Question

A vessel of uniform cross-section of length $250cm$ as shown in figure is divided in two parts by a weightless and frictionless piston one part contains $5moles$ of $He\left(g\right)$ and other part $2moles$ of $H_2\left(g\right)$ and $4mole$ of $O_2\left(g\right)$ added at the same temperature and pressure, in which reaction takes place finally vessel cooled to $300K$ and $1atm$. What is the length of $He$ compartment? (Assume volume of piston and volume of $H_{2}O\left(l\right)$ formed are negligible)

• A. $187.5cm$
• B. $300cm$
• C. $312.5cm$
• D. $noneofthese$

Answer 1

Answer: (C)

$312.5cm$

Moles of $O_2$ remaining after reaction $=4-1=3$.
$V\propto n$ is due to same $T$ and $P$ in each compartment after reaction.
$\therefore$ Length of $He$ compartment,
$\frac{5}{5+3}\times 500=312.5cm$.