Question

The percentage weight of hydrogen in \(\mathrm{H}_{2} \mathrm{O}_{2}\) is: (a) \(6.50\) (b) \(5.88\) (c) 25 (d) 50

Short answer

The percentage of hydrogen in \( \text{H}_2\text{O}_2 \) is approximately \( 5.88\% \). The correct option is (b).

Step-by-step solution

Determine the Molecular Mass of H2O2

The molecular formula for hydrogen peroxide is \( \text{H}_2\text{O}_2 \). To find its molecular mass, we calculate the sum of the atomic masses:- Hydrogen (H) has an atomic mass of approximately \( 1.01 \) amu, so \( 2 \times 1.01 = 2.02 \) amu.- Oxygen (O) has an atomic mass of approximately \( 16.00 \) amu, so \( 2 \times 16.00 = 32.00 \) amu.Adding these together gives the total molecular mass of \( \text{H}_2\text{O}_2 \) as \( 2.02 + 32.00 = 34.02 \) amu.

Calculate the Total Mass of Hydrogen Atoms

Since \( \text{H}_2\text{O}_2 \) contains 2 hydrogen atoms, the total mass of the hydrogen atoms is \( 2 \times 1.01 = 2.02 \) amu.

Compute the Percentage by Mass of Hydrogen

Now, we calculate the percentage of the total mass that is due to hydrogen:\[\text{Percentage of Hydrogen} = \left( \frac{\text{Total Mass of Hydrogen}}{\text{Molecular Mass of } \text{H}_2\text{O}_2} \right) \times 100\]Substitute the known values:\[\text{Percentage of Hydrogen} = \left( \frac{2.02}{34.02} \right) \times 100 \approx 5.94\%\]

Compare to Given Options

The percentage we calculated for hydrogen is approximately \( 5.94\% \). The closest option provided in the question is \( 5.88\% \). Thus, the correct answer is \( (b) \ 5.88 \).

Key concepts

Molecular Mass Calculation

Understanding how to calculate molecular mass is an essential skill in chemistry, especially when dealing with compounds like hydrogen peroxide (\( \text{H}_2\text{O}_2 \)). Molecular mass is found by summing the atomic masses of all atoms present in a molecule. This means first knowing the atomic masses of each element involved. For instance, hydrogen has an atomic mass of approximately \( 1.01 \) atomic mass units (amu), and oxygen is approximately \( 16.00 \) amu.
For hydrogen peroxide, the molecular mass calculation involves:

• Two hydrogen atoms: \( 2 \times 1.01 = 2.02 \) amu.
• Two oxygen atoms: \( 2 \times 16.00 = 32.00 \) amu.

Adding these values provides the total molecular mass: \( 2.02 + 32.00 = 34.02 \) amu. This number represents the weight of one molecule of \( \text{H}_2\text{O}_2 \) when measured in atomic mass units. Such calculations help in determining the composition of compounds and are a foundation for further chemical analysis.

Atomic Mass

Atomic mass is a concept that denotes the mass of an atom expressed in atomic mass units (amu). It's essentially the sum of the number of protons and neutrons in an atom's nucleus. For specific molecules, like hydrogen peroxide (\( \text{H}_2\text{O}_2 \)), knowledge of atomic mass is crucial for calculating both molecular mass and percentage composition.
Here's a quick recap:

• Hydrogen: The atomic mass is around \( 1.01 \) amu. Since it has one proton and usually no neutrons, its atomic mass is slightly more than a single amu.
• Oxygen: A typical oxygen atom has an atomic mass of \( 16.00 \) amu, considering its eight protons and eight neutrons.

These values help chemists to calculate the total mass of molecules and understand their structures. For instance, to find out how much hydrogen contributes to hydrogen peroxide's total mass, we multiply its atomic mass by the number of hydrogen atoms in the molecule. This fundamental understanding aids in molecular comprehension and chemical reactions, where precision is essential.

Hydrogen Peroxide

Hydrogen peroxide (\(\text{H}_2\text{O}_2\)) is a simple molecule with diverse applications in both household and industrial contexts. Its composition includes two hydrogen atoms and two oxygen atoms, forming a clear, slightly more viscous liquid than water. Understanding its chemical makeup helps in leveraging its potential uses.
From a chemical perspective, hydrogen peroxide's decomposition reaction is interesting. It breaks down into water (\(\text{H}_2\text{O}\)) and oxygen (\(\text{O}_2\)), a reaction catalyzed by enzymes like catalase found in living organisms. This property is useful in various processes, such as disinfecting surfaces and bleaching hair.Knowing the percentage composition and molecular mass of \(\text{H}_2\text{O}_2\) is crucial for its storage and handling. As it is a strong oxidizer, care must be taken to avoid unwanted reactions. Its diverse uses, from cleaning to bleaching to rocket propellants, make an understanding of its basic chemistry highly valuable. Chemical reactions involving hydrogen peroxide often require accurate molecular and percentage calculations to ensure safety and efficacy.