Question

A stopcock connecting two bulbs of volume 10 litre and 5 litre containing an ideal gas at 6 atm and 9 atm respectively, is opened. What is the final pressure if the temperature remains the same?

• A. 7 atm
• B. 8 atm
• C. 15 atm
• D. 7.5 atm

Answer 1

The correct option is A 7 atm

After opening of the stop cock the pressure in both the bulb becomes equal to the final value.

At the beginning, the no. of moles of gas in $A=\frac{10\times 6}{RT}=\frac{60}{RT}$
At the beginning, the no. of moles of gas in $B=\frac{5\times 9}{RT}=\frac{45}{RT}$
$\therefore$Total no. of moles at the beginning $n_{total}=\frac{60}{RT}+\frac{45}{RT}=\frac{105}{RT}$
$\text{Total number of moles of gas before opening the stopcock = Total number of moles of gas after opening stopcock}$$=\frac{105}{RT}$
$\therefore$ Pressure after the opening the stopcock
$P_{total}=\frac{n_{total}RT}{V_{total}}$
$P_{total}=\frac{105}{RT}\times \frac{RT}{V_{total}}=\frac{105}{10+5}=7\text{atm}$