STATEMENT-1 : 1 mol of `H_(2)` and `O_(2)` each occupy 22.7 L of volume at `0^(@)C` and 1 bar pressure, considering ideal behaviour.
STATEMENT-2 : Molar volume for all ideal gases at the same temperature and pressure are equal.

Options

A. If both the statement are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statement are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To solve the question, we need to analyze both statements provided and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** 1 mol of \( H_2 \) and \( O_2 \) each occupy 22.7 L of volume at \( 0^\circ C \) and 1 bar pressure, considering ideal behavior.

1. **Ideal Gas Law**: The ideal gas law is given by the equation \( PV = nRT \).
- Where:
- \( P \) = pressure (in atm or bar)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol) or 8.314 J/(K·mol))
- \( T \) = temperature (in Kelvin)

2. **Given Values**:
- \( n = 1 \, \text{mol} \)
- \( P = 1 \, \text{bar} \) (which is approximately 0.9869 atm)
- \( T = 0^\circ C = 273 \, \text{K} \)

3. **Convert Pressure**:
- Since 1 bar = 0.9869 atm, we can use either unit, but let's convert to atm for consistency with \( R \).
- Therefore, \( P = 1 \, \text{bar} \approx 0.9869 \, \text{atm} \).

4. **Calculate Volume**:
- Using the ideal gas equation:
\[ V = \frac{nRT}{P} \]
- Substituting the values:
\[ V = \frac{1 \, \text{mol} \times 0.0821 \, \text{L·atm/(K·mol)} \times 273 \, \text{K}}{0.9869 \, \text{atm}} \]
- Calculating this gives:
\[ V \approx \frac{22.414 \, \text{L}}{0.9869} \approx 22.7 \, \text{L} \]

5. **Conclusion for Statement 1**:
- The calculation confirms that both \( H_2 \) and \( O_2 \) occupy approximately 22.7 L under the given conditions, thus Statement 1 is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** Molar volume for all ideal gases at the same temperature and pressure are equal.

1. **Understanding Molar Volume**:
- Molar volume is defined as the volume occupied by one mole of a gas at a given temperature and pressure.
- According to the ideal gas law, if temperature and pressure are constant, the volume is directly proportional to the number of moles.

2. **Conclusion for Statement 2**:
- Since all ideal gases behave similarly under the same conditions (same temperature and pressure), they will occupy the same volume when measured in moles. Therefore, Statement 2 is also **correct**.

### Final Conclusion
- Both Statement 1 and Statement 2 are correct, and Statement 2 provides a correct explanation for Statement 1.