How many faraday are required to liberate 8 g of hydrogen ?

Options

A. 2
B. 4
C. 8
D. 18

Explanation

To determine how many Faraday are required to liberate 8 g of hydrogen, we can follow these steps:

### Step 1: Understand the Reaction
The liberation of hydrogen gas (H2) from hydrogen ions (H+) involves a reduction reaction where H+ ions gain electrons. The balanced half-reaction can be represented as:
\[ 2H^+ + 2e^- \rightarrow H_2 \]
This shows that 2 moles of electrons are required to produce 1 mole of hydrogen gas.

### Step 2: Calculate the Molar Mass of Hydrogen
The molar mass of hydrogen (H2) is calculated as follows:
- The atomic mass of hydrogen (H) is approximately 1 g/mol.
- Therefore, the molar mass of H2 is:
\[ 2 \times 1 \, \text{g/mol} = 2 \, \text{g/mol} \]

### Step 3: Determine the Moles of Hydrogen
Next, we need to find out how many moles of hydrogen correspond to 8 g:
\[ \text{Moles of } H_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{8 \, \text{g}}{2 \, \text{g/mol}} = 4 \, \text{mol} \]

### Step 4: Calculate the Moles of Electrons Required
From the balanced reaction, we know that to produce 1 mole of H2, 2 moles of electrons are required. Therefore, for 4 moles of H2:
\[ \text{Moles of electrons} = 4 \, \text{mol H}_2 \times 2 \, \text{mol e}^- / \text{mol H}_2 = 8 \, \text{mol e}^- \]

### Step 5: Convert Moles of Electrons to Faraday
1 mole of electrons is equivalent to 1 Faraday. Therefore, the number of Faraday required to liberate 8 moles of electrons is:
\[ \text{Faraday required} = 8 \, \text{mol e}^- \times 1 \, \text{Faraday/mol e}^- = 8 \, \text{Faraday} \]

### Final Answer
Thus, to liberate 8 g of hydrogen, **8 Faraday** are required.

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