# How many N atoms are there in one mole of N_2?

Oct 3, 2016

$2 \times {N}_{\text{A}}$

#### Explanation:

You know that one molecule of nitrogen gas, ${\text{N}}_{\textcolor{b l u e}{2}}$, contains two atoms of nitrogen, $\textcolor{b l u e}{2} \times \text{N}$.

Now, a mole is simply a very, very large collection of particles. In order to have one mole of things, let's say particles, you need to have $6.022 \cdot {10}^{23}$ particles $\to$ this is known as Avogadro's constant and acts as the definition of the mole.

So, in one mole of nitrogen gas you have $6.022 \cdot {10}^{23}$ molecules of nitrogen gas, ${\text{N}}_{2}$. But since each individual molecule consists of $2$ atoms of nitrogen, the number of moles of nitrogen atoms will be twice that of nitrogen gas molecules.

6.022 * 10^(23)color(red)(cancel(color(black)("molecules N"_2))) * (color(blue)(2)color(white)(a)"atoms of N")/(1color(red)(cancel(color(black)("molecule N"_2))))

$= 1.2044 \cdot {10}^{24} \text{taoms of N}$

Alternatively, you can express this as $\textcolor{b l u e}{2} \times {N}_{\text{A}}$, where ${N}_{\text{A}}$ is Avogadro's constant..