# What coefficients correctly balance the formula NH_4NO_2 -> N_2 + H_2O?

Mar 12, 2016

$1 , 1 , 2$

#### Explanation:

You're dealing with the decomposition of ammonium nitrite, ${\text{NH"_4"NO}}_{2}$.

As you can see, ammonium nitrite decomposes to form nitrogen gas, ${\text{N}}_{2}$, and water, $\text{H"_2"O}$, according to the unbalanced chemical equation

${\text{NH"_4"NO"_text(2(s]) stackrel(color(red)(Delta)color(white)(aa))(->) "N"_text(2(g]) + "H"_2"O}}_{\textrm{\left(g\right]}}$

Now, the Law of Mass Conservation tells you that matter can neither be created, nor destroyed, in a chemical reaction.

This tells you that the total number of atoms present on the reactants' side must be equal to the total number of atoms present on the products' side.

In other words, all the atoms initially present in one formula unit of ammonium nitrite must be accounted for on the products' side.

One formula uni of ammonium nitrite contains

• two atoms of nitrogen, $2 \times \text{N}$
• four atoms of hydrogen, $4 \times \text{H}$
• two atoms of oxygen, $2 \times \text{O}$

According to the unbalanced chemical equation, the products' side has

• two atoms of nitrogen, $2 \times \text{N"" } \textcolor{g r e e n}{\sqrt{}}$
• two atoms of hydrogen, $2 \times \text{H"" } \textcolor{red}{\times}$
• one atom of oxygen, $1 \times \text{O"" } \textcolor{red}{\times}$

As you can see, the atoms of nitrogen are already balanced. However, you need twice as many atoms of hydrogen and of oxygen on the products' side.

The great part about that is that hydrogen and oxygen are part of the same chemical compound on the products' side, i.e. water.

This means that if you multiply water by $\textcolor{p u r p \le}{2}$, you can double the number of atoms of both elements in one go.

The balanced chemical equation for this decomposition reaction will thus be

${\text{NH"_4"NO"_text(2(s]) stackrel(color(red)(Delta)color(white)(aa))(->) "N"_text(2(g]) + color(purple)(2)"H"_2"O}}_{\textrm{\left(g\right]}}$

Therefore, the stoichiometric coefficients that balance the initial equation are $1$, $1$, and $2$.