Two flasks A and B of equal capacity of volume contain `SO_3` and CO gas respectively under similar conditions of temperature and pressure. Then, which of the following statement is true?

Options

A. A has twice the number of moles as that of B
B. B has twice the number of moles as that of A
C. A and B have equal number of moles
D. B has twice the number of atoms as that of A

Answer

To solve the problem, we need to analyze the information provided about the two flasks A and B containing different gases under the same conditions of temperature and pressure.

### Step-by-Step Solution:

1. **Identify the Gases and Their Conditions**:
- Flask A contains sulfur trioxide (SO₃).
- Flask B contains carbon monoxide (CO).
- Both flasks have equal volume and are under the same temperature and pressure conditions.

2. **Apply the Ideal Gas Law**:
- The ideal gas law is given by the equation:
\[ PV = nRT \]
- Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature

3. **Calculate the Number of Moles**:
- Rearranging the ideal gas law to find the number of moles (\( n \)):
\[ n = \frac{PV}{RT} \]
- Since pressure (\( P \)), volume (\( V \)), \( R \), and temperature (\( T \)) are the same for both flasks, we can conclude that the number of moles of gas in each flask is the same.

4. **Conclusion about the Number of Moles**:
- Therefore, the number of moles in flask A (SO₃) is equal to the number of moles in flask B (CO):
\[ n_A = n_B \]

5. **Analyze the Statements**:
- The first statement claims A has twice the number of moles as B: **False**.
- The second statement claims B has twice the number of moles as A: **False**.
- The third statement claims A and B have equal number of moles: **True**.
- The fourth statement claims B has twice the number of atoms as A: **False** (since SO₃ has 4 atoms and CO has 2 atoms).

6. **Final Answer**:
- The correct statement is: **A and B have equal number of moles.**