During the electrolysis of water 4 mol of electrons were transferred from anode to cathode. The total volume of gases produced at STP will be approximately

Options

A. 67.2L
B. 22.4L
C. 44.8L
D. 89.4L

Answer

To solve the problem of determining the total volume of gases produced during the electrolysis of water when 4 moles of electrons are transferred, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Electrolysis of Water**:
The overall reaction for the electrolysis of water is:
\[ 2H_2O(l) \rightarrow 2H_2(g) + O_2(g) \]
This means that for every 2 moles of water, 2 moles of hydrogen gas and 1 mole of oxygen gas are produced.

2. **Identify the Role of Electrons**:
During the electrolysis, oxidation occurs at the anode and reduction at the cathode. The transfer of electrons can be related to the amount of gas produced.

3. **Calculate Moles of Gases Produced**:
From the balanced reaction, we can see that:
- 4 moles of electrons correspond to the production of 2 moles of hydrogen gas and 1 mole of oxygen gas.
- The stoichiometry of the reaction shows that 4 moles of electrons are needed to produce 2 moles of \(H_2\) and 1 mole of \(O_2\).

4. **Determine Total Moles of Gases**:
Since 4 moles of electrons are transferred:
- 2 moles of \(H_2\) + 1 mole of \(O_2\) = 3 moles of gases produced.

5. **Calculate Volume at STP**:
At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 liters. Therefore, the total volume of gases produced can be calculated as:
\[ \text{Total Volume} = \text{Total Moles} \times \text{Volume per mole at STP} \]
\[ \text{Total Volume} = 3 \, \text{moles} \times 22.4 \, \text{L/mole} = 67.2 \, \text{liters} \]

### Final Answer:
The total volume of gases produced at STP will be approximately **67.2 liters**.

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