Assertion (A) : 22.4 L of nitrogen at S.T.P and 5.6 L of oxygen at S.T.P contain equal number of molecules .
Reason (R) : Under similar condition of temperature and pressure all gases contain equal number of molecules .

Options

A. Both Assertion and Reason are true and Reason is the correct explanation of the Assertion.
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion .
C. Assertion is true but Reason is wrong .
D. Both Assertion and Reason are wrong .

Explanation

To solve the question regarding the assertion and reason provided, we will analyze both statements step by step.

### Step 1: Understand the Assertion (A)
The assertion states that "22.4 L of nitrogen at STP and 5.6 L of oxygen at STP contain equal number of molecules."

- At Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies 22.4 liters.
- Therefore, 22.4 L of nitrogen (N₂) corresponds to 1 mole of nitrogen.
- For oxygen (O₂), we need to determine how many moles are in 5.6 L.

**Calculation for Oxygen:**
\[ \text{Number of moles of O₂} = \frac{\text{Volume of O₂}}{\text{Molar volume at STP}} = \frac{5.6 \, \text{L}}{22.4 \, \text{L/mol}} = 0.25 \, \text{mol} \]

- Now, we can find the number of molecules in each gas using Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol.

**Molecules in Nitrogen:**
\[ \text{Number of molecules of N₂} = 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{23} \, \text{molecules} \]

**Molecules in Oxygen:**
\[ \text{Number of molecules of O₂} = 0.25 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 1.5055 \times 10^{23} \, \text{molecules} \]

- Since \(6.022 \times 10^{23} \neq 1.5055 \times 10^{23}\), the assertion is **false**.

### Step 2: Understand the Reason (R)
The reason states that "Under similar conditions of temperature and pressure, all gases contain equal number of molecules."

- This statement is misleading. While it is true that under the same conditions of temperature and pressure, equal volumes of gases contain the same number of molecules (Avogadro's Law), the statement does not hold when the volumes are different.
- Therefore, the reason is also **false**.

### Conclusion
Both the assertion (A) and the reason (R) are false.

### Final Answer
Both Assertion (A) and Reason (R) are false.

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