Problem 91 - A Complete Resource Book in Chemistry for JEE Main

Question

During the decomposition of \(\mathrm{H}_{2} \mathrm{O}_{2}\) to give oxygen, \(48 \mathrm{~g} \mathrm{O}_{2}\) is formed per minute at a certain point of time. The rate of formation of water at this point is (a) \(0.75 \mathrm{~mol} \min ^{1}\) (b) \(1.5 \mathrm{~mol} \mathrm{~min}^{-1}\) (c) \(2.25 \mathrm{~mol} \mathrm{~min}^{-1}\) (d) \(3.0 \mathrm{~mol} \mathrm{~min}^{-1}\)

Step-by-Step Solution

Answer

(d) 3.0 \( \mathrm{~mol} \mathrm{~min}^{-1} \)

Step 1: Understand the Chemical Reaction

The decomposition of hydrogen peroxide is represented by the chemical reaction: \( 2\, \text{H}_2\text{O}_2 (aq) \rightarrow 2\, \text{H}_2\text{O} (l) + \text{O}_2 (g) \). This shows that 2 moles of \(\text{H}_2\text{O}_2\) produce 1 mole of \(\text{O}_2\).

Step 2: Calculate the Moles of Oxygen Formed

We are given that \(48\, \text{g}\) of \(\text{O}_2\) is formed per minute. The molar mass of \(\text{O}_2\) is \(32\, \text{g/mol}\). Therefore, the moles of \(\text{O}_2\) formed per minute is calculated as follows: \[ \frac{48\, \text{g}}{32\, \text{g/mol}} = 1.5\, \text{mol/min}. \]

Step 3: Determine the Moles of Water Formed

According to the balanced chemical equation, for every 1 mole of \(\text{O}_2\) produced, 2 moles of \(\text{H}_2\text{O}\) are formed. Since \(1.5\, \text{mol/min}\) of \(\text{O}_2\) is produced, the moles of \(\text{H}_2\text{O}\) formed is twice that amount, which is \(2 \times 1.5 = 3.0\, \text{mol/min}.\)

Key Concepts

Hydrogen Peroxide

Hydrogen peroxide (\(\text{H}_2\text{O}_2\)) is a remarkable chemical compound, known for its role as a disinfectant and bleaching agent. It is a pale blue liquid in its pure form, slightly more viscous than water. Hydrogen peroxide naturally decomposes into water (\(\text{H}_2\text{O}\)) and oxygen (\(\text{O}_2\)), a process that can be hastened by catalysts.

• Chemical Formula: \(\mathrm{H}_{2} \mathrm{O}_{2}\) signifies it has 2 hydrogen atoms and 2 oxygen atoms.
• Decomposition Reaction: It breaks down into water and oxygen, releasing oxygen gas.
• Common Uses: Besides disinfection, it’s used in cosmetic applications and as a rocket propellant.

Despite its usefulness, hydrogen peroxide must be handled carefully as it can be corrosive in higher concentrations. Understanding its decomposition is crucial for practical uses like cleaning and hygiene.

Rate of Reaction

The rate of reaction refers to how quickly or slowly reactants are converted into products in a chemical reaction. In our scenario, it pertains to how fast hydrogen peroxide decomposes to produce oxygen and water.
Chemical reactions take place at various speeds, and knowing the rate is essential for predicting how long a process will take. Factors influencing the rate include:

• Concentration of Reactants: Higher concentrations generally increase reaction rates.
• Temperature: Raising the temperature usually speeds up reactions as it provides more energy for collisions.
• Catalysts: Substances that increase the rate without being consumed, like manganese dioxide for hydrogen peroxide.

Considering these factors, during the decomposition of hydrogen peroxide, the rate is typically measured in the formation of products per unit time, such as moles of oxygen produced per minute.

Stoichiometry

Stoichiometry is a branch of chemistry focusing on the quantitative relationships of elements and compounds during chemical reactions. It uses balanced chemical equations to determine the proportions of reactants needed and products formed.
In the decomposition of hydrogen peroxide, the stoichiometry is outlined by this balanced equation: 2\(\text{H}_2\text{O}_2\) (aq) \(\rightarrow\) 2\(\text{H}_2\text{O}\) (l) + \(\text{O}_2\) (g).This tells us:

• 2 moles of \(\text{H}_2\text{O}_2\) decompose to form 1 mole of \(\text{O}_2\) and 2 moles of \(\text{H}_2\text{O}\).
• From this, you determine that if 1.5 moles of \(\text{O}_2\) are produced each minute, then 3 moles of \(\text{H}_2\text{O}\) will also be produced every minute.

Stoichiometry helps in scaling reactions safely and effectively, whether in laboratories or industrial settings.

Oxygen Formation

Oxygen formation during the decomposition of hydrogen peroxide is a key outcome of the reaction. The process can be visualized as \(\text{H}_2\text{O}_2\) breaking apart into components that form water and release oxygen gas.
Here’s why understanding oxygen formation is important:

• Safety and Monitoring: Ensuring controlled oxygen production is crucial. Sudden releases can be dangerous if not managed correctly.
• Applications: This reaction is harnessed in various industries, from water treatment to rocket propulsion, for the pure oxygen it releases.
• Environmental Impact: Oxygen produced in situ (at the point of use) minimizes the need for large-scale oxygen storage.

In practice, knowing how much oxygen is produced allows us to optimize conditions and enhance efficiency, ensuring that reactions occur as desired without unwanted side effects.