\( \require{mhchem} \)

In the video, you learned that Avogadro's number is used as a conversion factor in converting the number of moles of a substance to the number of particles of that substance. Recall that conversion factors are set up in a way that all the units cancel except the units that are required for the answer.

Converting Moles to Particles

To convert from moles of a substance to the number of representative particles of that substance, multiply the number of moles by:

\( \frac{6.022 \times 10^{23} \text{ representative particles}}{1 \text{ mole}} \)

For Example

Convert 2.5 mol to number of particles.

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Step 1: Write the given number and unit.	2.5 mol
Step 2: Set up a conversion factor so the given units cancel.	2.5 mol \( \times \frac{6.022 \times 10^{23} \text{ particles}}{1 \text{ mol}} \)
Step 3: Cancel units and solve.	2.5 mol \( \times \frac{6.022 \times 10^{23} \text{ particles}}{1\ \require{enclose}\enclose{horizontalstrike}{\text{mol}}} = \) 1.5 \( \times \) 1024 particles

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 particles.

Avogadro's number is also used as a conversion factor in converting the number of particles in a substance to the number of moles of that substance. The conversion factor used to convert particles to moles is the reciprocal of the conversion factor used to convert moles to particles. The unit you are converting from will need to be in the denominator of the conversion factor for it to cancel out, leaving you with the unit you are converting to.

Converting Particles to Moles

To convert from number of representative particles of a substance to moles, multiply the number of representative particles by:

\( \frac{1 \text{ mole}}{6.022 \times 10^{23} \text{ representative particles}} \)

Another Example

Convert 3.1 \( \times \) 10²⁵ particles to number of moles.

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Step 1: Write the given number and unit.	3.1 \( \times \) 1025 particles
Step 2: Set up a conversion factor so the given units cancel.	3.1 \( \times \) 1025 particles \( \times \frac{1 \text{ mole}}{6.022 \times 10^{23} \text{ particles}} \)
Step 3: Cancel units and solve.	3.1 \( \times \) 1025 particles \( \times \frac{1 \text{ mole}}{6.022 \times 10^{23}\ \require{enclose}\enclose{horizontalstrike}{\text{particles}}} = \) 51 moles

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

Question

How are the conversion factors used to convert from particles to moles and from moles to particles related to each other?

Answer

The conversion factor used to convert from particles to moles and from moles to particles are reciprocals.