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Avogadro's Number Example Chemistry Problem

Finding Number of Molecules in a Known Mass

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Avagadro'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.

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