Problem 5 - Chemistry in 30 days

Question

In an electrolysis of an aqueous solution of sodium sulphate, \(2.4 \mathrm{~L}\) of oxygen at STP was liberated at anode. The volume of hydrogen at STP liberated at cathode would be (a) \(1.2 \mathrm{~L}\) (b) \(2.4 \mathrm{~L}\) (c) \(2.6 \mathrm{~L}\) (d) \(4.8 \mathrm{~L}\)

Step-by-Step Solution

Answer

(d) 4.8 L

Step 1: Understand the Electrolysis Reaction

During the electrolysis of an aqueous sodium sulfate solution, water is electrolyzed, leading to the formation of hydrogen gas at the cathode and oxygen gas at the anode. The chemical reactions are:At the cathode: \[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \]At the anode: \[ 2H_2O \rightarrow O_2 + 4H^+ + 4e^- \]

Step 2: Apply the Stoichiometry for Volume Ratios

From the reactions, every 2 moles of water produces 1 mole of oxygen gas \((O_2)\) at the anode and 2 moles of hydrogen gas \((H_2)\) at the cathode. Therefore, the volume ratio of hydrogen to oxygen gas produced is 2:1 at STP.

Step 3: Calculate the Volume of Hydrogen Gas

Given that 2.4 L of oxygen gas is liberated at the anode, and knowing that the ratio of hydrogen to oxygen is 2:1, the volume of hydrogen gas liberated will be:\[ \text{Volume of } H_2 = 2 \times 2.4 = 4.8 \text{ L} \]

Step 4: Choose the Correct Option

Based on the calculation, the volume of hydrogen gas produced is 4.8 L, which corresponds to option (d).

Key Concepts

Aqueous Solution

An aqueous solution is one where water is the solvent. It is a medium in which substances dissolve to form solutions. In the context of electrolysis, an aqueous sodium sulfate solution is used. Here, sodium sulfate is the solute that dissolves in water, creating an environment conducive for electrolysis to occur.

• Water acts as a powerful solvent.
• Dissolved ions can move freely, allowing electrical conduction.

As electrolysis begins, water molecules break down into ions, facilitating the generation of gases at the electrodes. In an aqueous solution, the presence of water is crucial, as it's not just about the solute, but also how the solution behaves under electrical current.

Sodium Sulfate

Sodium sulfate ( ext{Na}_2 ext{SO}_4) serves as an inert electrolyte in the electrolysis process. It means it does not participate directly in the chemical reaction but aids in conducting electricity. Its major roles are:

• Enabling the flow of electric current through the solution.
• Helping stabilize the pH of the solution.

Sodium sulfate dissociates into sodium ( ext{Na}^+) and sulfate ( ext{SO}_4^{2-}) ions in water. These ions carry a charge allowing a path for electricity.
Its neutrality prevents interference with electrolysis, ensuring that the primary reactions involving water occur efficiently.

Stoichiometry

Stoichiometry is the study of the quantitative relationships or ratios between reactants and products in chemical reactions. In the context of electrolysis of sodium sulfate, stoichiometry helps to determine how much of each gas—hydrogen and oxygen—is produced. By analyzing the balanced chemical equations:

• Cathode: \[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \]
• Anode: \[ 2H_2O \rightarrow O_2 + 4H^+ + 4e^- \]
• Every 2 molecules of water produce 1 molecule of oxygen and 2 molecules of hydrogen.

This 2:1 ratio of hydrogen to oxygen is vital. Knowing the amount of oxygen produced allows us to use stoichiometry to accurately calculate the hydrogen generated.

Hydrogen and Oxygen Gas Production

Understanding the production of hydrogen and oxygen gases in electrolysis involves observing their behavior at electrodes. During electrolysis, the electrical current provides the energy needed to split water into hydrogen and oxygen gases.

• At the anode: Oxygen gas \[ (O_2) \] is liberated.
• At the cathode: Hydrogen gas \[ (H_2) \] is produced.

The balanced chemical reactions indicate that for every 2.4 L of oxygen gas produced at the anode, 4.8 L of hydrogen gas is produced at the cathode. This is due to water's composition and how its decomposition transpires under electrolysis. Understanding these processes ensures accurate predictions and calculations of gas volumes.