Question #c26f4

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 `"44.01 g mol"^(-1)`. This tells you that `1` mole of carbon dioxide has a mass of `"44.01 g"`.

In other words, if you have `6.022 * 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 `"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.