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 cm³ (option b).

Step 1: Understand the Electrolysis Reaction

When water is electrolyzed, it breaks down into hydrogen and oxygen gases. The balanced chemical equation for the electrolysis of water is: \[2H_2O(l) \rightarrow 2H_2(g) + O_2(g)\]This means 2 moles of water produce 2 moles of hydrogen gas and 1 mole of oxygen gas.

Step 2: Determine the Volume Ratio

From the balanced chemical equation, notice that the ratio of hydrogen gas to oxygen gas by volume is 2:1. This is because 2 moles of hydrogen gas (\(H_2\)) are produced for every mole of oxygen gas (\(O_2\)).

Step 3: Apply the Ratio to Given Volumes

Given that the volume of hydrogen liberated is 5.6 cm³, apply the 2:1 ratio to find the volume of oxygen:Since \(V_{H_2} : V_{O_2} = 2 : 1\), the volume of oxygen gas \(V_{O_2}\) should be half that of hydrogen, i.e., \[V_{O_2} = \frac{5.6 \text{ cm}^3}{2} = 2.8 \text{ cm}^3\]

Step 4: Compare to Answer Choices

The calculated oxygen volume of 2.8 cm³ matches option (b). Thus, option (b) is the correct answer.

Key Concepts

Balanced Chemical Equation

The balanced chemical equation for the electrolysis of water is essential for understanding the reaction. During electrolysis, water (\(H_2O\) is decomposed into hydrogen gas (\(H_2\)) and oxygen gas (\(O_2\)). This is expressed in the balanced equation:
\[2H_2O(l) \rightarrow 2H_2(g) + O_2(g)\]
This equation shows us that two moles of water produce two moles of hydrogen and one mole of oxygen.

• The equation is balanced, meaning that the number of each type of atom is conserved on both sides of the equation.
• The coefficients (the numbers in front of molecules) indicate the ratio in which substances react or are produced.

Balancing helps us predict the amounts of products formed, such as the volumes of gases released during electrolysis.

Gas Volume Ratio

When analyzing the gas volume ratio, it's important to understand that gases occupy space according to their molar amounts when formed in reactions. The electrolysis of water produces gases that follow a specific volume ratio derived from the balanced chemical equation.
From the equation:
\[2H_2O(l) \rightarrow 2H_2(g) + O_2(g)\]
We see that for every two moles of hydrogen gas produced, one mole of oxygen gas is generated. This gives a hydrogen to oxygen gas volume ratio of 2:1.

• This ratio tells us that hydrogen gas will have twice the volume of oxygen for the same number of water molecules decomposed.
• When calculating volumes, ensure that conditions like temperature and pressure, usually considered, are constant.

This volume ratio is crucial in exercises to determine the amount of each gas released during electrolysis.

Electrolysis Reaction

Electrolysis is a fascinating electrochemical reaction where electrical energy is used to drive a chemical change—in this case, the decomposition of water into hydrogen and oxygen gases.

• An electric current is passed through water, usually with an electrolyte added to enhance conductivity, initiating a non-spontaneous reaction.
• In water electrolysis, positively charged ions move towards the cathode (negative electrode) where hydrogen gas is liberated, while negatively charged ions move towards the anode (positive electrode) where oxygen gas is produced.

This process is useful for producing gases in pure forms and illustrates how energy can be used to break chemical bonds. The practical result is two distinct gases from what was once just water. Understanding electrolysis helps in exploring how energy input can alter chemical bonds and provides insights into industrial gas production, energy storage, and conversion systems.