On passing one faraday of electricity through a dilute solution of an acid, the volume of hydrogen obtained at NTP is:

Options

A. 22400 mL
B. 1120 mL
C. 2240 mL
D. 11200 mL

Answer

To solve the question of how much hydrogen gas is produced when one Faraday of electricity is passed through a dilute solution of an acid, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Faraday's Law of Electrolysis**:
Faraday's law states that the amount of substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. One Faraday (F) corresponds to the charge of one mole of electrons, which is approximately 96485 coulombs.

2. **Identifying the Reaction**:
In the case of an acid solution, hydrogen ions (H⁺) are present. The reduction of hydrogen ions to form hydrogen gas (H₂) can be represented by the half-reaction:
\[ 2H^+ + 2e^- \rightarrow H_2(g) \]
This indicates that 2 moles of H⁺ ions will produce 1 mole of H₂ gas.

3. **Calculating Moles of Hydrogen Gas Produced**:
When 1 Faraday of electricity is passed, it can provide 1 mole of electrons. Since it takes 2 moles of electrons to produce 1 mole of hydrogen gas, the amount of hydrogen gas produced can be calculated as follows:
\[ \text{Moles of } H_2 = \frac{1 \text{ mole of electrons}}{2 \text{ moles of electrons per mole of } H_2} = 0.5 \text{ moles of } H_2 \]

4. **Calculating Volume of Hydrogen Gas at NTP**:
At Normal Temperature and Pressure (NTP), 1 mole of any ideal gas occupies 22.4 liters. Therefore, the volume of 0.5 moles of hydrogen gas can be calculated as:
\[ \text{Volume of } H_2 = 0.5 \text{ moles} \times 22.4 \text{ L/mole} = 11.2 \text{ liters} \]

5. **Final Answer**:
Thus, the volume of hydrogen obtained at NTP when one Faraday of electricity is passed through a dilute solution of an acid is **11.2 liters**.

### Summary:
The volume of hydrogen gas produced is **11.2 liters**.