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

Anode: \( \text{H}_2(g) \rightarrow 2\text{H}^+(aq) + 2e^- \), Cathode: \( \text{O}_2(g) + 4\text{H}^+(aq) + 4e^- \rightarrow 2\text{H}_2\text{O}(l) \). Cell potential: 1.23 V.

Step 1: Anode Reaction

In a hydrogen-oxygen fuel cell, hydrogen gas \( \text{H}_2 \) is oxidized at the anode. The chemical reaction is: \[ \text{H}_2(g) \rightarrow 2\text{H}^+(aq) + 2e^- \] This indicates that hydrogen gas splits into protons and electrons.

Step 2: Cathode Reaction

At the cathode, oxygen gas \( \text{O}_2 \) undergoes reduction. The chemical reaction is: \[ \text{O}_2(g) + 4\text{H}^+(aq) + 4e^- \rightarrow 2\text{H}_2\text{O}(l) \] This indicates that oxygen gas combines with protons and electrons to form water.

Step 3: Combined Cell Reaction

The overall reaction in the cell is obtained by adding the anode and cathode reactions: \[ \text{2H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l) \] This manages the formation of water from hydrogen and oxygen.

Step 4: Standard Cell Potential

The standard cell potential \( E^0 \) is calculated using the standard reduction potentials from tables: * Anode: \( \text{H}_2(g) \rightarrow 2\text{H}^+(aq) + 2e^- \), \( E^0 = 0 \text{ V} \) (as it's the standard hydrogen electrode)* Cathode: \( \text{O}_2(g) + 4\text{H}^+(aq) + 4e^- \rightarrow 2\text{H}_2\text{O}(l) \), \( E^0 = 1.23 \text{ V} \) The standard cell potential is: \[ E^0_{cell} = E^0_{cathode} - E^0_{anode} = 1.23 \text{ V} - 0 \text{ V} = 1.23 \text{ V} \]

Key Concepts

Anode Reaction

In a hydrogen-oxygen fuel cell, the anode is where oxidation occurs. Here, hydrogen gas (\(\text{H}_2\)) breaks apart into protons and electrons. The specific reaction at the anode can be represented by the equation:\[ \text{H}_2(g) \rightarrow 2\text{H}^+(aq) + 2e^- \]- Hydrogen molecules separate into two protons.- Each hydrogen atom loses an electron resulting in two free electrons.This process of losing electrons is termed oxidation. The electrons released at the anode are then directed towards the cathode through an external circuit, providing electrical energy to power devices, such as those in a space shuttle. Meanwhile, the protons move through the electrolyte to reach the cathode.

Cathode Reaction

In the hydrogen-oxygen fuel cell, the cathode is the site of the reduction reaction. It involves oxygen gas (\(\text{O}_2\)) reacting with protons (\(\text{H}^+\)) and electrons arriving from the anode. This is shown by the equation:\[ \text{O}_2(g) + 4\text{H}^+(aq) + 4e^- \rightarrow 2\text{H}_2\text{O}(l) \]- Oxygen combines with four protons and four electrons.- This reaction forms two molecules of water (\(\text{H}_2\text{O}\)).Reduction means gaining electrons, and this process is essential to complete the circuit. When electrons reach the cathode, they join oxygen and protons to safely form water, a clean byproduct making fuel cells environmentally friendly.

Standard Cell Potential

The standard cell potential (\(E^0_{cell}\)) is a measure of the voltage produced by a cell under standard conditions. It's calculated using the standard reduction potentials of the electrodes involved. Here's how it's done for the hydrogen-oxygen fuel cell:- Anode Reaction Potential: For hydrogen conversion to protons and electrons, the standard potential is set as 0 V (the standard hydrogen electrode).- Cathode Reaction Potential: For oxygen reacting with hydrogen ions and electrons, the standard reduction potential is 1.23 V.The standard cell potential is calculated with the formula:\[E^0_{cell} = E^0_{cathode} - E^0_{anode} = 1.23 \text{ V} - 0 \text{ V} = 1.23 \text{ V}\]- The higher the cell potential, the greater the potential energy converted into electrical energy.- A standard cell potential of 1.23 V indicates a highly efficient energy conversion process, essential for practical applications, especially those requiring reliability and sustainability.