`4.5 g` of aluminium (at mass `27 u`) is deposited at cathode from `Al^(3+)` solution by a certain quantity of electric charge. The volume of hydrogen gas produced at `STP` from `H^(+)` ions in solution by the same quantity of electric charge will be:

Options

A. `44.8L`
B. 11.2L
C. 22.4L
D. 5.6L

Answer

To solve the problem step by step, we will follow the outlined reasoning from the video transcript.

### Step 1: Calculate the Equivalent Weight of Aluminium
The equivalent weight of a substance can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Atomic Mass}}{\text{Valency}} \]
For aluminium (Al), the atomic mass is `27 u` and the valency (since Al is in the +3 oxidation state) is `3`.

\[ \text{Equivalent Weight of Al} = \frac{27 \, \text{g/mol}}{3} = 9 \, \text{g/equiv} \]

### Step 2: Calculate the Equivalent of Aluminium Deposited
Using the mass of aluminium deposited, we can find the equivalent by using the formula:
\[ \text{Equivalent} = \frac{\text{Mass}}{\text{Equivalent Weight}} \]
Given that the mass of aluminium deposited is `4.5 g`:

\[ \text{Equivalent of Al} = \frac{4.5 \, \text{g}}{9 \, \text{g/equiv}} = 0.5 \, \text{equiv} \]

### Step 3: Relate the Equivalent of Aluminium to the Equivalent of Hydrogen
According to Faraday's law, the equivalent of aluminium deposited is equal to the equivalent of hydrogen gas produced. Therefore:

\[ \text{Equivalent of H}_2 = \text{Equivalent of Al} = 0.5 \, \text{equiv} \]

### Step 4: Calculate the Volume of Hydrogen Gas at STP
At standard temperature and pressure (STP), 1 equivalent of hydrogen gas (H₂) occupies a volume of `22.4 L`. Since we have `0.5 equiv` of H₂, the volume can be calculated as follows:

\[ \text{Volume of H}_2 = \text{Equivalent} \times \text{Volume per Equivalent} \]
\[ \text{Volume of H}_2 = 0.5 \, \text{equiv} \times 22.4 \, \text{L/equiv} = 11.2 \, \text{L} \]

### Final Answer
The volume of hydrogen gas produced at STP from H⁺ ions in solution by the same quantity of electric charge is **11.2 liters**.

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