The volume of hydrogen gas liberated at STP when a current of 5.36 ampere is passed through dil. `H_(2)SO_(4)` for 5 hours will be

Options

A. 5.6L
B. 11.2L
C. 16.8L
D. 22.4L

Explanation

To find the volume of hydrogen gas liberated at STP when a current of 5.36 amperes is passed through dilute H₂SO₄ for 5 hours, we can follow these steps:

### Step 1: Convert Time from Hours to Seconds
Given time is 5 hours. We need to convert this into seconds.

\[ \text{Time in seconds} = 5 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 18000 \text{ seconds} \]

### Step 2: Calculate the Total Charge (Q)
The total charge (Q) passed through the solution can be calculated using the formula:

\[ Q = I \times t \]

Where:
- \(I = 5.36 \, \text{A}\)
- \(t = 18000 \, \text{s}\)

\[ Q = 5.36 \, \text{A} \times 18000 \, \text{s} = 96768 \, \text{C} \]

### Step 3: Calculate the Number of Equivalents of Hydrogen
Using Faraday's constant (F = 96500 C/mol), we can find the number of equivalents (n) of hydrogen produced:

\[ n = \frac{Q}{F} = \frac{96768 \, \text{C}}{96500 \, \text{C/mol}} \approx 1.003 \, \text{mol} \]

### Step 4: Determine the Moles of Hydrogen Gas Produced
From the electrolysis of dilute H₂SO₄, we know that 2 moles of electrons produce 1 mole of H₂. Therefore, the number of moles of H₂ produced is:

\[ \text{Moles of } H_2 = \frac{n}{2} = \frac{1.003}{2} \approx 0.5015 \, \text{mol} \]

### Step 5: Calculate the Volume of Hydrogen Gas at STP
At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters. Thus, the volume (V) of hydrogen gas produced is:

\[ V = \text{Moles of } H_2 \times 22.4 \, \text{L/mol} = 0.5015 \, \text{mol} \times 22.4 \, \text{L/mol} \approx 11.23 \, \text{L} \]

### Final Answer
The volume of hydrogen gas liberated at STP is approximately **11.2 liters**.

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