`H_(2)O_(2)` can be produced by the ammonium hydrogen sulphate. Reactions occuring in electrolytic cell,
`NH_(4)HSO_(4)rarrNH_(4)^(-)+2e^(-)` (Anode)
`2SO_(4)^(2-)rarrS_(2)O_(8)^(2-)+2e^(-)`
`2H^(+)+2e^(-)rarrH_(2)` (Cathode)
Hydrolysis of ammonium persulphate:
`(NH_(4))_(2)S_(2)O_(8)+2H_(2)Orarr2NH_(4)HSO_(4)+H_(2)O_(2)` Assume 100% yield of hydrolysis reaction.
What volume of hydrogen gas at 1 atm and 273 K will be produced in cathode in previous question?

Options

A. `22.4L`
B. `11.2L`
C. `5.6 L`
D. `2.8L`

Answer

To solve the problem of determining the volume of hydrogen gas produced at the cathode during the electrolysis of ammonium hydrogen sulfate, we can follow these steps:

### Step 1: Analyze the Reactions
The reactions occurring in the electrolytic cell are:
1. **Anode Reaction**:
\[ NH_4HSO_4 \rightarrow NH_4^+ + 2e^- \]
This indicates that for every mole of ammonium hydrogen sulfate, two electrons are released.

2. **Anode Reaction**:
\[ 2SO_4^{2-} \rightarrow S_2O_8^{2-} + 2e^- \]
This shows that two moles of sulfate ions produce one mole of persulfate, also releasing two electrons.

3. **Cathode Reaction**:
\[ 2H^+ + 2e^- \rightarrow H_2 \]
Here, two moles of hydrogen ions combine with two electrons to produce one mole of hydrogen gas.

### Step 2: Determine Moles of Hydrogen Produced
From the cathode reaction, we see that 2 moles of hydrogen ions produce 1 mole of hydrogen gas. Since the ammonium persulfate hydrolysis is assumed to have a 100% yield, we can conclude that for every mole of ammonium hydrogen sulfate, we will produce half a mole of hydrogen gas.

### Step 3: Calculate the Volume of Hydrogen Gas
At standard temperature and pressure (STP: 1 atm and 273 K), 1 mole of any ideal gas occupies 22.4 liters. Since we are producing 0.5 moles of hydrogen gas, we can calculate the volume as follows:

\[ \text{Volume of } H_2 = \text{moles of } H_2 \times \text{volume of 1 mole at STP} \]
\[ \text{Volume of } H_2 = 0.5 \, \text{moles} \times 22.4 \, \text{L/mole} = 11.2 \, \text{L} \]

### Conclusion
The volume of hydrogen gas produced at the cathode is **11.2 liters**.

### Final Answer
The correct option is **B: 11.2 liters**.

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