# How many molecules of nitrogen monoxide are in a 22.5 gram sample?

Mar 24, 2016

$4.52 \cdot {10}^{23}$

#### Explanation:

Your strategy here will be to use the molar mass of nitric oxide, $\text{NO}$, to determine how many moles you get in that sample.

Once you know that, you can use Avogadro's number as a conversion factor to help you determine how many molecules would be present in that many moles.

So, nitric oxide has a molar mass of ${\text{30.01 g mol}}^{- 1}$, which means that one mole of nitric oxide has a mass of $\text{30.01 g}$.

Since your sample is about $\text{8 g}$ short of the mass of one mole, you can say for a fact that you're dealing with less than one mole of nitric oxide.

More precisely, you will have

22.5 color(red)(cancel(color(black)("g"))) * " 1 mole NO"/(30.01 color(red)(cancel(color(black)("g")))) = "0.7498 moles NO"

Now, according to Avogadro's number, one mole of any substance contains $6.022 \cdot {10}^{23}$ molecules of that substance. This means that $0.7498$ moles of nitric oxide will contain

0.7498 color(red)(cancel(color(black)("moles NO"))) * overbrace((6.022 * 10^(23)"molec. NO")/(1color(red)(cancel(color(black)("mole NO")))))^(color(purple)("Avogadro's number")) = "4.5153 molec. NO"

Rounded to three sig figs, the number of sig figs you have for the mass of nitric oxide, the answer will be

$\text{no. of molecules} = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 4.52 \cdot {10}^{23} \textcolor{w h i t e}{\frac{a}{a}} |}}}$