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?

1 Answer
Jun 16, 2017

Answer:

#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.