The number of moles of water which must be electrolyzed to produce `22.4L` of `O_(2)` at `273K` and 2 atmospheric pressure is

Options

A. `1`
B. `2`
C. `4`
D. none of these

Explanation

To solve the problem of determining the number of moles of water that must be electrolyzed to produce 22.4 L of O₂ at 273 K and 2 atm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Reaction**: The electrolysis of water can be represented by the following balanced chemical equation:
\[ 2H_2O \rightarrow 2H_2 + O_2 \]
This equation shows that 2 moles of water produce 1 mole of oxygen gas (O₂).

2. **Determine the Volume of O₂ at STP**: At standard temperature and pressure (STP), which is 273 K and 1 atm, 1 mole of any ideal gas occupies 22.4 L. Since we are given that we need to produce 22.4 L of O₂, we can conclude that:
\[ 22.4 \, \text{L of O}_2 = 1 \, \text{mole of O}_2 \]

3. **Relate Moles of O₂ to Moles of H₂O**: From the balanced equation, we know that 1 mole of O₂ is produced from 2 moles of H₂O. Therefore, to find the number of moles of water required to produce 1 mole of O₂, we can set up the following relationship:
\[ \text{Moles of H₂O} = 2 \times \text{Moles of O₂} \]
Since we have 1 mole of O₂, we can calculate:
\[ \text{Moles of H₂O} = 2 \times 1 = 2 \, \text{moles} \]

4. **Conclusion**: Thus, the number of moles of water that must be electrolyzed to produce 22.4 L of O₂ at 273 K and 2 atm is 2 moles.

### Final Answer:
The number of moles of water that must be electrolyzed is **2 moles**.

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