Question

Given, 100 grams of Oxygen (${{O}_{2}}$ ) gas and 100 grams of helium (He) gas are in separate containers of equal volume at ${{100}^{o}}C$. Which one of the following statements is correct?
(A) Both gases would have the same pressure
(B) The average kinetic energy of ${{O}_{2}}$ molecules is greater than that of He molecules
(C) The pressure of He gas would be greater than that of the ${{O}_{2}}$ gas
(D) The average kinetic energy of He and ${{O}_{2}}$ molecules is the same.

Answer 1

Hint: A theoretical gas composed of a set of randomly moving particles that interact only elastic collisions is called an ideal gas. The ideal gas concept useful for a simplified equation of a state which obeys the ideal gas laws and is amenable to analysis under statistical mechanics.

Complete answer:
Ideal gas equation:
This equation of the state of a hypothetical ideal gas from the ideal gas law. The ideal gas equation has a good approximation to the behavior of many gases under several conditions and limitations.
$PV=nRT$
Given the two gases in a separate container with equal volumes and the same temperature ${{100}^{o}}C$
For 100 grams of ${{O}_{2}}$ ,
 ${{P}_{{{O}_{2}}}}\times V=\dfrac{100}{32}\times R\times T$ --- (1)
For 100 grams of He,
${{P}_{He}}\times V=\dfrac{100}{4}\times R\times T$ --- (2)
Dividing equation (1) by equation (2),
$\dfrac{{{P}_{{{O}_{2}}}}}{{{P}_{He}}}=\dfrac{1}{8}$
$\Rightarrow {{P}_{He}}=8{{P}_{{{O}_{2}}}}$
Hence, ${{P}_{He}}>{{P}_{{{O}_{2}}}}$
Therefore, the pressure of He gas would be greater than that of the ${{O}_{2}}$ gas.

So, the correct answer is option C.

Note:
The ideal gas laws which deal with ideal gases naturally and laws are Boyle’s law, Charles law, and Avogadro’s law. The specific gas constant observed that when a molecular mass of any gas multiplied with R is always the same for all gases. This product is called the universal gas constant.