Question

An open vessel containing air is heated from 300 to 400K . The fraction of air originally present which goes out of it is:
(A) 3/4
(B) 1/4
(C) 2/3
(D) 1/8

Answer 1

Hint: The state of an amount of gas is determined by its pressure, volume, and temperature. The modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature: the appropriate SI unit is the kelvin.

Complete step by step answer:
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. The ideal gas law is often written in an empirical form: PV=nRT
Where P, T and V are the pressure, volume and temperature; n is the amount of substance; and R is the ideal gas constant. It is the same for all gases.
As the vessel is open, the pressure remains constant.There is no change in the volume of the vessel. Hence, the volume is also constant.
Since P and V are constant and R is already a universal constant therefore, the ideal gas equation will become,
\[\dfrac{{{n}_{1}}}{{{n}_{2}}}=\dfrac{{{T}_{2}}}{{{T}_{1}}}\]
Where ${{n}_{1}}$ is the number of moles of gas initially at 300K, and ${{n}_{2}}$ is the number of moles of gas at 400K.Let us take ${{n}_{1}}$ as 1 and ${{n}_{2}}$ as x.
${{T}_{1}}$=300K and ${{T}_{2}}$=400K
Therefore, substituting value in the equation,
\[\begin{align}
& \Rightarrow \dfrac{1}{x}=\dfrac{400}{300} \\
& \Rightarrow x=\dfrac{3}{4} \\
\end{align}\]
Therefore the fraction of air present in the vessel is $\dfrac{3}{4}$. Therefore, the gas escaped out will be, $1-\dfrac{3}{4}\Rightarrow \dfrac{1}{4}$.

Therefore, the correct answer is the B option.

Note: It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law.