# Question 4c9dc

Jul 18, 2017

$1 \cdot {10}^{21}$

#### Explanation:

Start by converting the initial mass of carbon dioxide to moles by using the compound's molar mass

200 color(red)(cancel(color(black)("mg"))) * (1color(red)(cancel(color(black)("g"))))/(10^3color(red)(cancel(color(black)("mg")))) * "1 mole CO"_2/(44.01 color(red)(cancel(color(black)("g")))) = 4.54 * 10^(-3) ${\text{moles CO}}_{2}$

Now, you know that after $\text{X}$ molecules of carbon dioxide are removed from the sample, you are left with $2.89 \cdot {10}^{- 3}$ moles of carbon dioxide.

This means that you actually removed

$4.54 \cdot {10}^{- 3} \textcolor{w h i t e}{.} {\text{moles CO"_2 - 2.89 * 10^(-3)color(white)(.)"moles CO"_2 = 1.65 * 10^(-3)color(white)(.)"moles CO}}_{2}$

All you have to do now is use Avogadro;s constant to convert the number of moles of carbon dioxide that were removed from the sample to molecules.

You know that

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{\text{1 mole CO"_2 = 6.022 * 10^(23)color(white)(.)"molecules CO}}_{2}}}}$

which means that you have

1.65 * 10^(-3)color(red)(cancel(color(black)("moles CO"_2))) * overbrace((6.022 * 10^(23)color(white)(.)"molecules CO"_2)/(1color(red)(cancel(color(black)("mole CO"_2)))))^(color(blue)("Avogadro's constant"))#

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{1 \cdot {10}^{21} \textcolor{w h i t e}{.} {\text{molecules CO}}_{2}}}}$

The answer must be rounded to one significant figure, the number of sig figs you have for the initial mass of carbon dioxide.