How many molecules of aspirin are contained in a 100.0 g tablet of aspirin, #C_9H_8O_4#?

1 Answer
Apr 4, 2016

Answer:

#3.343 * 10^(23)"molecules"#

Explanation:

Your strategy her will be to

  • use the molar mass of aspirin to determine how many moles you have in that sample
  • use Avogadro's number to convert the number of moles to number of molecules

So, aspirin, #"C"_9"H"_8"O"_4#, has a molar mass of #"180.157 g mol"^(-1)#. This means that one mole of aspirin will have a mass of #"180.157 g"#.

You're dealing with a#"100.0-g"# sample of aspirin, which will be equivalent to

#100.0 color(red)(cancel(color(black)("g"))) * "1 mole aspirin"/(180.157color(red)(cancel(color(black)("g")))) = "0.55507 moles aspirin"#

Now that you know how many moles of aspirin you have in your sample, use the fact that one mole of a substance contains #6.022 * 10^(23)# molecules of that substance - this is known as Avogadro's number.

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 mole" = 6.022 * 10^(23)"molcules")color(white)(a/)|))) -># Avogadro's number

Use Avogadro's number as a conversion factor to calculate how many molecules you get in #0.55507# moles of aspirin

#0.55507color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"molecules")/(1color(red)(cancel(color(black)("mole")))) = color(green)(|bar(ul(color(white)(a/a)3.343 * 10^(23)"molecules"color(white)(a/a)|)))#

The answer is rounded to three sig figs, the number of sig figs you have for the mass of aspirin.