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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 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.

### Avogadro's Number Problem Key Takeaways

- Avogadro's number is 6.02 x 10
^{23}. 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.