Question

What is the mass of `9.76xx10^12` atoms of nitrogen?

Answer 1

`2.27 * 10^(-10)"g"`

Explanation:

To make this problem more interesting, let's calculate the mass of a single atom of nitrogen first, then use that value as a conversion factor to determine the mass of `9.76 * 10^(12)` atoms of nitrogen.

The starting point here will be the molar mass of nitrogen, which is listed as

`M_("M N") = "14.00674 g mol"^(-1)`

This tells you that one mole of nitrogen has a mass of `"14.00674 g"`. Since one mole of any element contains `6.022 * 10^(23)` atoms of that element, you can say that the mass of a single atom of nitrogen will be

`1 color(red)(cancel(color(black)("atom N"))) * "14.00674 g"/(6.022 * 10^(23)color(red)(cancel(color(black)("atoms N")))) = 2.326 * 10^(-23)"g"`

Now all you have to do is multiply this value by the number of atoms given to you to find

`9.76 * 10^(12) color(red)(cancel(color(black)("atoms N"))) * (2.326 * 10^(-23)"g")/(1color(red)(cancel(color(black)("atom N")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(2.27 * 10^(-10)"g")color(white)(a/a)|)))`

The answer is rounded to three sig figs.