Question

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?

Answer 1

`3`

Explanation:

You know that magnesium chlorate, `"Mg"("ClO"_3)_2`, undergoes thermal decomposition to produce magnesium chloride, `"MgCl"_2`, and oxygen gas, `"O"_2`.

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

`"Mg"("ClO"_ 3)_ (color(blue)(2)(s)) stackrel(color(white)(acolor(red)(Delta)aaa))(->) "MgCl"_ (2(s)) + "O"_ (2(g))`

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

• one magnesium cation, `1 xx "Mg"^(2+)`
• two chlorate anions, `color(blue)(2) xx "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, `color(blue)(2) xx 1 xx "Cl"`
• six atoms of oxygen, `color(blue)(2) xx 3 xx "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

`"Mg"("ClO"_ 3)_ (color(blue)(2)(s)) stackrel(color(white)(acolor(red)(Delta)aaa))(->) "MgCl"_ (2(s)) + 3"O"_ (2(g))`

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.