Problem 70 - Chemistry Matter and Change

Question

Space Travel The space shuttle uses a \(\mathrm{H}_{2} / \mathrm{O}_{2}\) fuel cell to produce electricity. a. What is the reaction at the anode? At the cathode? b. What is the standard cell potential for the fuel cell?

Step-by-Step Solution

Answer

The half-reactions in a hydrogen-oxygen fuel cell are: Anode: \(2H_2 \rightarrow 4H^+ + 4e^-\) Cathode: \(O_2 + 4e^- \rightarrow 2O^{2-}\). The overall reaction is: \(2H_2 + O_2 \rightarrow 4H_2O\). The standard cell potential for the fuel cell is 1.23 V.

Step 1: Identify Half-Reactions

In a hydrogen-oxygen fuel cell, hydrogen gas (\(H_2\)) is oxidized at the anode and oxygen gas (\(O_2\)) is reduced at the cathode. Thus, the half-reactions are as follows: Anode: \(H_2 \rightarrow 2H^+ + 2e^-\) Cathode: \(O_2 + 4e^- \rightarrow 2O^{2-}\)

Step 2: Determine the Overall Reaction

To find the overall reaction, we will combine the half-reactions from Step 1. First, we need to balance the number of electrons in both half-reactions. The anode reaction produces 2 electrons and the cathode reaction consumes 4 electrons, so we need to multiply the anode reaction by 2: Anode: \(2H_2 \rightarrow 4H^+ + 4e^-\) Now we can combine the two balanced half-reactions: Overall Reaction: \(2H_2 + O_2 \rightarrow 4H^+ + 4e^- + 4e^- + 2O^{2-}\) Simplifying, we get: Overall Reaction : \(2H_2 + O_2 \rightarrow 4H_2O\)

Step 3: Calculate the Standard Cell Potential

To calculate the standard cell potential for the fuel cell, we will use the standard reduction potentials for the half-reactions as follows: Standard cell potential = Cathode's standard reduction potential - Anode's standard reduction potential The standard reduction potential for hydrogen is 0 V, and the standard reduction potential for oxygen is 1.23 V. Thus, we have: Standard cell potential = \(1.23 \,V - 0\,V = 1.23 \,V\) So, the standard cell potential of a hydrogen-oxygen fuel cell is 1.23 V.

Key Concepts

Electrode Reactions

In a hydrogen-oxygen fuel cell, the processes occurring at the electrodes are crucial for generating electricity. At the anode, hydrogen gas (H_2) undergoes oxidation. This means that hydrogen loses electrons, which are then used to produce electricity. The specific half-reaction happening at the anode is:
\[H_2 \rightarrow 2H^+ + 2e^-\]
This oxidation process releases electrons.
On the other hand, at the cathode, oxygen gas (O_2) undergoes a reduction reaction. Here, oxygen gains electrons to form water. The reduction half-reaction is written as:
\[O_2 + 4e^- \rightarrow 2O^{2-}\]
This reduction process consumes the electrons generated at the anode.
To sum it up:

• The anode is the site of oxidation, releasing electrons.
• The cathode is where reduction happens, consuming electrons.

The two half-reactions are combined to get the overall cell reaction which takes part in generating electrical power.

Standard Cell Potential

When assessing any cell, including the hydrogen-oxygen fuel cell, it's vital to understand the 'standard cell potential.' This potential indicates how much energy can be generated by the cell. The standard cell potential (E^°_{cell}) is calculated by using the standard potential values of the reactions occurring at both the cathode and the anode.
For the hydrogen-oxygen fuel cell:

• The standard reduction potential at the cathode is 1.23 V (for oxygen).
• The standard reduction potential at the anode is 0 V (for hydrogen since it is set as the reference point).

The formula to calculate the standard cell potential is:
\[E^°_{cell} = E^°_{cathode} - E^°_{anode} \]Plugging the values into the formula:
\[ E^°_{cell} = 1.23 \, V - 0 \, V \]
Thus, the standard cell potential (E^°_{cell}) of the hydrogen-oxygen fuel cell is 1.23 V. This means the cell can theoretically produce 1.23 volts of electrical potential under standard conditions.

Oxidation and Reduction Reactions

Oxidation and reduction reactions, often known collectively as redox reactions, are central to the workings of a hydrogen-oxygen fuel cell.
These reactions transfer electrons from one molecule to another, which is what allows the fuel cell to produce electricity.
**Oxidation:**
Occurs at the anode where hydrogen gas (H_2) loses electrons. The equation characterizing this is:
\[H_2 \rightarrow 2H^+ + 2e^-\]
Through oxidation, hydrogen is transformed into protons and electrons, which are then free to migrate through the cell to produce power.
**Reduction:**
Takes place at the cathode, where oxygen (O_2) gains electrons. This reduction process completes the redox reaction and results in the formation of water:
\[O_2 + 4e^- \rightarrow 2O^{2-}\]
Water is produced as a byproduct in the cathode.
Overall, in a fuel cell, these redox reactions result in the continuous flow of electrons through an external circuit, which is how electricity is generated effectively. Ensuring these reactions are balanced is key to the efficiency of the cell.