An ideal gas at pressure P and temperature T is enclosed in a vessel of volume V. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to P'. Assume that the temperature of the gas remains constant during the leakage. What is the number of moles of the gas that have leaked ?

Options

A. `V/(RT)(P+P')`
B. `(2V)/(RT)(P+P')`
C. `(V)/(RT)(P-P')`
D. `(V)/(2RT)(P-P')`

Answer

C

Explanation

Suppose that initially there are n moles of the gas.
Since `PV=nRT" "thereforen=(PV)/(RT)" "...(1)`
`therefore` Suppose that, after leakage, the number of moles of the gas that remained in the vessel is n'.
Since V and T remain constant.
`thereforen'=(P'V)/(RT)` where P' is the reduced pressure
`thereforeDeltan=n-n'=(PV)/(RT)-(P'V)/(RT)=V/(RT)(P-P')`