Now that we have finished nomenclature, we can learn how to convert between number of atoms and number of ions in a compound. For example, if we have 6.75 grams of MgCl₂, how many chlorine ions are in this amount of MgCl₂? Convert g to number of chlorine ions. The roadmap is:

g MgCl₂ → moles MgCl₂ → moles Cl^– → # of Cl^– ions

We will need one equivalence per arrow in the roadmap. There are 3 arrows.

The molar mass of MgCl₂ is 95.211 g/mol. First we convert g to moles using the following equivalence: 95.211 g MgCl₂ = 1 mole MgCl₂. The two conversion factors are:

\(\displaystyle \frac{1\;mol\;MgCl_2}{95.211\;g\;MgCl_2}\;\;or\;\;\frac{95.211\;g\;MgCl_2}{1\;mol\;MgCl_2}\)
 

Next, we determine the number of moles of Cl^– ions in 1 mole of MgCl₂. There are 2 moles of Cl^– in 1 mole of MgCl₂. The conversion factors are:

\(\displaystyle \frac{1\;mol\;MgCl_2}{2\;mol\;Cl^-}\;\;or\;\;\frac{2\;mol\;Cl^-}{1\;mol\;MgCl_2}\)
 
To convert the moles of Cl^– to number of Cl^– ions, we use the equivalence, 1 mole Cl^– = 6.02 x 10²³ Cl^– ions. The conversion factors are:

\(\displaystyle \frac{1\;mol\;Cl^-}{6.02\times 10^{23}\;Cl^-}\;\;or\;\;\frac{2\;mol\;Cl^-}{1\;mol\;MgCl_2}\)
 
We can now set up the problem:

\(\displaystyle 6.75\;g\;MgCl_2\times\frac{1\;mol\;MgCl_2}{95.211\;g}\times\frac{2\;mol\;Cl^-}{1\;mol\;MgCl_2}\times\frac{6.02\times\;10^{23}\;ions}{1\;mol\;Cl^-}=8.54\times 10^{22}\;ions\)
 
In 6.75 grams of MgCl₂, there are 8.54 x 10²² chloride ions.

When asked how many ions, atoms, molecules, etc., use Avogadro’s number.

In this example, we have 0.250 g of caffeine, C₈H₁₀N₄O₂. How many carbon atoms are in this 0.250 g of sample?

The road map is: g caffeine → moles caffeine → moles C → # C atoms

Our equivalences are: 1 mole caffeine = 194.19 g, 8 mol C = 1 mole caffeine, 1 mol C = 6.02 x 10²³ C atoms

Now, we set up the problem.

\(\displaystyle 0.250\;g\;\mathrm{caffeine}\times\frac{1\;mol\;\mathrm{caffeine}}{194.19\;g}\times\frac{8\;mol\;C}{1\;mol\;\mathrm{caffeine}}\times\frac{6.02\times10^{23}C\;atoms}{1\;mol\;C}=\)
6.20 x 10²¹ C atoms

Worksheet: Conversions Using Moles, Grams, Molecules, and Ions

Exercises

Exercise 1. How many carbon dioxide, CO₂, molecules are in 0.845 moles?

Check Answer/Solution to Exercise 1

Exercise 2. A sample contains 255.25 g of FeCl₂. How many Fe²⁺ ions are in this sample?

Check Answer/Solution to Exercise 2

Exercise 3. How many sodium ions and how many phosphate ions are in 22.65 g of Na₃PO₄?

Check Answer/Solution to Exercise 3

Exercise 4. How many oxygen atoms are in 45.52 g of Al₂(CO₃)₂?

Check Answer/Solution to Exercise 4

Exercise 5. A sample of MgS has 2.64 x 10²⁴ sulfur ions. What is the mass of the original sample of MgS?

Check Answer/Solution to Exercise 5

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