Problem 5 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The volume strength of \(1 \mathrm{M} \mathrm{H}_{2} \mathrm{O}_{2}\) is : (Molar mass of \(\mathrm{H}_{2} \mathrm{O}_{2}=34 \mathrm{~g} \mathrm{~mol}^{-1}\) ) (a) \(5.6\) (b) \(16.8\) (c) \(11.35\) (d) \(22.4\)

Step-by-Step Solution

Answer

The volume strength is 11.2; none of the provided options exactly match.

Step 1: Understanding Volume Strength

The volume strength of hydrogen peroxide ( H₂O₂) solution refers to the volume of oxygen gas liberated at standard temperature and pressure (STP) by 1 liter of the hydrogen peroxide solution. It tells us how much oxygen is released when the solution decomposes.

Step 2: Decomposition Reaction of H₂O₂

The decomposition reaction of hydrogen peroxide is:\[2 \mathrm{H}_2\mathrm{O}_2 (aq) \rightarrow 2 \mathrm{H}_2\mathrm{O} (l) + \mathrm{O}_2 (g)\]From this reaction, 2 moles of H₂O₂ decompose to produce 1 mole of O₂ gas.

Step 3: Calculate Moles of H₂O₂ in 1 Liter

Since we have a 1 M solution, it means there is 1 mole of H₂O₂ in 1 liter of the solution.

Step 4: Calculate Moles of O₂ Liberated

According to the balanced equation, 2 moles of H₂O₂ produce 1 mole of O₂. Therefore, 1 mole of H₂O₂ will produce \( \frac{1}{2} \) mole of O₂.

Step 5: Calculate Volume of O₂ at STP

At STP, 1 mole of a gas occupies 22.4 liters. Therefore, \( \frac{1}{2} \) mole of O₂ occupies:\[\frac{1}{2} \times 22.4 = 11.2 \text{ liters}\]Hence, the volume strength of 1 M hydrogen peroxide is 11.2.

Key Concepts

Decomposition Reaction of Hydrogen Peroxide

The decomposition reaction of hydrogen peroxide is a straightforward process. In this reaction, hydrogen peroxide (\(\text{H}_2\text{O}_2\)) breaks down into water (\(\text{H}_2\text{O}\)) and oxygen gas (\(\text{O}_2\)). The balanced chemical equation for this reaction is:
\[2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2\]
This means that 2 moles of hydrogen peroxide decompose to produce 2 moles of water and 1 mole of oxygen gas. It is important to fully balance the equation to ensure the number of atoms is consistent on both sides.

• 1 mole of oxygen gas is generated from 2 moles of H₂O₂.
• The reaction is a fundamental example of a decomposition reaction, where a single compound breaks down into simpler substances.

Recognizing the stoichiometry of this reaction is crucial for understanding the volume strength of hydrogen peroxide.

Calculation of Moles

Understanding the concept of moles is key to chemistry. A mole is a unit that measures the amount of substance. One mole contains exactly 6.022 \(\times 10^{23}\) entities, be it atoms, molecules, or ions.

When dealing with a solution, the molarity indicates the number of moles of solute per liter of solution. For a 1 molar (\(1 \, \text{M}\)) hydrogen peroxide solution, this means:

• 1 mole of \(\text{H}_2\text{O}_2\) is present in 1 liter of solution.

Using the decomposition equation, \(2 \, \text{H}_2\text{O}_2 \rightarrow \text{O}_2\), we see that:

• 2 moles of \(\text{H}_2\text{O}_2\) produce 1 mole of \(\text{O}_2\)
• Therefore, 1 mole of \(\text{H}_2\text{O}_2\) will yield \(\frac{1}{2}\) a mole of \(\text{O}_2\)

Grasping how moles relate to the chemical reaction is essential for further calculations.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, abbreviated as STP, is a term in chemistry that provides a reference framework so that scientists can accurately compare different sets of data. It is defined as:

• Temperature: 0°C or 273.15 K
• Pressure: 1 atm or 101.325 kPa

Many gas laws and calculations, such as the volume of gases, are referenced to STP.
At STP conditions, 1 mole of a gas occupies 22.4 liters of volume. This relationship is important in our case because it allows us to determine the volume strength of hydrogen peroxide. For instance:

• If \(\frac{1}{2}\) mole of \(\text{O}_2\) is liberated, it will occupy a volume of:\[\frac{1}{2} \times 22.4 \text{ L} = 11.2 \text{ L}\]

This calculation provides insight into the practical implications of gas volume in reactions under standard conditions.

Molar Mass

Molar mass is a critical concept that links the mass of a substance to the amount of substance in moles. It is numerically equal to the average mass of one mole of a substance and is expressed in grams per mole (\(\text{g/mol}\)).
For hydrogen peroxide (\(\text{H}_2\text{O}_2\)), we calculate its molar mass as follows:

• Hydrogen (\(\text{H}\)) has an atomic mass of 1 gram/mole.
• Oxygen (\(\text{O}\)) has an atomic mass of 16 grams/mole.
• Thus, \(\text{H}_2\text{O}_2\) has a molar mass of 2(1) + 2(16) = 34 grams/mole.

Using the molar mass, one can convert the mass of a substance to moles and vice versa, an essential step in stoichiometric calculations. In the context of the volume strength of hydrogen peroxide, the molar mass helps quantify how much \(\text{H}_2\text{O}_2\) is present in a given solution, further assisting in calculating the oxygen generated.