# How do you balance Na(s) + NaNO_3(aq) -> Na_2O(aq) + N_2(g)?

Mar 5, 2016

$10 {\text{Na"(s) + 2"NaNO"_3(aq) -> 6"Na"_2"O"(aq) + "N}}_{2} \left(g\right)$

#### Explanation:

After balancing the equation, you should see that the number of $\text{Na}$, $\text{O}$ and $\text{N}$ should be the same on both sides of the equation. This is the original equation.

${\text{Na" + "NaNO"_3 -> "Na"_2"O" + "N}}_{2}$

When balancing the equations, I omit the state symbols. I will add them back in the final balanced equation.

The trick to balancing the equation is to fix the compound with the most elements present to a ratio of $1$. In this case, it is ${\text{NaNO}}_{3}$, as it contains all 3 elements.

Next, we start of by balancing the elements that have the least occurrence. $\text{Na}$ appeared in 3 times, while $\text{N}$ and $\text{O}$ appeared only 2 times, so we start with $\text{N}$ first.

$\textcolor{g r e e n}{\text{Balancing N}}$

There is 1 $\text{N}$ on the left-hand side (LHS) and 2 $\text{N}$ on the right-hand side (RHS). To balance $\text{N}$, we only need half the amount of ${\text{N}}_{2}$ on the RHS.

${\text{Na" + "NaNO"_3 -> "Na"_2"O" + 1/2 "N}}_{2}$

$\textcolor{g r e e n}{\text{Balancing O}}$

There are 3 $\text{O}$ on the LHS and 1 $\text{O}$ on the RHS. To balance $\text{O}$, we need 3 times the amount of $\text{Na"_2"O}$ on the RHS.

${\text{Na" + "NaNO"_3 -> 3"Na"_2"O" + 1/2 "N}}_{2}$

$\textcolor{g r e e n}{\text{Balancing Na}}$

There are 2 $\text{Na}$ on the LHS and 6 $\text{Na}$ on the RHS. Both the number of ${\text{NaNO}}_{3}$ and $\text{Na"_2"O}$ are fixed already, which means that we can only change the number of $\text{Na}$. To balance $\text{Na}$, we need 5 more $\text{Na}$ on the LHS.

$5 {\text{Na" + "NaNO"_3 -> 3"Na"_2"O" + 1/2 "N}}_{2}$

The balancing is now complete. However, some people do not like fractions as coefficients. So to get rid of the $\frac{1}{2}$, multiply everything by $2$. It becomes

$10 {\text{Na" + 2"NaNO"_3 -> 6"Na"_2"O" + "N}}_{2}$

Remember to put back the state symbols!