Problem 44

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

Verified
Answer
Cathode: \( 2 ext{H}_2 ext{O}(l) + 2e^- \rightarrow ext{H}_2(g) + 2 ext{OH}^-(aq) \), Anode: \( ext{S}^{2-}(aq) \rightarrow ext{S}(s) + 2e^- \).
1Step 1: Identify Half-Reaction at the Cathode
During electrolysis, reduction occurs at the cathode. In the given scenario, hydrogen gas (\( ext{H}_2 \)) and hydroxide ion (\( ext{OH}^- \)) are formed from water. The half-reaction representing the reduction is:\[2 ext{H}_2 ext{O}(l) + 2e^- \rightarrow ext{H}_2(g) + 2 ext{OH}^-(aq)\]
2Step 2: Identify Half-Reaction at the Anode
In electrolysis, oxidation occurs at the anode. For sulfur to be the primary product, sulfide ions (\( ext{S}^{2-} \)) in solution are oxidized to sulfur. The half-reaction for this oxidation is:\[ ext{S}^{2-}(aq) \rightarrow ext{S}(s) + 2e^-\]

Key Concepts

Half-reactionCathode reactionAnode reactionHydrogen gas productionSulfur formation
Half-reaction
In electrolysis, understanding half-reactions is crucial.
These reactions occur at the electrodes and involve either the gain or loss of electrons.
Half-reactions are divided into two categories:
  • Reduction: Gain of electrons
  • Oxidation: Loss of electrons
In the given exercise, the half-reaction at the cathode involves the reduction of water to form hydrogen gas and hydroxide ions.
Meanwhile, at the anode, sulfide ions are oxidized to produce sulfur. Each of these half-reactions plays a pivotal role in the process of electrolysis.
Cathode reaction
The cathode is where reduction takes place.
In this exercise, water is reduced at the cathode, leading to the production of hydrogen gas and hydroxide ions:
\[2\text{H}_2\text{O}(l) + 2e^- \rightarrow \text{H}_2(g) + 2\text{OH}^-(aq)\]This equation shows the transformation of water molecules, with electrons being added (reduction), resulting in hydrogen gas bubbling out at the cathode.
It's important to remember that the cathode in electrolysis always involves a reduction process.
Anode reaction
At the anode, oxidation reactions occur.
In our scenario, sulfide ions in the solution get oxidized to form sulfur.
This reaction can be represented by the equation:
\[\text{S}^{2-}(aq) \rightarrow \text{S}(s) + 2e^-\]This indicates that sulfide ions lose electrons (oxidation), forming solid sulfur.
This is a key step in electrolysis that maintains the overall charge balance in the cell.
Hydrogen gas production
Hydrogen gas production during electrolysis is a straightforward process happening at the cathode.
The reduction of water leads to the formation of hydrogen gas, as illustrated by the half-reaction.
  • The hydrogen molecules (\(\text{H}_2\)) formed are released as gas bubbles.
  • This is a common method for producing hydrogen gas industrially.
Such reactions demonstrate how electrolysis can be used to decompose compounds into their basic elements.
Sulfur formation
Sulfur formation occurs at the anode where sulfide ions undergo oxidation.
This process results in the elementary formation of sulfur:
  • Sulfide ions (\(\text{S}^{2-}\)) release electrons to form sulfur solid (\(\text{S}\)).
  • This process is essential for industries that need elemental sulfur for various applications.
Through electrolysis, compounds can be broken down to produce valuable and useful substances.