Question

Consider a mixture of 10 billion \(\mathrm{O}_{2}\) molecules and 10 billion \(\mathrm{H}_{2}\) molecules. In what way is this mixture similar to a sample containing 10 billion hydrogen peroxide \(\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)\) molecules? In what way is it different?

Short answer

Both mixtures have the same total number of hydrogen and oxygen atoms. However, the atoms are bonded differently in the hydrogen peroxide sample compared to the separate \( \text{O}_{2} \) and \( \text{H}_{2} \) mixture.

Step-by-step solution

Title - Understand the composition

Analyze the composition of both the mixtures. One mixture has 10 billion \(\text{O}_{2}\) molecules and 10 billion \(\text{H}_{2}\) molecules, while the other sample contains 10 billion \(\text{H}_{2}\text{O}_{2}\) molecules.

Title - Compare the number of atoms

Count the total number of atoms in both mixtures. In the mixture with \( \text{O}_{2} \) and \( \text{H}_{2} \) molecules, there are 20 billion oxygen atoms and 20 billion hydrogen atoms (since each \( \text{O}_{2} \) molecule has 2 oxygen atoms and each \( \text{H}_{2} \) molecule has 2 hydrogen atoms). Similarly, in the \( \text{H}_{2} \text{O}_{2} \) sample, there are also 20 billion oxygen atoms and 20 billion hydrogen atoms (since each \( \text{H}_{2} \text{O}_{2} \) molecule has 2 hydrogen atoms and 2 oxygen atoms).

Title - Discuss the similarity

State that both the mixture and the sample have the same total number of hydrogen and oxygen atoms, making them similar in terms of the total count of atoms.

Title - Discuss the difference

Note the difference in how the atoms are bonded. In the mixture with \( \text{O}_{2} \) and \( \text{H}_{2} \) molecules, the oxygen and hydrogen atoms are not bonded together as they are in \( \text{H}_{2} \text{O}_{2} \). In the \( \text{H}_{2} \text{O}_{2} \) sample, each molecule consists of hydrogen atoms bonded to oxygen atoms forming hydrogen peroxide.

Key concepts

Molecular Composition

The concept of molecular composition is essential when comparing mixtures and compounds. A mixture contains different substances that are not chemically bonded. In our example, the mixture includes 10 billion \(\text{O}_{2}\) molecules and 10 billion \(\text{H}_{2}\) molecules. Each \(\text{O}_{2}\) molecule is made up of 2 oxygen atoms, and each \(\text{H}_{2}\) molecule is made up of 2 hydrogen atoms.
In contrast, hydrogen peroxide \( \text{H}_{2}\text{O}_{2} \) is a compound where each molecule consists of 2 hydrogen atoms and 2 oxygen atoms chemically bonded together. This means that all hydrogen and oxygen atoms in hydrogen peroxide are part of the same molecule, not separate as they are in the mixture.

Atomic Bonds

Atomic bonds determine the structure and properties of substances. In the mixture of \(\text{O}_{2}\) and \(\text{H}_{2}\), oxygen atoms bond only with other oxygen atoms, and hydrogen atoms bond only with other hydrogen atoms. There are no bonds between hydrogen and oxygen atoms in this mixture.
However, in hydrogen peroxide \( \text{H}_{2}\text{O}_{2} \), each molecule includes bonds between hydrogen and oxygen atoms, forming a single, distinct entity. These bonds are important because they affect the substance's properties, like reactivity and stability.
In comparing the mixture to the hydrogen peroxide sample, the key difference is the presence of direct hydrogen-oxygen bonds in hydrogen peroxide, which change the chemical properties significantly.

Chemical Mixtures

A chemical mixture comprises two or more different substances mixed together but not chemically bonded. For instance, our earlier mixture has both \(\text{O}_{2}\) molecules and \(\text{H}_{2}\) molecules present together without any bonds forming between different atoms.
This is unlike a compound where a substance is made up of different elements that are chemically bonded. Mixtures like the one in our example can often be separated by physical means since the substances retain their individual properties. Examples include separating oxygen and hydrogen gases from their mixture.
Such important characteristics distinguish mixtures from compounds, helping us understand their respective behaviors and uses.

Hydrogen Peroxide

Hydrogen peroxide \( \text{H}_{2}\text{O}_{2} \) is a compound you might be familiar with as a disinfectant. It consists of molecules with two hydrogen atoms and two oxygen atoms bonded together. These bonds create a substance with properties distinct from those of individual hydrogen and oxygen gases.
Hydrogen peroxide is reactive and can decompose into water and oxygen over time or when catalyzed. This reactivity is due to the chemical bonds between hydrogen and oxygen within each molecule.
Compared to a simple mixture, hydrogen peroxide's bonded structure gives it unique chemical properties, making it useful in various applications from cleaning to medical uses.