# Question 55cb4

May 6, 2017

The answer is (a) $3.0 \cdot {10}^{19}$

#### Explanation:

The first thing you need to do here is to convert the mass of ethanol to moles by using the compound's molar mass

2.3 * 10^(-3) color(red)(cancel(color(black)("g"))) * "1 mole ethanol"/(46.07color(red)(cancel(color(black)("g")))) = 4.992 * 10^(-5) $\text{moles ethanol}$

Now, you should know that a mole of a molecular compound contains $6.022 \cdot {10}^{23}$ molecules of said compound. This implies that $1$ mole of ethanol will contain

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 mole ethanol" = 6.022 * 10^(23)color(white)(.)"molecules C"_2"H"_5"OH}}}}$

You can thus say that your sample of ethanol will contain

4.992 * 10^(-5) color(red)(cancel(color(black)("moles C"_2"H"_5"OH"))) * (6.022 * 10^(23)color(white)(.)"molecules C"_2"H"_5"OH")/(1color(red)(cancel(color(black)("mole C"_2"H"_5"OH"))))#

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{3.0 \cdot {10}^{19} \textcolor{w h i t e}{.} \text{molecules C"_2"H"_5"OH}}}}$

The answer is rounded to two sig figs.