Question

The stopcock connecting the two bulbs of volume $5\text{litre}\text{and}10\text{litre}$ containing an ideal gas at $9\text{atm}\text{and}6\text{atm}$ respectively. What is the final pressure if the temprature remains the same?

• A. $5\text{atm}$
• B. $4\text{atm}$
• C. $8\text{atm}$
• D. $7\text{atm}$

Answer 1

The correct option is D $7\text{atm}$

Given, $P_1=6\text{atm and}{V}_1=10\text{L}$
$P_2=9\text{atm and}{V}_2=5\text{L}$
Total volume $=V_1+V_2=10\text{L}+5\text{L}=15\text{L}$
The ideal gas equation when the valve is opened is as follows :
$P_f(V_1+V_2)=(n_1+n_2)RT$
$n_1=\frac{P_1{V}_1}{RT}\text{and}{n}_2=\frac{P_2{V}_2}{RT}$
$P_f(V_1+V_2)=(\frac{P_1{V}_1}{RT}+\frac{P_2{V}_2}{RT})RT$
$\Rightarrow P_f\times 15\text{L}=6\text{atm}\times 10\text{L}+9\text{atm}\times 5\text{L}$
$\Rightarrow P_f=\frac{105\text{atm}\text{L}}{15\text{L}}$
$P_f=7\text{atm}$​​​​​​