During an electrolysis of conc. `H_(2)SO_(4)`, peroxydisulphuric acid `(H_(2)S_(2)O_(8))` and `O_(2)` form in an equimolar amount. The moles of `H_(2)` that will be formed simultaneously will be

Options

A. Thrice that of `O_(2)`
B. Twice that of `O_(2)`
C. Equal to that of `O_(2)`
D. Half of the of `O_(2)`

Answer

To solve the problem, we need to analyze the electrolysis of concentrated sulfuric acid (H₂SO₄) and determine the relationship between the moles of hydrogen (H₂) produced and the moles of oxygen (O₂) formed during the process.

### Step-by-Step Solution:

1. **Understanding the Electrolysis Process**:
- During the electrolysis of concentrated H₂SO₄, two main products are formed: peroxydisulfuric acid (H₂S₂O₈) and oxygen (O₂).
- It is given that these products are formed in equimolar amounts.

2. **Identifying the Reactions at the Electrodes**:
- At the anode, the oxidation reaction occurs. The relevant reactions can be summarized as follows:
- 2 H₂SO₄ → H₂S₂O₈ + 2 H⁺ + 2 e⁻ (formation of peroxydisulfuric acid)
- 2 H₂O → O₂ + 4 H⁺ + 4 e⁻ (formation of oxygen)
- At the cathode, the reduction reaction occurs:
- 2 H₂O + 2 e⁻ → H₂ + 2 OH⁻ (formation of hydrogen gas)

3. **Combining the Reactions**:
- To find the overall reaction, we need to balance the number of electrons transferred in the reactions. The anode reaction produces 4 electrons, while the cathode reaction consumes 2 electrons. Therefore, we need to multiply the cathode reaction by 2 to balance the electrons:
- 4 H₂O + 4 e⁻ → 2 H₂ + 4 OH⁻

4. **Total Reaction**:
- Now, we can write the overall reaction by combining the anode and cathode reactions:
- 2 H₂SO₄ + 4 H₂O → H₂S₂O₈ + O₂ + 2 H₂ + 4 H⁺
- Here, we see that for every 1 mole of O₂ produced, 2 moles of H₂ are produced.

5. **Relating Moles of H₂ to Moles of O₂**:
- Since it is given that peroxydisulfuric acid and O₂ are formed in equimolar amounts, we can conclude that if we have 1 mole of O₂, we will have 2 moles of H₂ produced simultaneously.

6. **Final Conclusion**:
- Therefore, the moles of H₂ that will be formed simultaneously are twice that of O₂.

### Answer:
The moles of H₂ that will be formed simultaneously will be **2 times that of O₂**.

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