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

Apr 4, 2016

#### Answer:

$3.343 \cdot {10}^{23} \text{molecules}$

#### 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, ${\text{C"_9"H"_8"O}}_{4}$, has a molar mass of ${\text{180.157 g mol}}^{- 1}$. This means that one mole of aspirin will have a mass of $\text{180.157 g}$.

You're dealing with a$\text{100.0-g}$ 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 $6.022 \cdot {10}^{23}$ 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

$0.55507 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))) * (6.022 * 10^(23)"molecules")/(1color(red)(cancel(color(black)("mole")))) = color(green)(|bar(ul(color(white)(a/a)3.343 * 10^(23)"molecules} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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