# Question 7908b

Jun 12, 2017

$65.0$ ${\text{g N}}_{2}$

#### Explanation:

Any time you want to convert between moles and grams of a substance, you must know that substance's molar mass, which is the mass of one mole of that substance. (One mole is equal to Avogadro's number ($6.022 \times {10}^{23}$) of individual particles/molecules of that substance.)

To find the molar mass of a nitrogen molecule, we'll first realize its chemical formula, which is ${\text{N}}_{2}$.

Most periodic tables list the molar masses (same number as atomic mass) of all the elements under their chemical symbol. For nitrogen, the molar mass is $14.01 \text{g"/"mol}$, that is, one mole of pure nitrogen atoms has a mass of $14.01$ grams.

Since there are two nitrogen atoms per nitrogen molecule, the molar mass of ${\text{N}}_{2}$ is double that of elemental nitrogen:

$2 \times 14.01 \text{g"/"mol" = color(red)(28.02"g"/"mol}$

Now, we can use dimensional analysis to convert between moles and grams of ${\text{N}}_{2}$:

$2.32$ cancel("mol N"_2)((color(red)(28.02"g N"_2))/(1cancel("mol N"_2))) = color(blue)(65.0 color(blue)("g N"_2

rounded to color(purple)(3 significant figures, the amount given in the problem.

Thus, $2.32$ moles of pure nitrogen gas has a mass of color(blue)(65.0# grams.