Question

A commercial sample of hydrogen peroxide is labeled as 10 volume, its percentage strength is: (a) \(1 \%\) (b) \(3 \%\) (c) \(10 \%\) (d) \(90 \%\)

Short answer

(b) 3%

Step-by-step solution

Understand the Problem

Hydrogen peroxide labeled as 10 volume means that 1 litre of hydrogen peroxide will release 10 litres of oxygen gas when it decomposes. We need to find the percentage strength of hydrogen peroxide corresponding to this property.

Relate Volume to Concentration

We use the fact that 1 mole of hydrogen peroxide, H₂O₂, decomposes to produce 0.5 moles of oxygen (O₂) gas. Under standard conditions, 1 mole of O₂ gas occupies 22.4 litres.

Calculate Moles of Oxygen Produced

Given that 10 litres of O₂ is produced, the number of moles of O₂ is determined by the ratio: \[\text{Moles of } O₂ = \frac{10}{22.4}\approx 0.446 \, \text{moles}\]

Relate Moles of Oxygen to Moles of Hydrogen Peroxide

Since 1 mole of H₂O₂ produces 0.5 moles of O₂, the moles of H₂O₂ needed corresponds to twice the amount of moles of O₂ produced:\[\text{Moles of } H₂O₂ = 2 \times 0.446\approx 0.892 \, \text{moles}\]

Convert Moles of H₂O₂ to Mass

The molar mass of hydrogen peroxide is approximately 34 g/mol. Thus, the mass of H₂O₂ corresponding to 0.892 moles is:\[\text{Mass of } H₂O₂ = 0.892 \times 34\approx 30.3 \, \text{grams}\]

Calculate the Percentage Strength

Percentage strength is defined as the mass of solute (H₂O₂) per 100 ml of solution. Assuming density is approximately 1 g/ml, 100 ml of solution corresponds to 100 g, hence:\[\text{Percentage Strength} = \frac{30.3}{100} \times 100ton\approx 3\%\]

Conclusion

The percentage strength of the hydrogen peroxide solution labeled as 10 volume is 3%. Therefore, the correct answer is (b) 3%.

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that relates the amount of substance to counted entities, like atoms, ions, or molecules. One mole contains exactly Avogadro's number of entities, approximately \(6.022 \times 10^{23}\) units. This concept simplifies dealing with vast quantities of tiny particles.

• The molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). For hydrogen peroxide (H₂O₂), its molar mass is calculated based on the atomic weights of hydrogen (H) and oxygen (O). With hydrogen having a molar mass of about 1 g/mol and oxygen 16 g/mol, H₂O₂ has a molar mass of approximately 34 g/mol.
• Understanding the mole concept allows us to convert between mass (in grams) and the number of moles, enabling calculations of reactants and products in chemical reactions.

In the context of the hydrogen peroxide problem, the mole concept enables us to convert available information into a meaningful calculation of the percentage strength, relating product volume to reactant quantity.

Volume Strength

Volume strength relates to the amount of a substance, particularly gases, generated from a given liquid volume. With regards to hydrogen peroxide, a label stating '10 volume' indicates that 1 liter of this solution releases 10 liters of oxygen gas upon decomposition.

• The volume strength serves as a measure of the oxidizing power of hydrogen peroxide. The higher the volume, the more oxygen the solution is capable of producing.
• This measure applies well to hydrogen peroxide since it decomposes to produce oxygen gas, which can be directly measured. For example, 10 volume hydrogen peroxide indicates that it can release significant oxygen, which is impractical to measure solely by mass but is straightforward when using volume strength.

Volume strength provides a practical understanding of the solution's concentration in a manner that aligns with its practical application and effectiveness.

Percentage Composition

Percentage composition expresses the concentration of a solution in terms of the percentage of a solute in the solution. When applied to hydrogen peroxide, it communicates the relative mass of hydrogen peroxide in a given amount of the solution.

• Given the molar mass of hydrogen peroxide is 34 g/mol, converting moles to mass helps calculate the percentage strength by determining how much hydrogen peroxide is in a standard volume like 100 mL.
• In solving our exercise: the solution's percentage composition relates to the mass per volume, where 3% implies there are 3 grams of hydrogen peroxide per 100 mL of solution.
• The percentage strength is a direct conversion of its mass compared to the entire solution's weight, assuming density approximates the density of water. This assumption is particularly important in calculating solutions where precision is essential since volume density directly affects the calculation accuracy.

Effective communication of concentration via percentage strength gives a clear sense of the reactive capability of a substance, necessary for understanding chemical properties and safe handling guidelines.

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It ensures that calculations based on the mole concept are extended to predict how substances interact in a chemical process.

• In the decomposition of hydrogen peroxide, stoichiometry helps determine how much oxygen gas is produced from a given amount of hydrogen peroxide.
• The relationship between moles of reactants and products follows the balanced chemical equation. For hydrogen peroxide, \(2\) moles decompose to form \(1\) mole of oxygen gas and \(2\) moles of water. The relationship reflects that half a mole of oxygen gas will arise per mole of hydrogen peroxide decomposed.
• Stoichiometry's utility extends beyond simple reactions; it is vital for predicting the quantity and behavior of products and determining the efficient use of materials in industrial or laboratory settings.

Through stoichiometry, you calculate how a given amount of a substance will fully react or what quantity of products will form, playing a crucial role in the predictive aspect of chemical reactions.