Avagadro's Number Example Problem - Number of molecules in a given mass

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 thePeriodic 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 = 3.34 x 10¹⁶ molecules/gram

There are 3.34 x 10¹⁶ H₂O molecules in 1 g of H₂O.

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

X molecules of H₂O = 3.34 x 10¹⁶ molecules/gram · (1 g /1000 mg )
X molecules of H₂O = 3.34 x 10¹³ molecules/mg

Answer

There are 3.34 x 10¹³ H₂O molecules in a 1 mg snowflake.