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How well can you use Avogadro's number to convert moles to number of particles and number of particles to moles?

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You learned on the previous page that the fractions used to convert from moles to particles and particles to moles are reciprocals. These conversion factors can be used to convert between the number of moles and the number of representative particles, like molecules and atoms, of a substance.

Let's Practice

Practice converting from moles to particles and particles to moles by completing this activity. Answer the question on each tab, then check your answer.

How many molecules of H2 are in 1.4 moles of H2?

8.4 \( \times \) 1023 molecules H2

If you need help arriving at this answer, click the Solution button.

Step 1: Write the given number and unit.

1.4 mol H2

Step 2: Set up a conversion factor.

1.4 mol H2 \( \times \frac{6.022 \times 10^{23} \text{ molecules } H_{2}}{1 \text{ mol } H_{2}} \)

Step 3: Cancel units and solve.

1.4 mol H2 \( \times \frac{6.022 \times 10^{23} \text{ molecules } H_{2}} {1\ \require{enclose}\enclose{horizontalstrike}{\text{ mol } H_{2}}} = \) 8.4 \( \times \) 1023 molecules H2

Notice that in step 2 the number of moles is in the denominator of the conversion factor so that in step 3 moles are eliminated, leaving the number of molecules.

How many atoms of He are in 3.3 moles of He?

2.0 \( \times \) 1024 atoms He

If you need help arriving at this answer, click the Solution button.

Step 1: Write the given number and unit.

3.3 mol He

Step 2: Set up a conversion factor.

3.3 mol He \( \times \frac{6.022 \times 10^{23} \text{ atoms } He}{1 \text{ mol } He} \)

Step 3: Cancel units and solve.

3.3 mol He \( \times \frac{6.022 \times 10^{23} \text{ atoms } He}{1\ \require{enclose}\enclose{horizontalstrike}{\text{mol } He}} = \) 2.0 \( \times \) 1024 atoms He

Notice that in step 2 the number of moles is in the denominator of the conversion factor so that in step 3 moles are eliminated, leaving the number of atoms.

How many moles of C are in a sample containing 3.90 \( \times \) 1026 atoms of C?

648 mol C

If you need help arriving at this answer, click the Solution button.

Step 1: Write the given number and unit.

3.90 \( \times \) 1026 atoms C

Step 2: Set up a conversion factor.

3.90 \( \times \) 1026 atoms C \( \times \frac{1 \text{ mole}}{6.022 \times 10^{23} \text{ atoms } C} \)

Step 3: Cancel units and solve.

3.90 \( \times \) 1026 atoms C \( \times \frac{1 \text{ mole}}{6.022 \times 10^{23}\ \require{enclose}\enclose{horizontalstrike}{\text{atoms } C}} = \) 648 mol C

Notice that in step 2 the number of atoms is in the denominator of the conversion factor so that in step 3 atoms are eliminated, leaving the number of moles.