Avogadro's Number Example Chemistry Problem - Water in a Snowflake

Avogadro's number is used in chemistry when you need to work with very large numbers. It's the basis for the mole unit of measurement, which provides an easy way to convert between moles, mass, and the number of molecules. For example, you can use the number to find the number of water molecules in a single snowflake. (Hint: It's an enormous number!)

Avogadro's Number Example Problem - Number of Molecules in a Given Mass

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

Solution:

Step 1 - Determine the mass of 1 mole of H₂O

Snowflakes are made of water, or H₂O. To obtain the mass of 1 mole of water, look up the atomic masses for hydrogen and oxygen from the Periodic Table. There are two hydrogen atoms and one oxygen for every H₂O molecule, so the mass of H₂O is:

mass of H₂O = 2 (mass of H) + mass of O
mass of H₂O = 2 ( 1.01 g ) + 16.00 g
mass of H₂O = 2.02 g + 16.00 g
mass of H₂O = 18.02 g

Step 2 - Determine the number of H₂O molecules in one gram of water

One mole of H₂O is 6.022 x 10²³ molecules of H₂O (Avogadro's number). This relation is then used to 'convert' a number of H₂O molecules to grams by the ratio:

mass of X molecules of H₂O / X molecules = mass of a mole of H₂0 molecules / 6.022 x 10²³ molecules

Solve for X molecules of H₂O

X molecules of H₂O = ( 6.022 x 10²³ H₂O molecules ) / ( mass of a mole H₂O · mass of X molecules of H₂O

Enter the values for the question:
X molecules of H₂O = ( 6.022 x 10²³ H₂O molecules ) / ( 18.02g · 1 g )
X molecules of H₂O = 3.35 x 10²² molecules/gram

There are 3.35 x 10²² H₂O molecules in 1 g of H₂O.

Our snowflake weighs 1 mg and 1 g = 1000 mg.

X molecules of H₂O = 3.35 x 10²² molecules/gram · (1 g /1000 mg )
X molecules of H₂O = 3.35 x 10¹⁹ molecules/mg

Answer

There are 3.35 x 10¹⁹ H₂O molecules in a 1 mg snowflake.

Avogadro's Number Problem Key Takeaways

• Avogadro's number is 6.02 x 10²³. It is the number of particles in a mole.
• You can use Avogadro's number to convert between mass and the number of molecules of any pure substance.
• If you are given the mass of a sample (such as a snowflake), convert the mass to moles, and then use Avogadro's number to convert from moles to molecules.