Problem 31 - Introductory Chemistry Atoms First

Question

What is the mass percent of each element in hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2} ?\)

Step-by-Step Solution

Answer

In hydrogen peroxide (\(\mathrm{H}_{2}\mathrm{O}_{2}\)), the mass percent of hydrogen is approximately 5.88% and the mass percent of oxygen is approximately 94.12%.

Step 1: Find the molar mass of hydrogen peroxide

The molecular formula of hydrogen peroxide is \(\mathrm{H}_{2}\mathrm{O}_{2}\). To find the molar mass, we need to add up the molar masses of all the elements in the molecule. The molar masses of hydrogen (H) and oxygen (O) are respectively 1 g/mol and 16 g/mol. So, the molar mass of hydrogen peroxide is: Molar mass of \(\mathrm{H}_{2}\mathrm{O}_{2} = 2 \times 1 + 2 \times 16 = 34\,\text{g/mol}\).

Step 2: Calculate the mass percent of hydrogen

Now that we have the molar mass of hydrogen peroxide, we can determine the mass percent of hydrogen (H). The mass of 2 moles of hydrogen in the molecule is: Mass of hydrogen = 2 × 1 = 2 g Next, we'll calculate the mass percentage of hydrogen: Mass percent of hydrogen = \(\frac{\text{mass of hydrogen}}{\text{molar mass of }\mathrm{H}_{2}\mathrm{O}_{2}}\) × 100% = \(\frac{2}{34}\times100\% \approx 5.88\%\)

Step 3: Calculate the mass percent of oxygen

Next, we calculate the mass percent of oxygen (O). The mass of 2 moles of oxygen in the molecule is: Mass of oxygen = 2 × 16 = 32 g Now, determine the mass percentage of oxygen: Mass percent of oxygen = \(\frac{\text{mass of oxygen}}{\text{molar mass of }\mathrm{H}_{2}\mathrm{O}_{2}}\) × 100% = \(\frac{32}{34}\times100\% \approx 94.12\%\) So, the mass percent of hydrogen and oxygen in hydrogen peroxide (\(\mathrm{H}_{2}\mathrm{O}_{2}\)) are approximately 5.88% and 94.12%, respectively.

Key Concepts

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry that relates to the mass of one mole of a substance. Simply put, it tells us how much one mole of that substance weighs, in grams per mole (g/mol). To determine molar mass, you need to know the atomic weights of the elements involved.

• The periodic table provides the atomic weights: hydrogen (H) is approximately 1 g/mol, and oxygen (O) is about 16 g/mol.
• For compounds, molar mass is the sum of the atomic masses of all atoms present in a molecule.

In this exercise, the molar mass of hydrogen peroxide (\(\mathrm{H}_{2}\mathrm{O}_{2}\)) was found by adding the atomic masses of its components: two hydrogen atoms and two oxygen atoms. Calculations go as follows: \(2 \times 1 + 2 \times 16 = 34\,\text{g/mol}\). This results in a molar mass of 34 g/mol for hydrogen peroxide.

Exploring Hydrogen Peroxide

Hydrogen peroxide is a simple compound with a chemical formula of \(\mathrm{H}_{2}\mathrm{O}_{2}\). It's well-known for its antiseptic properties and is commonly used for cleaning wounds.

• This compound consists of two hydrogen atoms and two oxygen atoms.
• It's a pale blue liquid in its pure form, but often appears colorless.
• It's readily miscible with water due to its similar hydrogen bonding capacity.

In practical contexts, hydrogen peroxide serves a variety of roles, from a disinfectant in households to a bleaching agent. Understanding the basic composition helps illuminate why it's effective in these roles.

Introduction to Elemental Analysis

Elemental analysis is a crucial technique in chemistry, allowing us to determine the elemental composition of a compound. It's the quantitative breakdown of a compound's constituents. Through this process, we identify the proportion of each element by mass.

• The analysis often uses techniques like mass spectrometry or combustion analysis.
• Mass percent composition, as calculated here, provides insight into the distribution of elements within a compound.

In this exercise, elemental analysis was demonstrated by finding the mass percent of hydrogen and oxygen in hydrogen peroxide. By knowing the mass of each element and the total molar mass, one can determine the contribution of each element to the whole.

Chemical Formulas Explained

Chemical formulas are symbolic representations of the elements in a compound and show the ratio of these elements. They serve as a fundamental tool for chemists to convey information concisely.

• Subscripts in a chemical formula denote the number of atoms of each element in a molecule.
• For example, \(\mathrm{H}_{2}\mathrm{O}_{2}\) indicates two hydrogen atoms and two oxygen atoms per molecule.
• These formulas are instrumental in chemical equations, stoichiometry, and understanding reactions.

In practical applications, knowing the chemical formula of a substance helps predict its behavior and reactivity. With \(\mathrm{H}_{2}\mathrm{O}_{2}\), such understanding is critical in both industrial uses and everyday applications.