Problem 45 - Chemistry and Chemical Reactivity

Question

An aqueous solution of KBr is placed in a beaker with two inert platinum electrodes. When the cell is attached to an external source of electrical energy, electrolysis occurs. (a) Hydrogen gas and hydroxide ion form at the cathode Write an equation for the halfreaction that occurs at this electrode. (b) Bromine is the primary product at the anode. Write an equation for its formation.

Step-by-Step Solution

Answer

(a) \( 2H_2O(l) + 2e^- \rightarrow H_2(g) + 2OH^-(aq) \); (b) \( 2Br^-(aq) \rightarrow Br_2(l) + 2e^- \).

Step 1: Understand the Concept of Electrolysis

Electrolysis is a process where electrical energy is used to drive a non-spontaneous chemical reaction. In an aqueous solution containing KBr, the electrolyte dissociates into K⁺ and Br⁻ ions, and water can also undergo electrolysis to produce H⁺ and OH⁻ ions.

Step 2: Identify the Cathode Reaction

The cathode is the site where reduction occurs. In the presence of H₂O and considering standard reduction potentials, water is more likely to be reduced than K⁺ ions. Thus, at the cathode, water is reduced to produce hydrogen gas and hydroxide ions. The half-reaction at the cathode is: \[ 2H_2O(l) + 2e^- \rightarrow H_2(g) + 2OH^-(aq) \]

Step 3: Identify the Anode Reaction

The anode is where oxidation occurs. For an aqueous solution containing bromide ions, the Br⁻ ions are oxidized to bromine molecules. The half-reaction at the anode is: \[ 2Br^-(aq) \rightarrow Br_2(l) + 2e^- \]

Step 4: Combine Half-Reactions for Full Understanding

By combining the half-reactions, we can understand the full process that occurs in the electrolytic cell. At the cathode, water is reduced to hydrogen gas and hydroxide ions, and at the anode, bromide ions are oxidized to bromine. However, the question only requires the separate half-reactions identified in steps 2 and 3.

Key Concepts

Cathode reaction

In electrolysis, the **cathode** is the electrode where **reduction** occurs. During the electrolysis of an aqueous solution of KBr, you'll find that the substances susceptible to reduction are the cations in the solution and water itself. Since water has a more favorable reduction potential compared to potassium ions (K⁺), it undergoes reduction at the cathode.

The half-reaction for this reduction process is:
\[ 2H_2O(l) + 2e^- \rightarrow H_2(g) + 2OH^-(aq) \]
This equation shows how two molecules of water gain electrons to form hydrogen gas (H₂) and hydroxide ions (OH⁻). Notice that:

• Hydrogen gas is produced as a byproduct and can be observed as bubbles forming on the electrode.
• Hydroxide ions increase the solution's alkalinity near the cathode.

Understanding this reaction helps explain why a substance undergoes reduction and what products you can expect at the cathode in an electrolytic cell.

Anode reaction

The **anode** is the electrode where **oxidation** takes place in an electrolysis process. For the aqueous solution of KBr, the anode reaction involves the oxidation of bromide ions (Br⁻). The reason bromide ions oxidize at the anode rather than water or other ions is due to their oxidation potential.

The oxidation half-reaction at the anode is:
\[ 2Br^-(aq) \rightarrow Br_2(l) + 2e^- \]
This reaction illustrates how bromide ions lose electrons to form bromine (Br₂). Key points to note include:

• Bromine forms as a dark, reddish-brown liquid, which might be observed at the anode.
• Electrons produced in this reaction travel through the external circuit towards the cathode.

By understanding the anode reaction, you can predict the main products and appreciate the electron transfer process in the electrolytic cell.

Reduction and oxidation reactions

In electrolysis, understanding **reduction** and **oxidation** reactions is crucial for predicting the behavior of the solutions and the nature of the electrode products. Reduction and oxidation are two halves of the same cell reaction, often abbreviated as REDOX reactions.

**Reduction**:

• Involves the gain of electrons by an ion or molecule.
• Occurs at the cathode in an electrolytic cell.
• For our KBr solution, the water molecules undergo reduction forming hydrogen gas and hydroxide ions.

**Oxidation**:

• Involves the loss of electrons by an ion or molecule.
• Occurs at the anode in an electrolytic cell.
• For the KBr solution, bromide ions undergo oxidation to form bromine.

In conclusion, examining the respective reduction and oxidation half-reactions gives a complete picture of the chemical changes occurring in an electrolysis process. Understanding these concepts not only covers specific reactions in exercises but also provides insight into the general principles governing electrolytic cells.