The label on a bottle of 3% (by volume) hydrogen peroxide, H₂O₂, purchased at a grocery store, states that the solution should be stored in a cool, dark place. H₂O₂ decomposes slowly over time, and the rate of decomposition increases with an increase in temperature and in the presence of light. However, the rate of decomposition increases dramatically if a small amount of powdered MnO₂ is added to the solution. The decomposition products are H₂O and O₂. MnO₂ is not consumed in the reaction.

(a) Write the equation for the decomposition of H₂O₂.

(b) What role does MnO₂ play?

(c) In the chemistry lab, a student substituted a chunk of MnO₂ for the powdered compound. The reaction rate was not appreciably increased. What is one possible explanation for this observation?

(d) Is MnO₂ part of the stoichiometry of the decomposition of H₂O₂?