Question

Reaction of 2.0 \(\mathrm{L}\) of hydrogen gas with 1.0 \(\mathrm{L}\) of oxygen gas yields 2.0 \(\mathrm{L}\) of water vapor. All gases are at the same temperature and pressure. Show how these data support the idea that oxygen gas is a diatomic molecule. Must we consider hydrogen to be a diatomic molecule to explain these results?

Short answer

The given information shows that 2.0 L of hydrogen gas (\(H_2\)) reacts with 1.0 L of oxygen gas (\(O_2\)) to form 2.0 L of water vapor (\(H_2O\)). By balancing the chemical equation, we get \(2H_2 + O_2 \rightarrow 2H_2O\), which indicates that both hydrogen and oxygen are diatomic molecules. Applying Avogadro's law further confirms that the reaction supports the idea of oxygen and hydrogen being diatomic molecules.

Step-by-step solution

Determine the stoichiometry of the reaction

According to the given statement, the reaction proceeds as follows: Hydrogen gas + Oxygen gas → Water vapor However, the coefficients (stoichiometry) have not been mentioned in the exercise. These need to be determined from the balanced chemical equation.

Balancing the chemical equation

In order to balance the equation, we need to ensure that the number of atoms for each element is the same on both the reactant and product sides. Starting with hydrogen (H) and oxygen (O), we have the balanced chemical equation as: \[ 2H_2 + O_2 \rightarrow 2H_2O \] This balanced chemical equation show that it's a diatomic molecule for both oxygen and hydrogen.

Apply the gas law to compare the reaction volumes

When reactant and product volumes are given, we can apply Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. Based on this law, we can assume that the number of molecules in 2.0 L of hydrogen gas is double the number of molecules in 1.0 L of oxygen gas.

Verifying the idea of diatomic molecules using given data

From the balanced chemical equation and applying Avogadro's law: For hydrogen gas: 2.0 L of \(\displaystyle H_{2}\) contains 2 moles of \(\displaystyle H_{2}\) molecules For oxygen gas: 1.0 L of \(\displaystyle O_{2}\) contains 1 mole of \(\displaystyle O_{2}\) molecules For water vapor: 2.0 L of \(\displaystyle H_{2}O\) contains 2 moles of \(\displaystyle H_{2}O\) molecules The balanced chemical equation shows that one mole of oxygen gas (\(\displaystyle O_{2}\)) reacts with two moles of hydrogen gas (\(\displaystyle H_{2}\)) to form two moles of water vapor (\(\displaystyle H_{2}O\)).

Conclusion

Based on the given information, the reaction supports the idea that oxygen gas is a diatomic molecule, as evidenced by the balanced chemical equation and Avogadro's law. Moreover, the same data also helps us conclude that hydrogen must be considered a diatomic molecule to properly explain these results.

Key concepts

Stoichiometry

Stoichiometry is a concept used to understand the quantitative relationships in a chemical reaction. It involves calculating the exact amounts of reactants and products involved in a reaction. In our exercise, we start by looking at the reaction between hydrogen and oxygen gases forming water vapor.
The balanced chemical equation for the reaction is:

• 2H₂ + O₂ → 2H₂O

This equation is balanced, showing that two molecules of hydrogen react with one molecule of oxygen to produce two molecules of water. Stoichiometry helps in understanding these ratios and allows us to predict the quantities needed or produced in a reaction.
If we know the volume of one gas at a given temperature and pressure, stoichiometry helps us calculate the others using ratios derived from the balanced equation.

Avogadro's Law

Avogadro's law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. This principle is crucial in our exercise because we are dealing with volumes of gases reacting.
According to Avogadro’s law, the 2.0 liters of hydrogen gas and 1.0 liter of oxygen gas correlate directly to the number of particles (or moles) of those gases.

• 2.0 liters of hydrogen gas corresponds to 2 moles of H₂
• 1.0 liter of oxygen gas corresponds to 1 mole of O₂

This understanding ties back into our stoichiometric calculations, as we need to know how many molecules (or moles) of each gas are present to predict how they will react to form water vapor. Avogadro's law thus confirms that the volumetric ratios used in our balanced chemical equation naturally adhere to the laws governing molecular quantities.

Balanced Chemical Equation

A balanced chemical equation is fundamental to chemical reactions as it ensures the conservation of mass. This means having the same number of each type of atom on both sides of the equation. For the reaction given, the equation is:

• 2H₂ + O₂ → 2H₂O

The equation above is balanced because:

• We have 4 hydrogen atoms on each side (2 from each H₂ molecule)
• We have 2 oxygen atoms on each side (2 from O₂ and 2 in two molecules of H₂O)

When balancing chemical equations, it’s key to adjust coefficients to achieve equal numbers of atoms, not to change the chemical formulas themselves. This balanced equation shows us the exact stoichiometric relationships required for the reaction to go to completion, exemplifying how a balanced chemical equation reflects real chemical processes.

Molecular Theory

Molecular theory explains the behaviors and properties of atoms and molecules. In our exercise, it helps to understand why gases react in certain volumes. According to molecular theory, gases are composed of widely spaced molecules in constant, random motion.
These molecules interact under defined energy conditions, which influence how chemical reactions like the hydrogen and oxygen reaction occur. The theory provides the framework to understand that:

• Hydrogen and oxygen are diatomic molecules, meaning each molecule consists of two atoms.
• In a given volume of gas, measured under the same conditions, there will be predictable behavior based on molecular composition and interactions.

The exercise's conclusion, that both hydrogen and oxygen are diatomic, relies heavily on this theory. It supports the idea that each diatomic molecule of oxygen will bond with two diatomic molecules of hydrogen to form water, fitting the quantitative details provided by stoichiometry and Avogadro's law.