth of a millionth of a nanogram, which is itself one billionth of a gram. This of course cannot be directly measured; we instead have to indirectly measure the mass of one molecule. The relative atomic mass of oxygen (not the relative molecular mass of oxygen, which is double the value, as oxygen forms diatomic molecules) is 15.9994. The relative atomic mass of an atom of hydrogen is 1.00794. The formula for water is H2O, so there are two hydrogen atoms and one oxygen atom in a water molecule. By multiplying the relative atomic mass of hydrogen by two and adding the relative atomic mass of oxygen to it, we get the relative molecular mass of water. This comes to 18.01528 to five decimal places. The mass of one mole of water should therefore be 18.01528 grams, and it is known that one mole of any substance contains L units of that substance, where L is Avogadro's constant, 6.022142x10-23 to six decimal places. (For example, a mole of sand contains L grains of sand, which is a large enough amount of sand to cover the United Kingdom to a depth of a hundred miles.) To calculate the mass of one molecule of water, we therefore have to divide the relative molecular mass of water by Avogadro's constant. This comes to the figure quoted in the first line, 2.9907x10-23g. Avogadro never calculated the value for his constant, but he was the first chemist to realise that the mass of a pure sample depended on the number of particles in that sample. He denoted L as the number of particles in a sample that yeilded the relative formula mass of the sample in grams.

The Avogadro constant is calculated experimentally from the amount of charge in coulombs of one Faraday (which is defined as the amount of charge contained by one mole of electrons), and dividing this by the charge on one electron. Scientific American states that: "The best estimate of the value of a Faraday, according to the National Institute of Standards and Technology (NIST), is 96,485.3383 coulombs per mole of electrons. The best estimate of the charge on an electron based on modern experiments is 1.60217653 x 10-19 coulombs per electron. If you divide the charge on a mole of electrons by the charge on a single electron you obtain a value of Avogadro's number of 6.02214154 x 1023 particles per mole." The full article is here: www.scientificamerican.com/article.cfm?id=how-was-avogadros-
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Vin Ravun answered
1 mole (6.022 x 1023 molecules) of H2O molecules weigh 18 grams.So 1 molecule of H2O weighs  18 / 6.022 x 1023   .= 2.9890 x 10 -23  grams.
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