The total volume of dry gaseous products at STP, when 3 moles of electrons are transferred from anode to cathode in the electrolysis of water is `:`
( Volume of gas a STP =22.4L )

Options

A. 67.2L
B. 50.4L
C. 44.8L
D. 56.0L

Answer

To solve the problem of determining the total volume of dry gaseous products at STP when 3 moles of electrons are transferred during the electrolysis of water, we can follow these steps:

### Step 1: Understand the Electrolysis of Water
In the electrolysis of water, water (H₂O) is split into hydrogen (H₂) and oxygen (O₂) gases. The reactions occurring at the electrodes are:
- At the anode (oxidation):
\[ 2H_2O \rightarrow O_2 + 4H^+ + 4e^- \]
- At the cathode (reduction):
\[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \]

### Step 2: Determine Moles of Gases Produced
From the reactions:
- To produce 1 mole of O₂, 4 moles of electrons are needed.
- To produce 1 mole of H₂, 2 moles of electrons are needed.

### Step 3: Calculate Moles of Oxygen Produced
Given that 3 moles of electrons are transferred:
- The moles of O₂ produced can be calculated as follows:
\[ \text{Moles of O₂} = \frac{3 \text{ moles of electrons}}{4 \text{ moles of electrons per mole of O₂}} = 0.75 \text{ moles of O₂} \]

### Step 4: Calculate Moles of Hydrogen Produced
- The moles of H₂ produced can be calculated as follows:
\[ \text{Moles of H₂} = \frac{3 \text{ moles of electrons}}{2 \text{ moles of electrons per mole of H₂}} = 1.5 \text{ moles of H₂} \]

### Step 5: Convert Moles to Volume at STP
Using the molar volume of a gas at STP (22.4 L/mol):
- Volume of O₂ produced:
\[ \text{Volume of O₂} = 0.75 \text{ moles} \times 22.4 \text{ L/mol} = 16.8 \text{ L} \]
- Volume of H₂ produced:
\[ \text{Volume of H₂} = 1.5 \text{ moles} \times 22.4 \text{ L/mol} = 33.6 \text{ L} \]

### Step 6: Calculate Total Volume of Gases
Now, we can find the total volume of the gases produced:
\[ \text{Total Volume} = \text{Volume of O₂} + \text{Volume of H₂} = 16.8 \text{ L} + 33.6 \text{ L} = 50.4 \text{ L} \]

### Final Answer
The total volume of dry gaseous products at STP when 3 moles of electrons are transferred is **50.4 liters**.

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