Question

Sumit evacuated a cylinder and filled in $4g$ of gas $A$ at temperature ${25}^{o}C$. The pressure was found to be $1atm$. His friend Vineet, filled another $8g$ of gas $B$ in the cylinder at the same temperature. The final pressure was found to be $1.5atm$. The ratio of molecular masses of $A$ and $B$ (assuming ideal gas behaviour) is ____.

• A. $1:1$
• B. $1:2$
• C. $1:8$
• D. $1:4$

Answer 1

The correct option is D $1:4$

Option $D.$

Using $PV=nRT$ for gas $A.$

$1\times V=n_{A}RT$

$V=\left(\frac{4}{M_A}\right)RT⟶i.$

After addition of gas $B,$

$1.5V=(\frac{4}{M_A}+\frac{8}{M_B})RT⟶ii$

$\frac{\left(2\right)}{\left(1\right)}⟹1.5=(\frac{4}{M_A}+\frac{8}{M_B})\frac{M_A}{4}=1+2\frac{M_A}{M_B}$

$0.5=2\frac{M_A}{M_B}$

$\frac{M_A}{M_B}=\frac{0.5}{2}=\frac{1}{2\times 2}=\frac{1}{4}$