# A mixture containing 10 mL of a nitrogen oxide and 30 ml of hydrogen reacts completely to form 10 mL of nitrogen. What is the formula for the nitrogen oxide?

Jun 2, 2017

The molecular formula of the compound is ${\text{N"_2"O}}_{3}$.

#### Explanation:

Step 1. Summarize the information

$\textcolor{w h i t e}{l} \text{N"_x"O"_y +color(white)(ll) "H"_2 → color(white)(m)"N"_2 + "H"_2"O}$
$\text{10 mL"color(white)(ml)"30 mL"color(white)(m)"10 mL}$

Step 2. Assume that the reaction involves 1 mol of the compound

Then the partially balanced equation is

$\text{1N"_x"O"_y +"3H"_2 → "1N"_2 + "H"_2"O}$

Step 3. Balance $\text{N}$

We have 2 atoms of $\text{N}$ on the right, so we need 2 atoms of $\text{N}$ on the left.

$x = 2$ and

$\text{N"_2"O"_y + "3H"_2 → "N"_2 + "H"_2"O}$

Step 4. Balance $\text{H}$

We have 6 $\text{H}$ on the left, so we need 6 $\text{H}$ on the right.

Put a 3 in front of $\text{H"_2"O}$.

$\text{N"_2"O"_y + "3H"_2 → "N"_2 + "3H"_2"O}$

Step 5. Balance $\text{O}$.

We have 3 $\text{O}$ on the right, so we need 3 $\text{O}$ on the left.

$y = 3$ and

$\text{N"_2"O"_3 + "3H"_2 → "N"_2 + "3H"_2"O}$

The formula of the compound is ${\text{N"_2"O}}_{3}$.