A vessel of volume `3V` contains a gas at pressure `4 P_(0)` and another vessel of volume `2V` contains same gas at pressure `1.5 P_(0)`. Both vessels have same temperature. When both vessels are connected by a tube of negligible volume, the equilibrium is `IP_(0)`, where `I` is an integer. Find the value of `I`.

Options

A. `P_(0)`
B. `2P_(0)`
C. `3P_(0)`
D. `4P_(0)`

Answer

C

Explanation

No change of temperature
So, `(n_(1) + n_(2))_(i) = (n_(1) + n_(2))_(f)`
`(P_(1)V_(1))/(RT) + (P_(2)V_(2))/(RT) = (PV_(1))/(RT) + (PV_(2))/(RT)`
So, `P = (P_(1)V_(1) + P_(2)V_(2))/(V_(1) + V_(2))`
`= ((4P_(0)) (3v) + (1.5 P_(0)) (2V))/(5V)`
`= 3 P_(0)`