# How many molecules are in 35.5 g of "Cl"_2 ?

Jul 30, 2016

$3.02 \cdot {10}^{23}$

#### Explanation:

Your strategy here will be to

• use the molar mass of chlorine gas, ${\text{Cl}}_{2}$, to calculate how many moles you have in that sample
• use Avogadro's number to convert the number of moles to number of molecules

Chlorine gas has a molar mass of ${\text{70.906 g mol}}^{- 1}$, which tells you that one mole of chlorine gas has a mass of $\text{70.906 g}$. Use the molar mass as a conversion factor to help you go from grams of chlorine gas to moles

35.5 color(red)(cancel(color(black)("g"))) * "1 mole Cl"_2/(70.906color(red)(cancel(color(black)("g")))) = "0.5007 moles Cl"_2

Now, a mole of a molecular compound is defined as $6.022 \cdot {10}^{23}$ molecules of said compound $\to$ this is known as Avogadro's number.

In your case, the sample of chlorine gas will contain

0.5007 color(red)(cancel(color(black)("moles Cl"_2))) * (6.022 * 10^(23)"molec. Cl"_2)/(1color(red)(cancel(color(black)("mole Cl"_2)))) = color(green)(|bar(ul(color(white)(a/a)color(black)(3.02 * 10^(23)"molec Cl"_2)color(white)(a/a)|)))

The answer is rounded to three sig figs.