# Question c26f4

Nov 5, 2017

$7.31 \cdot {10}^{- 22}$ $\text{g}$

#### Explanation:

A useful thing to know in order to be able to calculate the mass of $10$ molecules of carbon dioxide would be the mass of a single molecule of this substance.

As you know, carbon dioxide has a molar mass of ${\text{44.01 g mol}}^{- 1}$. This tells you that $1$ mole of carbon dioxide has a mass of $\text{44.01 g}$.

In other words, if you have $6.022 \cdot {10}^{23}$ molecules of carbon dioxide, the number of molecules needed to get $1$ mole--this is known as Avogadro's constant--you can say that the sample has a mass of $\text{44.01 g}$.

"44.01 g " implies " "overbrace(6.022 * 10^(23)color(white)(.)"molecules CO"_2)^(color(blue)("equivalent to 1 mole of CO"_2))

This means that a single molecule of carbon dioxide will have a mass of

1 color(red)(cancel(color(black)("molecule CO"_2))) * "44.01 g"/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules CO"_2)))) = 7.31 * 10^(-23)color(white)(.)"g"

Therefore, you can say that $1$ molecules of carbon dioxide will have a mass of

10 color(red)(cancel(color(black)("molecules CO"_2))) * (7.31 * 10^(-23)color(white)(.)"g")/(1color(red)(cancel(color(black)("molecule CO"_2)))) = color(darkgreen)(ul(color(black)(7.31 * 10^(-22)color(white)(.)"g"#

I'll leave the answer rounded to three sig figs.