Question

The molecular weight of $O_2$ and $SO_2$ are 32 and 64 respectively. At $15^{\circ}C$ and 150 mmHg pressure, 1L of $O_2$ contains -N - molecules. The number of molecules in 2L of $SO_2$ under the same conditions of temperature and pressure will be

• A. N/2
• B. N
• C. 2 N
• D. 4 N

Answer 1

The Correct Option is C

To determine the number of molecules in 2L of $SO_2$ under the given conditions, we need to first understand the relationship between volume, pressure, temperature, and the number of molecules using the Ideal Gas Law and Avogadro's principle.

Step 1: Understand Avogadro's Principle

According to Avogadro's principle, equal volumes of all gases at the same temperature and pressure contain an equal number of molecules. This means that the number of molecules in a given volume of gas only depends on temperature and pressure and not on the type of gas.

Step 2: Analyze the Given Conditions

We are given that 1L of $O_2$ contains N molecules at $15^{\circ}C$ and 150 mmHg pressure.

Now, we need to find the number of molecules in 2L of $SO_2$ at the same temperature and pressure.

Step 3: Calculate the Number of Molecules in 2L of SO₂

Since the volume is doubled (2L instead of 1L) and the temperature and pressure remain constant, the number of molecules is directly proportional to the volume.

Thus, the number of molecules in 2L of $SO_2$ is calculated as:

2 \times N = 2N

Conclusion: Therefore, the number of molecules in 2L of $SO_2$ under the same conditions is 2N.