# Question 51110

Jul 29, 2015

Number of atoms: $3.61 \cdot {10}^{24}$

Number of molecules: $4.51 \cdot {10}^{23}$

#### Explanation:

The question wants you to determine how many molecules and how many atoms of sulfur you get in $\text{192 g}$ of sulfur.

The important thing to know here is that sulfur atoms form octatomic molecules, which are molecules that contain $8$ sulfur atoms bonded covalently. So, if it takes $8$ atoms of sulfur to form $1$ molecule of sulfur, you should expect the number of atoms to be $8$ times bigger than the number of molecules of sulfur you get in $\text{192 g}$.

Now, in order to be able to determine how many molecules of sulfur you're dealing, you first need to determine how many moles of sulfur you get in that mass.

This is why they give you sulfur's molar mass, which is equal to ${\text{32 g mol}}^{- 1}$. This tells you that one mole of sulfur atoms, $\text{S}$, has a mass of $\text{32 g}$.

This means that $\text{192 g}$ will contain

192color(red)(cancel(color(black)("g"))) * "1 mole S"/(32color(red)(cancel(color(black)("g")))) = "6.00 moles S"

Next, use Avogadro's number to figure out how many $\text{S}$ atoms you get in $6$ moles, knowing that one mole of an element contains exactly $6.022 \cdot {10}^{23}$ atoms of that element.

So, $6$ moles means that you get six time more atoms than you would get in one mole, so you have

6.00color(red)(cancel(color(black)("moles S"))) * (6.022 * 10^(23)"atoms")/(1color(red)(cancel(color(black)("mole S")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(3.61 * 10^(24)"atoms S")color(white)(a/a)|)))

Finally, use the fact that you need $8$ atoms of sulfur to form $1$ molecule of sulfur, ${\text{S}}_{8}$, to get the number of molecules

3.61 * 10^(24)color(red)(cancel(color(black)("atoms S"))) * "1 molecule S"_8/(8color(red)(cancel(color(black)("atoms S")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(4.51 * 10^(23)"molecules of S"_8)color(white)(a/a)|)))#

The answers are rounded to three sig figs, the number of sig figs you gave for the mass of sulfur.

So remember, you can go from mass to moles by using molar mass, then from moles to molecules / atoms by using Avogadro's number.