In the electrolysis of `H_(2)SO_(4)`, 9.72 litres and 2.35 litres of `H_(2)` and `O_(2)` were liberated. Number of equivalent of persulphuric acid `(H_(2)S_(2)O_(8))` produced is

Options

A. 0.448
B. 0.224
C. 0.868
D. 0.42

Explanation

To solve the problem regarding the electrolysis of \( H_2SO_4 \) and the production of persulphuric acid \( H_2S_2O_8 \), we can follow these steps:

### Step 1: Understand the Electrolysis Process
During the electrolysis of sulfuric acid, hydrogen gas \( H_2 \) is produced at the cathode, and oxygen gas \( O_2 \) is produced at the anode. The overall reactions can be summarized as follows:
- At the cathode: \( 2H^+ + 2e^- \rightarrow H_2 \)
- At the anode: \( 2H_2O \rightarrow O_2 + 4H^+ + 4e^- \)

### Step 2: Calculate the Equivalent of Hydrogen Gas
The volume of hydrogen gas liberated is given as 9.72 liters. The equivalent of hydrogen can be calculated using the molar volume of a gas at standard conditions, which is 22.4 liters per mole. The number of equivalents of hydrogen can be calculated using the formula:

\[ \text{Equivalent of } H_2 = \frac{\text{Volume of } H_2}{\text{Molar Volume}} = \frac{9.72 \, \text{L}}{22.4 \, \text{L/mol}} = 0.433 \, \text{mol} \]

### Step 3: Calculate the Equivalent of Oxygen Gas
The volume of oxygen gas liberated is given as 2.35 liters. Similarly, we can calculate the equivalent of oxygen:

\[ \text{Equivalent of } O_2 = \frac{\text{Volume of } O_2}{\text{Molar Volume}} = \frac{2.35 \, \text{L}}{22.4 \, \text{L/mol}} = 0.105 \, \text{mol} \]

### Step 4: Relate the Equivalents to Persulphuric Acid
In the electrolysis process, the equivalents of \( H_2S_2O_8 \) produced will be equal to the difference between the equivalents of hydrogen and oxygen, since each mole of \( H_2S_2O_8 \) corresponds to the consumption of 2 moles of hydrogen and 1 mole of oxygen:

\[ \text{Equivalent of } H_2S_2O_8 = \text{Equivalent of } H_2 - \text{Equivalent of } O_2 \]

Substituting the values we calculated:

\[ \text{Equivalent of } H_2S_2O_8 = 0.433 - 0.105 = 0.328 \]

### Step 5: Final Calculation
The number of equivalents of persulphuric acid produced is:

\[ \text{Number of equivalents of } H_2S_2O_8 = 0.328 \, \text{mol} \]

### Conclusion
Thus, the number of equivalents of persulphuric acid produced is approximately **0.328 equivalents**.