READ: Conversions Between Moles and Number of Particles

READ: Conversions Between Moles and Number of Particles 

Using our unit conversion techniques, we can use the mole label to convert back and forth between the number of particles and moles.

Sample Problem 1: Converting Number of Particles to Moles

The element carbon exists in two primary forms: graphite and diamond.  How many moles of carbon atoms is 4.72 × 10²⁴ atoms of carbon?

Step 1: List the known quantities and plan the problem.

Known

• number of C atoms = 4.72 × 10²⁴
• 1 mole = 6.02 × 10²³atoms

Unknown

• 4.72 × 10²⁴ = ? mol C

One conversion factor will allow us to convert from the number of C atoms to moles of C atoms.

Step 2: Calculate.

4.72×1024 atoms C×1 mol C6.02×1023 atoms C=7.84 mol C

Step 3: Think about your result.

The given number of carbon atoms was greater than Avogadro’s number, so the number of moles of C atoms is greater than 1 mole.  Since Avogadro’s number is a measured quantity with three significant figures, the result of the calculation is rounded to three significant figures.

Suppose that you wanted to know how many hydrogen atoms were in a mole of water molecules.  First, you would need to know the chemical formula for water, which is H₂O.  There are two atoms of hydrogen in each molecule of water.  How many atoms of hydrogen would there be in two water molecules?  There would be 2 × 2 = 4 hydrogen atoms. How about in a dozen?  In that case a dozen is 12 so 12 × 2 = 24 hydrogen atoms in a dozen water molecules.  To get the answers, (4 and 24) you had to multiply the given number of molecules by two atoms of hydrogen per molecule.  So to find the number of hydrogen atoms in a mole of water molecules, the problem could be solved using conversion factors.

1 mol H2O×6.02×1023 molecules H2O1 mol H2O×2 atoms H1 molecule H2O=1.20×1024 atoms H

The first conversion factor converts from moles of particles to the number of particles. The second conversion factor reflects the number of atoms contained within each molecule.

Sample Problem 2: Atoms, Molecules, and Moles

Sulfuric acid has the chemical formula H₂SO₄.  A certain quantity of sulfuric acid contains 4.89 × 10²⁵ atoms of oxygen.  How many moles of sulfuric acid is the sample?

Step 1: List the known quantities and plan the problem.

Known

• 4.89 × 10²⁵ = O atoms
• 1 mole = 6.02 × 10²³ molecules H₂SO₄

Unknown

• mol of H₂SO₄ molecules

Two conversion factors will be used.  First, convert atoms of oxygen to molecules of sulfuric acid.  Then, convert molecules of sulfuric acid to moles of sulfuric acid.

Step 2: Calculate.

4.89×1025 atoms O ×1 molecule H2SO44 atoms O×1 mol H2SO46.02×1023 molecules H2SO4=20.3 mol H2SO4

Step 3: Think about your result.

The original number of oxygen atoms was about 80 times larger than Avogadro’s number.  Since each sulfuric acid molecule contains 4 oxygen atoms, there are about 20 moles of sulfuric acid molecules.

Summary

• Methods are described for conversions between moles, atoms, and molecules.

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