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

**Question:** How many H_{2}O molecules are there in a snowflake weighing 1 mg?

**Solution**

**Step 1** - Determine the mass of 1 mole of H_{2}O

Snowflakes are made of water, or H_{2}O. 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 H_{2}O molecule, so the mass of H_{2}O is:

mass of H_{2}O = 2 (mass of H) + mass of O

mass of H_{2}O = 2 ( 1.01 g ) + 16.00 g

mass of H_{2}O = 2.02 g + 16.00 g

mass of H_{2}O = 18.02 g

**Step 2** - Determine the number of H_{2}O molecules in one gram of water

One mole of H_{2}O is 6.022 x 10^{23} molecules of H_{2}O (Avogadro's number). This relation is then used to 'convert' a number of H_{2}O molecules to grams by the ratio:

mass of X molecules of H_{2}O / X molecules = mass of a mole of H_{2}0 molecules / 6.022 x 10^{23} molecules

Solve for X molecules of H_{2}O

X molecules of H_{2}O = ( 6.022 x 10^{23} H_{2}O molecules ) / ( mass of a mole H_{2}O · mass of X molecules of H_{2}O

Enter the values for the question:

X molecules of H_{2}O = ( 6.022 x 10^{23} H_{2}O molecules ) / ( 18.02g · 1 g )

X molecules of H_{2}O = 3.35 x 10^{22} molecules/gram

There are 3.35 x 10^{22} H_{2}O molecules in 1 g of H_{2}O.

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

X molecules of H_{2}O = 3.35 x 10^{22} molecules/gram · (1 g /1000 mg )

X molecules of H_{2}O = 3.35 x 10^{19} molecules/mg

**Answer**

There are 3.35 x 10^{19} H_{2}O molecules in a 1 mg snowflake.