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

Jul 29, 2016

$2.27 \cdot {10}^{- 10} \text{g}$

#### 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 $9.76 \cdot {10}^{12}$ 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 $\text{14.00674 g}$. Since one mole of any element contains $6.022 \cdot {10}^{23}$ 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.