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 ' $\text{P}'$ '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is

• A. $\frac{2 \text{ V}}{\text{RT}}(\text{P} - \text{P}')$
• B. $\frac{\text{V}}{\text{RT}}(\text{P} - \text{P}')$
• C. $\frac{\text{V}}{\text{RT}}(\text{P} + \text{P}')$
• D. $\frac{\text{V}}{2\text{RT}}(\text{P} + \text{P}')$

Hint:

At constant $V$ and $T$, pressure change is directly proportional to mole change.

Answer 1

The Correct Option is B

Step 1: Concept
Use the ideal gas equation $PV = nRT$, where $n$ is the number of moles.

Step 2: Meaning
Initial moles $n_1 = \frac{PV}{RT}$. Final moles after leakage $n_2 = \frac{P'V}{RT}$.

Step 3: Analysis
Number of leaked moles $\Delta n = n_1 - n_2$.
$\Delta n = \frac{PV}{RT} - \frac{P'V}{RT} = \frac{V}{RT}(P - P')$.

Step 4: Conclusion
The leaked moles are $\frac{V}{RT}(P - P')$. Final Answer: (B)