Question

A gas (1g) at 4 bars pressure. If we add 2gm of gas B then the total pressure inside the container is 6 bar. Which of the following is true?
(A) ${{M}_{A}}=2{{M}_{B}}$
(B) ${{M}_{B}}=2{{M}_{A}}$
(C) ${{M}_{A}}=4{{M}_{B}}$
(D) ${{M}_{B}}=4{{M}_{A}}$

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. The mole and volume relationship is Avogadro’s law.

Complete step by step solution:
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.
$PV=nRT$- (1)
Avogadro’s law:
This law states that the equal volumes of all gases at the same temperature and pressure have the same number of molecules.
According to this law, for a given mass of an ideal gas volume and moles of the gas are directly proportional when the temperature and pressure constant.
At constant temperature and volume, from equation (1),
$n \propto p$ - (2)
For a given gases ‘A’ and ‘B’, let the pressure and number of moles will be ${{p}_{A}}\And {{p}_{B}};{{n}_{A}}\And {{n}_{B}}$
Given ${{M}_{A}}\And {{M}_{B}}$ are the molar masses of gas ‘A’ and gas ‘B’
Then from equation (2),
$\dfrac{{{n}_{A}}}{{{p}_{A}}}=\dfrac{{{n}_{B}}}{{{p}_{B}}}$
Mass of gas ‘A’ = 1g and pressure = 4 bar
Mass of gas ‘B’ = 2g and pressure = 6 bar
Then substitute the values in the above equation,
$\dfrac{\dfrac{1}{{{M}_{A}}}}{4}=\dfrac{\dfrac{2}{{{M}_{B}}}}{6}$
Therefore, ${{M}_{B}}=4{{M}_{A}}$

So, the correct answer is option A.

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.