Problem 42 - Chemistry and Chemical Reactivity

Question

An aqueous solution of \(\mathrm{Na}_{2} \mathrm{S}\) is placed in a beaker with two inert platinum electrodes. When the cell is attached to an external battery, electrolysis occurs. (a) Hydrogen gas and hydroxide ion form at the cathode. Write an equation for the half-reaction that occurs at this electrode. (b) Sulfur is the primary product at the anode. Write an equation for its formation.

Step-by-Step Solution

Answer

At the cathode: \(2\mathrm{H}_2\mathrm{O} + 2e^- \rightarrow \mathrm{H}_2 + 2\mathrm{OH}^-\); at the anode: \(\mathrm{S}^{2-} \rightarrow \mathrm{S} + 2e^-\).

Step 1: Identify the Reactions at the Cathode

In an electrolytic cell, reduction occurs at the cathode. We know that hydrogen gas formation involves the reduction of protons or water. In an aqueous solution of \( \mathrm{Na}_{2} \mathrm{S} \), water is reduced to form hydrogen gas \((\mathrm{H}_{2})\) and hydroxide ions \((\mathrm{OH}^- )\). The half-reaction is given by the reduction of water: \[\text{Cathode: } 2\mathrm{H}_2\mathrm{O} + 2e^- \rightarrow \mathrm{H}_2 + 2\mathrm{OH}^-.\]

Step 2: Identify the Reactions at the Anode

At the anode, oxidation takes place. Considering that the primary product is sulfur, the oxidation of sulfide ions \((\mathrm{S}^{2-})\) to sulfur \((\mathrm{S})\) occurs. The half-reaction for this process is: \[\text{Anode: } \mathrm{S}^{2-} \rightarrow \mathrm{S} + 2e^-.\]

Step 3: Summarize the Reactions

To summarize, at the cathode, water is reduced to produce hydrogen gas and hydroxide ions, while at the anode, sulfide ions are oxidized to form sulfur. The overall reactions showcase the transformation of reactants through electrolysis into different products at both electrodes.

Key Concepts

Cathode Reaction

When examining electrolysis, it's essential to understand cathode reactions. The cathode is where reduction occurs, meaning it's where electrons are gained by the substances.In the case of an aqueous solution of \(\mathrm{Na}_2\mathrm{S}\), water at the cathode gets reduced. This means water molecules gain electrons to form hydrogen gas (\(\mathrm{H}_2\)) and hydroxide ions (\(\mathrm{OH}^-\)). This reaction can be represented by the equation \[2\mathrm{H}_2\mathrm{O} + 2e^- \rightarrow \mathrm{H}_2 + 2\mathrm{OH}^-\].

• Reduction: Gaining of electrons.
• Cathode: Site of reduction in an electrochemical cell.

Here, it's crucial to see how electrons provided by an external battery assist in the transformation of water into new substances.

Anode Reaction

Anode reactions are fundamental in understanding oxidation processes in electrolysis. The anode is where oxidation happens, meaning substances lose electrons.In our exercise, the aqueous solution's anode involves sulfide ions (\(\mathrm{S}^{2-}\)). These ions lose electrons to form sulfur. This oxidative process is expressed in the equation \[\mathrm{S}^{2-} \rightarrow \mathrm{S} + 2e^-\].

• Oxidation: Loss of electrons.
• Anode: Site of oxidation in an electrochemical cell.

Recognizing this shift in the electron count helps explain how sulfide ions convert into sulfur during electrolysis.

Aqueous Solution

An aqueous solution is simply any solution where water is the solvent. This is a critical environment for electrochemical reactions as it allows electrolytes to dissociate into ions.In the given scenario, sodium sulfide (\(\mathrm{Na}_2\mathrm{S}\)) dissolves in water, leading to the production of sodium ions (\(\mathrm{Na}^+\)) and sulfide ions (\(\mathrm{S}^{2-}\)). This ionization prepares these constituents for further reactions during electrolysis.

• Solvent: Water in aqueous solutions.
• Ions: Essential participants in conducting electricity in the solution.

Understanding the aqueous base is critical since it sets the stage for the reactions at the electrodes.

Reduction and Oxidation

Reduction and oxidation, commonly referred to as redox reactions, are the heart of electrolysis. They describe processes where electrons are gained (reduction) and lost (oxidation).
In electrolysis, these reactions occur concurrently. The cathode's reaction involves reduction, seen where water turns into hydrogen gas and hydroxide ions. Conversely, at the anode, oxidation is observed when sulfide converts to sulfur.

• Redox: A term combining reduction and oxidation processes.
• Electron transfer: Central to both processes.

Understanding redox reactions allows us to decode the changes at the anode and cathode during electrolysis.

Electrochemical Cell

An electrochemical cell is a core component in electrolysis, acting as a system that drives the redox processes through electric energy.
In our exercise, an external power source supplies electrons to the system, allowing the cathode to facilitate reduction and the anode to conduct oxidation.

• Power Source: Needed for electron flow and electrochemical reactions.
• Electrodes: Catalysts for reduction and oxidation.

By understanding the electrochemical cell setup, we gain insights into how external energy influences the chemical transformations, powering the entire process.