# Question #df311

Jul 6, 2017

You will need 9.0 L of ${\text{N}}_{2}$.

#### Explanation:

For this problem, we can use a modern statement of Gay-Lussac's Law of Combining Volumes:

If pressure and temperature are constant, the ratio of the volumes of the reactant gases and the products is the same as their molar ratios.

The balanced equation for the reaction is

$\textcolor{w h i t e}{l l} {\text{N"_2 + "3H"_2 → "2NH}}_{3}$
$\textcolor{w h i t e}{l l} \text{1 L"color(white)(mmmmmll)"2 L}$

According to Gay-Lussac, ${\text{1 L"color(white)(l) "of N}}_{2}$ forms ${\text{2 L of NH}}_{3}$.

${\text{Volume of N"_2 = 18 color(red)(cancel(color(black)("L" color(white)(l)"NH"_3))) × ("1 L"color(white)(l) "N"_2)/(2 color(red)(cancel(color(black)("L"color(white)(l) "NH"_3)))) = "9.0 L"color(white)(l)"NH}}_{3}$