Avogadro's Number

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Problem

How many H₂O molecules are there in a snowflake weighing 1 mg?

Solution

Snowflakes are made of water, H₂O. First, we need to find the mass of one mole (Avogadro's number or 6.022 x 10²³) of H₂O molecules. To obtain this number, first look up the atomic masses for H and O from the Periodic Table. There are two hydrogen atoms and one oxygen atom in water, so the mass of one mole of water is:

1.01 g x 2 + 16.00 g x 1 = 18.01 g

This relation is used to determine how many molecules of water there are in 1 gram:

number of molecules per gram = 6.022 x 10²³ H₂O molecules / 18.01 g

number of molecules per gram = 3.34 x 10¹⁶ g

Next, convert grams to milligrams. There are 1000 milligrams in a gram, so move the decimal point three places to the right or add three to the superscript in exponential notation:

number of molecules in 1 milligram = 3.34 x 10¹⁹

Answer

3 x 10¹⁹ H₂O molecules

I did not use all of the digits provided in the periodic table for atomic mass, but rounded the masses to the nearest hundredth of a gram. Note that I used one significant digit in the final answer. This is because there was only 1 significant digit in '1 mg'.

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