Question

A vessel of uniform cross-section of length 500 $cm$ as shown in figure is divided in two parts by a weightless & frictionless piston. One part contains 5 mole of $N_2\left(g\right)$ and other part contains 2 moles of $H_2\left(g\right)$ & 1 mole of $He\left(g\right)$ gaseous mixture at the same temperature and pressure.
What is the length of $N_2$ compartment?
(Assume volume of piston to be engligible)

• A. 187.5 $cm$
• B. 300 $cm$
• C. 312.5 $cm$
• D. none of these

Answer 1

Answer: (C)

312.5 $cm$

$V\propto n$ due to same $T$ & $P$ in each compartment.
Also $V\propto L$- the length of the container.
The number of moles in nitrogen compartment are 5
Total number of moles in the vessel are $5+1+2=8$
Total length of the vessel is 500 $cm$.
$\therefore$ length of $N_2$ compartment $\frac{5}{5+3}\times 500$
$\Rightarrow 312.5cm$
Hence, the length of the nitrogen compartment is 312.5 $cm$.