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

1 Answer
Mar 24, 2016

Answer:

#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)|)))#