Consider the adjacent diagram. Initially, flask `A` contained oxygen gas at `27^(@)C` and `950 mm` of `Hg`, and flask `B` contained neon gas at `27^(@)C` and `900 mm`. Finally, two flask were joined by means of a narrow tube of negligible volume equipped with a stopcock and gases were allowed to mixup freely. The final pressure in the combined system was found to be `910 mm` of `Hg`.

What is the correct relationship between volumes of the two flasks?

Options

A. `V_(B)=2V_(A)`
B. `V_(B)=4V_(A)`
C. `V_(B)=5V_(A)`
D. `V_(B)=5.5V_(A)`

Explanation

Given, Initial condition
`P_(A)=950mm`, `V_(A)=?`, `T_(A)=300 K`
`P_(B)=900mm`, `V_(B)=?`, `T_(A)=300 K`
`:. n_(total)=(PV)/(RT)=(950xxV_(A))/(Rxx300)+(900xxV_(B))/(Rxx300)`
Final condition
`P_(A)=910`, `V_(A)=? T_(A)=300`
`P_(B)=910`, `V_(B)=? T_(B)=300`
`:. n_(total)=(PV)/(RT)=(910xxV_(A))/(Rxx300)+(900xxV_(B))/(Rxx300)`
Since `n_(total)=` constant
`:. (950xxV_(A))/(Rxx300)+(900xxV_(B))/(Rxx300)=(910xxV_(A))/(Rxx300)+(910xxV_(B))/(Rxx300)`
Therefore, `V_(B)=4V_(A)`