# Question #146da

May 7, 2017

The number of molecules in 24 g of FeF3

$= 6.022 \cdot {10}^{23} \cdot \text{Mass of FeF3"/"Molar mass of FeF3}$

$= 6.022 \cdot {10}^{23} \cdot \frac{24}{112.841}$ $= 1.281 \cdot {10}^{23}$

#### Explanation:

By definition, the number of molecules in one mole of a substance is $6.022 \cdot {10}^{23}$. This number is the Avogadro constant. The number of molecules is then given by the number of moles multiplied by the Avogadro constant. For example, if you have one mole of FeF3, you will have $1 \cdot 6.022 \cdot {10}^{23}$ molecules. If you have 0.5 moles of FeF3, you have $0.5 \cdot 6.022 \cdot {10}^{23}$ molecules.

So now you just need the number of moles of FeF3. To get the number of moles use this expression:

$\text{number of moles" = "Mass of FeF3"/"Molar mass of FeF3}$

The molar mass is how much one mole of a substance weighs. The units are g/mol (note that mole is shortened to "mol"). This is given by the sum of the molar masses of each atom in the molecule. Individual molar masses are found in the periodic table.

Molar mass of Iron = 55.847 g/mol
Molar mass of fluorine = 18.998 g/mol

Therefore,
$\text{Molar mass of FeF3 = sum of molar masses of atoms}$
$= 55.847 + 3 \cdot 18.998$ $= 112.841$ g/mol

So if you have 112.841 g of FeF3, you have $\frac{112.841}{112.841}$ = 1 mol
In this case you have $\frac{24}{112.841} = 0.213$ moles of FeF3

Therefore, the number of molecules is$= 0.213 \cdot 6.022 \cdot {10}^{23} = 1.281 \cdot {10}^{23}$