Determining the Mass of Oxygen Involved in the Reaction with Hydrogen to Produce Water

In this article, we delve into the detailed calculations and principles behind the chemical reaction where hydrogen reacts with oxygen to produce a specific mass of water. We use the law of conservation of mass and stoichiometry to find the exact amount of oxygen required for a given amount of hydrogen.

Understanding the Reaction and the Law of Conservation of Mass

The reaction between hydrogen and oxygen to form water is governed by the law of conservation of mass. According to this principle, the total mass of the reactants must equal the total mass of the products in a chemical reaction. For the formation of water (H2O) from hydrogen (H2) and oxygen (O2), the balanced chemical equation is:

2 H2 O2 → 2 H2O

This reaction means that two moles of hydrogen gas react with one mole of oxygen gas to produce two moles of water.

Step-by-Step Calculation Using Known Masses and Stoichiometry

We begin with the known mass of water produced, which is 36.0 grams. Our goal is to find out how much oxygen is required to completely react with 4.0 grams of hydrogen to produce this amount of water.

Step 1: Determine the Mass of Water Produced

The mass of the water produced is already given as 36.0 grams.

Step 2: Calculate the Mass of Oxygen Needed

Let's use the law of conservation of mass to find the mass of oxygen needed:

mass of hydrogen (H2) mass of oxygen (O2) mass of water (H2O)

If we know the mass of hydrogen (4.0 grams), and we need to find the mass of oxygen (mO):

4.0 g H2 mO 36.0 g H2O

Solving for mO:

mO 36.0 g - 4.0 g 32.0 g

Therefore, 32.0 grams of oxygen are needed to completely react with 4.0 grams of hydrogen to produce 36.0 grams of water.

Step 3: Verification Using Stoichiometry

To verify this calculation, we can use stoichiometry to confirm the exact amounts of reactants and products.

Conveting Mass to Moles

First, we need to convert the given masses to moles:

4.0 g H2 32.0 g O2

The molar masses are:

Molar mass of H2 2.0 g/mol Molar mass of O2 32.0 g/mol Molar mass of H2O 18.0 g/mol

Calculate moles of H2:

moles of H2 4.0 g / 2.0 g/mol 2.0 mol

Calculate moles of H2O produced:

moles of H2O 36.0 g / 18.0 g/mol 2.0 mol

Using the balanced equation, 2 moles of H2 produce 2 moles of H2O, meaning 1 mole of O2 is required for 2 moles of H2 to produce 2 moles of H2O.

moles of O2 2.0 mol H2 / 2 1.0 mol O2

Convert moles of O2 to grams:

mass of O2 1.0 mol × 32.0 g/mol 32.0 g

This confirms that the mass of oxygen needed is indeed 32.0 grams.

Conclusion

The mass of oxygen that completely reacts with 4.0 grams of hydrogen to produce 36.0 grams of water is 32.0 grams. This example illustrates the practical application of the law of conservation of mass and stoichiometry in chemical reactions, ensuring that the mass of the reactants and products are consistent with the principles of chemistry.