Question

100 g of O2 and 100 g of He(g) are in separate containers of equal volume. Both gases are at 100°C. Which one of the following statements is true?

• A. Both gases would have the same pressure
• B. The average kinetic energy of the O\(_2\) molecules is greater than that of the He molecules
• C. There are equal numbers of He molecules and O\(_2\) molecules
• D. The pressure of the He (g) would be greater than that of the O\(_2\) (g)

Hint:

At the same temperature and volume, the gas with the higher number of moles will exert a higher pressure according to the ideal gas law.

Answer 1

The Correct Option is D

We are given that 100 g of both O\(_2\) and He are in separate containers of equal volume at the same temperature.
According to the ideal gas law \( PV = nRT \), the pressure depends on the number of moles of the gas. The number of moles of O\(_2\) and He can be calculated as: \[ \text{moles of O}_2 = \frac{100}{32} \quad \text{(molar mass of O}_2\text{ = 32 g/mol)} \] \[ \text{moles of He} = \frac{100}{4} \quad \text{(molar mass of He = 4 g/mol)} \] Thus, the moles of He are significantly greater than the moles of O\(_2\).
Since the gases are in the same volume and at the same temperature, the pressure is directly proportional to the number of moles.
Therefore, the pressure of He will be greater than that of O\(_2\).
Thus, the correct answer is (d).