Colorful fireworks often involve the decomposition of barium nitrate and potassium chlorate and the reaction of the metals magnesium ,alminium and iron with oxygen.
(a)write the formulas of barium nitrate and potassium chlorate
(b)the decomposition of solid potassium chlorateleads to the formaion of solid potassium chloride and diatomic oxygen gas write an equation for the reaction
(c) the decomposition of the solid barium nitrate leads to the formation of solid barium oxide, nitrogen gas and diatomic oxygen gas
(d)write separate equations for the reactions of the solid metals in magnesium aluminum with a diatomic oxygen gas to yield the corresponding metal oxide (assume iron oxide contains fe+ ions)

Fireworks owe their colors to reactions of combustion of the metals present. When Mg and Al burn, they emit a white bright light, whereas iron emits a gold light. Besides metals, oxygen is necesary for the combustion. The decomposition reactions of barium nitrate and potassium chlorate provide this element. At the same time, barium can burn emitting a green light.

(a) Barium nitrate is a salt formed by the cation barium Ba²⁺ and the anion nitrate NO₃⁻. Its formula is Ba(NO₃)₂. Potassium chlorate is a salt formed by the cation potassium K⁺ and the anion chlorate ClO₃⁻. Its formula is KClO₃.

(b) The balanced equation for the decomposition of potassium chloride is:

2KClO₃(s) ⇄ 2KCl(s) + 3O₂(g)

(c)  The balanced equation for the decomposition of barium nitrate is:

Ba(NO₃)₂(s) ⇄ BaO(s) + N₂(g) + 3O₂(g)

(d) The balanced equations of metals with oxygen to form metal oxides are:

answer is: c. the experiment shows that the red substance experienced a chemical change.

this is chemical change (chemical reaction), because two new substances are formed (metalig liquid and gas), the atoms are rearranged and the reaction is followed by an energy change.

this is example of chemical decomposition.

chemical decomposition (analysis) is the separation of a single chemical compound into its two or more elemental parts or to simpler compounds.  

chemical decomposition is opposite of chemical synthesis.

14 days is the half-life of phosphorus-32