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

##### 1 Answer

#### 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

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 **one mole** of any element contains **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**.