Two flasks A and B of 500 mL each are respectivelly filled with `O_(2)" and "SO_(2)` at 300 K and 1 atm. Pressure . The flasks will contain:

Options

A. the same number of atoms
B. the same number of molecules
C. more number of moles of molecules in flask A as compared to flask B
D. the same amount of gases

Explanation

To solve the problem, we need to determine the number of molecules in two flasks, A and B, which are filled with \( O_2 \) and \( SO_2 \) respectively, under the same conditions of temperature and pressure.

### Step-by-Step Solution:

1. **Identify Given Data**:
- Volume of each flask (V) = 500 mL = 0.5 L (since 1 L = 1000 mL)
- Temperature (T) = 300 K
- Pressure (P) = 1 atm

2. **Use 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 (0.0821 L·atm/(K·mol))
- \( T \) = temperature

3. **Calculate Number of Moles for Each Gas**:
Since both flasks are under the same conditions, we can calculate the number of moles for either gas. Let's calculate for \( O_2 \):
\[ n = \frac{PV}{RT} \]
Substituting the values:
\[ n_{O_2} = \frac{(1 \text{ atm})(0.5 \text{ L})}{(0.0821 \text{ L·atm/(K·mol)})(300 \text{ K})} \]
\[ n_{O_2} = \frac{0.5}{24.63} \approx 0.0203 \text{ moles} \]

Since the conditions are the same for \( SO_2 \):
\[ n_{SO_2} = \frac{(1 \text{ atm})(0.5 \text{ L})}{(0.0821 \text{ L·atm/(K·mol)})(300 \text{ K})} \approx 0.0203 \text{ moles} \]

4. **Conclusion**:
Since the number of moles of \( O_2 \) and \( SO_2 \) are equal, according to Avogadro's hypothesis, the number of molecules in both flasks will also be equal.

Thus, both flasks A and B will contain the same number of molecules.

### Final Answer:
Both flasks A and B will contain the same number of molecules.

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