# What is the coefficient of "O"_2 when the equation "Mg"("ClO"_3)_2(s) -> "MgCl"_2(s)+"O"_2(g) is balanced correctly using the smallest whole number coefficients?

Jun 16, 2017

$3$

#### Explanation:

You know that magnesium chlorate, "Mg"("ClO"_3)_2, undergoes thermal decomposition to produce magnesium chloride, ${\text{MgCl}}_{2}$, and oxygen gas, ${\text{O}}_{2}$.

The unbalanced chemical equation that describes this decomposition reaction looks like this

${\text{Mg"("ClO"_ 3)_ (color(blue)(2)(s)) stackrel(color(white)(acolor(red)(Delta)aaa))(->) "MgCl"_ (2(s)) + "O}}_{2 \left(g\right)}$

Now, you know that one formula units of magnesium chlorate contains

• one magnesium cation, $1 \times {\text{Mg}}^{2 +}$
• two chlorate anions, $\textcolor{b l u e}{2} \times {\text{ClO}}_{3}^{-}$

Since each chlorate anion contains $1$ atom of chlorine and $3$ atoms of oxygen, you can say that the reactant's side contains

• two atoms of chlorine, $\textcolor{b l u e}{2} \times 1 \times \text{Cl}$
• six atoms of oxygen, $\textcolor{b l u e}{2} \times 3 \times \text{O" = 6 xx "O}$

Notice that you have $1$ atom of magnesium on the reactant's side and on the products' side, so you know that magnesium is balanced.

The same can be said about chlorine since you have $2$ atoms of chlorine on the reactant's side and on the products' side.

Now, notice that you have a total of $6$ atoms of oxygen on the reactant's side and only $2$ atoms of oxygen on the products' side. In order to balance the atoms of oxygen, multiply the oxygen molecule by $3$.

You will now have

${\text{Mg"("ClO"_ 3)_ (color(blue)(2)(s)) stackrel(color(white)(acolor(red)(Delta)aaa))(->) "MgCl"_ (2(s)) + 3"O}}_{2 \left(g\right)}$

Since $1 : 1 : 3$ is the smallest ratio that can be used to balance the chemical equation using whole number coefficients, you can thus say that the oxygen molecule has a coefficient of $3$ in the balanced chemical equation that describes the decomposition of magnesium chlorate.