Question

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

Answer 1

`4.52 * 10^(23)`

Explanation:

Your strategy here will be to use the molar mass of nitric oxide, `"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 `"30.01 g mol"^(-1)`, which means that one mole of nitric oxide has a mass of `"30.01 g"`.

Since your sample is about `"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 * 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

`"no. of molecules" = color(green)(|bar(ul(color(white)(a/a)4.52 * 10^(23)color(white)(a/a)|)))`