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Question

What is the coefficient of O2 when the equation $$Mg (ClO_{3}) _{2} (s) \rightarrow  MhCl_{2} (s) + O_{2} (g)$$ is balanced correctly using the smallest whole number coefficients?


Solution

Answer 
$$3$$
Explanation :
You know that magnesium chlorate, $$Mg (ClO_{3}) $$  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
One magnesium cation , $$1 \times  Mg^{2 +}$$
two chlorate anoins , $$2\times  ClO^{-}_{3}$$
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 chorins $$ 2 \times  1 \times  Cl $$
six atoms of oxygen $$2, \times  3\times  O = 6 \times  O $$
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.
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
$$Mg (ClO_{3}) _{2(s)}  \overset{\bigtriangleup }{\rightarrow} MgCl_{2(s)}  + 3O_{2(g)}$$
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.

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