Problem 32 - A Complete Resource Book in Chemistry for JEE Main

Question

On electrolysis of acidified water, if volume of hydrogen liberated is \(5.6 \mathrm{~cm}^{3}\), then the volume of oxygen liberated equal to (a) \(1.4 \mathrm{~cm}^{3}\) (b) \(2.8 \mathrm{~cm}^{3}\) (c) \(8.2 \mathrm{~cm}^{3}\) (d) \(5.6 \mathrm{~cm}^{3}\)

Step-by-Step Solution

Answer

The volume of oxygen liberated is \(2.8 \mathrm{~cm}^3\).

Step 1: Understanding the Reaction

During the electrolysis of acidified water, water (\(H_2O\)) decomposes into hydrogen gas (\(H_2\)) and oxygen gas (\(O_2\)). The balanced chemical reaction is given by:\[ 2 H_2O \rightarrow 2 H_2 + O_2 \]This equation tells us that 2 volumes of hydrogen gas are produced for every 1 volume of oxygen gas.

Step 2: Applying the Volume Ratio

From the balanced equation, the ratio of the volumes of hydrogen and oxygen produced is 2:1. This means that for every volume of oxygen produced, there are twice as many volumes of hydrogen produced.

Step 3: Calculating the Volume of Oxygen

Given that the volume of hydrogen liberated is \(5.6 \mathrm{~cm}^3\), we use the 2:1 ratio to calculate the volume of oxygen:\[ \text{Volume of } O_2 = \frac{\text{Volume of } H_2}{2} = \frac{5.6}{2} = 2.8 \mathrm{~cm}^3\]

Step 4: Conclusion

Since the calculated volume of oxygen is \(2.8 \mathrm{~cm}^3\), option (b) is the correct answer.

Key Concepts

Balanced Chemical Equation

The process of electrolysis of water involves breaking down water molecules into oxygen and hydrogen gas. To understand this, a balanced chemical equation is crucial:\[ 2 H_2O \rightarrow 2 H_2 + O_2 \]This equation represents the law of conservation of mass, where the number of atoms for each element is the same on both sides. We have 4 hydrogens and 2 oxygens on each side of the equation. When breaking down water using electrolysis, it produces exactly these proportions of hydrogen and oxygen gas.

Volume Ratio

A key aspect of electrolysis of water is the volume ratio given by the balanced chemical equation. From the equation \(2 H_2O \rightarrow 2 H_2 + O_2\), we can see the volume ratio of the gases produced:

• 2 volumes of hydrogen gas \(H_2\)
• 1 volume of oxygen gas \(O_2\)

This means that for every 2 volumes of hydrogen produced, exactly 1 volume of oxygen is generated. This ratio is crucial for calculations involving the volumes of gases involved, regardless of the units used.

Liberation of Gases

During electrolysis, water splits into its component gases, hydrogen \(H_2\) and oxygen \(O_2\). The term "liberation of gases" refers to this release process where these gases are collected separately at the electrodes:

• Hydrogen gas collects at the cathode (negative electrode).
• Oxygen gas gathers at the anode (positive electrode).

This process is accomplished by applying electrical energy which facilitates the decomposition of water. The gases are liberated in the fixed ratio specified by the balanced chemical equation.

Stoichiometry

Stoichiometry is the calculation method used to understand the quantitative aspects of chemical reactions. In the electrolysis of water, stoichiometry allows us to determine the precise amounts of products formed from a given amount of reactants. By using the balanced equation:\[ 2 H_2O \rightarrow 2 H_2 + O_2 \]we apply the concept of moles to predict the volume of gases produced. For example, knowing 5.6 cm³ of hydrogen gas is produced, stoichiometry helps us calculate the corresponding volume of oxygen gas by using the 2:1 volume ratio.

Oxygen and Hydrogen Gas

Electrolysis of water primarily yields two gases: oxygen and hydrogen. These gases have distinct roles and properties:

• Hydrogen Gas \(H_2\): Flammable and often used as a clean energy source. It is the gas that forms in higher volumes during electrolysis.
• Oxygen Gas \(O_2\): Supports combustion, and is essential for respiration in many living organisms. It forms in smaller volumes but is equally essential.

Understanding the behavior and applications of these gases can provide insights into environmental and energy solutions. This simple setup of electrolysis demonstrates the basic principles of chemical gas production.