A common demonstration in chemistry courses involves adding a tiny speck of manganese(IV) oxide to a concentrated hydrogen peroxide \(\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)\) solution. Hydrogen peroxide decomposes quite spectacularly under these conditions to produce oxygen gas and steam (water vapor). Manganese(IV) oxide is a catalyst for the decomposition of hydrogen peroxide and is not consumed in the reaction. Write the balanced equation for the decomposition reaction of hydrogen peroxide.

First, we need to identify the reactants and products and write their respective chemical formulas for the decomposition reaction of hydrogen peroxide: Reactants: hydrogen peroxide (H₂O₂) Products: oxygen gas (O₂) and water vapor (H₂O) Next, we'll write the unbalanced chemical equation for the decomposition reaction: H₂O₂ → O₂ + H₂O

Now we need to balance the chemical equation by ensuring that the number of atoms of each element is equal on both sides of the equation. In the unbalanced equation: H₂O₂ → O₂ + H₂O We have 2 H atoms and 2 O atoms on the left (reactant) side, and 2 H atoms and 3 O atoms on the right (product) side. To begin balancing the equation, let's adjust the number of oxygen atoms by placing a coefficient in front of the reactant H₂O₂: 2 H₂O₂ → O₂ + H₂O Now we have 4 O atoms on the left side and 3 O atoms on the right side. To balance the oxygen atoms, place a coefficient of 2 in front of the product H₂O: 2 H₂O₂ → O₂ + 2 H₂O Now we have 4 O atoms on both sides, but we also have 4 H atoms on the left side and 2 H atoms on the right side. To balance the hydrogen atoms, place a coefficient of 2 in front of the product O₂: 2 H₂O₂ → 2 O₂ + 2 H₂O Now we have 4 O atoms and 4 H atoms on both sides of the equation, and the equation is balanced.

The balanced chemical equation for the decomposition reaction of hydrogen peroxide catalyzed by manganese(IV) oxide is: 2 H₂O₂ → 2 O₂ + 2 H₂O