In a decomposition reaction where hydrogen peroxide decomposes in the presence of manganese dioxide, how much of each (hydrogen peroxide and...

The decomposition of hydrogen peroxide (H2O2) is catalyzed by manganese dioxide and hence we do not need to show the catalyst in the chemical equation. The actual chemical equation can be written as:

`2H_2O2 -> 2H_2O + O_2`

In this reaction, 2 moles of hydrogen peroxide converts to 1 mole of oxygen and 2 moles of water. 

Assuming STP conditions, each mole occupies 22.4 l volume. Since the given volume of oxygen is 50 ml or 0.05 l, we have 0.05/22.4 moles of oxygen as a product.

To generate that product, we need 2 x 0.05/22.4 moles of hydrogen peroxide (using stoichiometry). In other words, we need

2 x 0.05/22.4 moles x 22.4 l/moles = 0.1 l = 100 ml.

Thus, 100 ml of hydrogen peroxide is needed to generate 50 ml of oxygen.

Manganese dioxide is a catalyst and hence is required in small quantities. The attached link suggests 1 spatula of catalyst for 50 ml, 30% hydrogen peroxide. Since, we have 100 ml of the peroxide, we can use 2 spatula full of the catalyst.

Hope this helps.