Problem 9 - Chemistry in 30 days

Question

How many faradays are required to reduce 1 mol of \(\mathrm{BrO}_{3}^{-}\)to \(\mathrm{Br}^{-}\)? (b) 5 (c) 6 (d) 4 (a) 3

Step-by-Step Solution

Answer

6 faradays are required, corresponding to option (c).

Step 1: Identify the Half-Reaction

First, we need to write the reduction half-reaction for the decrease of \( \mathrm{BrO}_3^- \) to \( \mathrm{Br}^- \). That reaction is: \[ \mathrm{BrO}_3^- + 6\mathrm{e}^- + 6\mathrm{H}^+ \rightarrow \mathrm{Br}^- + 3\mathrm{H}_2\mathrm{O} \]. This shows that the \( \mathrm{BrO}_3^- \) ion gains 6 electrons in this process.

Step 2: Calculate Faradays Required

One faraday is the charge of one mole of electrons, which is approximately equal to 96,485 coulombs. Since the reaction involves 6 moles of electrons to reduce 1 mole of \( \mathrm{BrO}_3^- \) to \( \mathrm{Br}^- \), we need 6 faradays for 1 mole of \( \mathrm{BrO}_3^- \).

Step 3: Confirm the Answer Choice

Verify which of the given options corresponds to the calculation. Given that 6 faradays are required, the options examined previously indicate that the correct choice is (c) 6.

Key Concepts

Understanding Half-Reactions

In electrochemistry, half-reactions are essential in breaking down redox reactions into two parts: oxidation and reduction. When analyzing a reduction scenario, like in the problem where bromate ions are reduced to bromide ions, it's crucial to understand that a half-reaction only considers one process. Here, the reduction half-reaction refers to the part where a species gains electrons. For example, the half-reaction for this exercise is:

• \( \mathrm{BrO}_3^- + 6\mathrm{e}^- + 6\mathrm{H}^+ \rightarrow \mathrm{Br}^- + 3\mathrm{H}_2\mathrm{O} \)

This half-reaction indicates that the bromate ion gains six electrons, showing a focus strictly on the reduction process without considering oxidation. This separation simplifies analyzing and calculating changes during electrochemical reactions.

Exploring the Reduction Process

The term "reduction" in chemistry refers to a gain of electrons by a molecule, atom, or ion. In a reduction process, electrons are added, which decreases the oxidation state. This is the opposite of oxidation, where electrons are lost. In the given exercise, the bromate ion \( \mathrm{BrO}_3^- \) undergoes reduction to form bromide ion \( \mathrm{Br}^- \). During this process, the molecule gains a total of 6 electrons:

• The reaction: \( \mathrm{BrO}_3^- + 6\mathrm{e}^- + 6\mathrm{H}^+ \rightarrow \mathrm{Br}^- + 3\mathrm{H}_2\mathrm{O} \) demonstrates the addition of these electrons.

This transaction is key to understanding how a substance can change form and charge by incorporating electrons.

Calculating Moles of Electrons

Moles of electrons are a significant concept when dealing with electrochemical reactions. Since electrons are the carriers of charge within these reactions, calculating the number of moles involved is crucial. In the reduction of \( \mathrm{BrO}_3^- \) to \( \mathrm{Br}^- \), the problem states that 6 moles of electrons are necessary. This means:

• To transform 1 mole of \( \mathrm{BrO}_3^- \) to 1 mole of \( \mathrm{Br}^- \), exactly 6 moles of electrons need to be transferred.
• This number directly correlates with the charge amount in electrochemical terms.

By understanding moles of electrons, students can better predict and balance redox reactions, thus bridging the gap between chemical reactions and electric charge flow.

The Core of Electrochemistry

Electrochemistry is the field of chemistry that studies the interaction between electrical energy and chemical changes. It combines the principles of electricity and chemistry to explain processes like electrolysis, where electrical energy drives a chemical reaction. Faraday's Law of Electrolysis is fundamental here, linking electrical charge to the movement of ions and electrons:

• In our exercise, 1 faraday corresponds to the transfer of 1 mole of electrons, about 96,485 coulombs of electric charge.
• Thus, reducing 1 mole of \( \mathrm{BrO}_3^- \) to \( \mathrm{Br}^- \) requires 6 faradays, reflecting 6 moles of electrons.

Each of these elements describes how reactions occur under the influence of electric currents, providing a physical picture of how matter changes during these interactions.