Question

Question #4c9dc

Answer 1

`1 * 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)` `"moles CO"_2`

Now, you know that after `"X"` molecules of carbon dioxide are removed from the sample, you are left with `2.89 * 10^(-3)` moles of carbon dioxide.

This means that you actually removed

`4.54 * 10^(-3)color(white)(.)"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

`color(blue)(ul(color(black)("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"))`

`= color(darkgreen)(ul(color(black)(1 * 10^(21)color(white)(.)"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.