Question

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 \(P^1\). Assuming that the temperature of the gas remains constant during the leakage, the number of moles of the gas that have leaked is

• A. \(\frac{P^1V}{RT}\)
• B. \(\frac{V}{RT}(P-P^1)\)
• C. \(\frac{2V}{RT}(P+P^1)\)
• D. \(\frac{V}{RT}(P+P^1)\)

Hint:

Moles leaked equal initial moles minus final moles.

Answer 1

The Correct Option is B

Step 1: Idea
The number of moles is proportional to pressure at fixed $V$ and $T$, so the fall in pressure measures the gas lost.

Step 2: Compute
Pressure drop is $P - P^1$. Converting to moles, $\Delta n = \dfrac{(P - P^1)V}{RT}$.

Step 3: Check
If $P^1 = 0$ the whole $\frac{PV}{RT}$ has leaked, as expected, and if $P^1 = P$ nothing has leaked.

Step 4: Answer
Option (B).

Final Answer:
Moles leaked equal V(P - P1)/(RT). This is option (B). \[ \boxed{\text{(B) }\frac{V}{RT}\left(P-P^1\right)} \]