A vessel of uniform cross-section of length 500 cm as shown in figure is divided in two parts by a weightless and frictionless piston one part contains 5 moles of He(g) and other part 2 moles of `H_(2)(g)` and 4 moles of `O_(2)(g)` added at the same temperature and pressure in which reaction takes place finally vessel cooled to 300 K and 1 atm. What is the length of He compartment?
(Assume volume of piston and vol. of `H_(2)O(l)` formed are negligible)

Options

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

Answer

c

Explanation

(c) Moles of `O_(2)` remaining after reaction=4 - 1 = 3
`V prop n` is due to same T and P in each compartment after reaction.
`:.` Length of He compartment
`(5)/(5+3)xx500=312.5cm`