Step 1: Understanding the Concept:
According to Faraday's Laws of Electrolysis, the amount of chemical change produced by an electric current is proportional to the quantity of electricity passed.
One Faraday (F) is the magnitude of electrical charge carried by one mole of electrons (\( 1 \text{ F} \approx 96485 \text{ C} \)).
To determine the number of Faradays required for a reaction, we must look at the stoichiometry of electrons in the balanced half-reaction.
Step 2: Key Formula or Approach:
1. Write the balanced reduction half-reaction for the given process.
2. Determine the number of moles of electrons (\( n \)) required to produce the specified amount of product.
3. The number of moles of electrons is numerically equal to the number of Faradays required.
Step 3: Detailed Explanation:
The question specifies the reduction of hydrogen ions (\( \text{H}^+ \)) to form hydrogen gas (\( \text{H}_2 \)).
Let's write the balanced half-reaction:
A single hydrogen ion requires one electron to become a hydrogen atom.
\[ \text{H}^+ + \text{e}^- \rightarrow \text{H} \]
However, hydrogen naturally exists as a diatomic gas (\( \text{H}_2 \)).
Therefore, to form one molecule of \( \text{H}_2 \), two hydrogen ions and two electrons are needed.
The balanced half-reaction is:
\[ 2\text{H}^+ + 2\text{e}^- \rightarrow \text{H}_2 \]
From the stoichiometry of this balanced equation, we can read directly:
To produce 1 mole of \( \text{H}_2 \) gas, 2 moles of electrons are consumed.
Since 1 mole of electrons equals 1 Faraday of charge, 2 moles of electrons equal 2 Faradays.
Step 4: Final Answer:
2 Faradays are required.