Question

When $2g$ of $A$ gas is introduced into an evacuated flask kept at ${25}^{\circ }C$, the pressure is found to be $1atm$. If $3g$ of another gas $B$ is then added to the same flask, the total pressure becomes $1.5atm$. The ratio of molecular weights is:

• A. $1:1$
• B. $1:2$
• C. $2:3$
• D. none of these

Answer 1

Answer: (D)

none of these

we know that

p$\alpha$ number of moles

let molecular weighgt of A is a fram

B is b gram

when pressure 1 atm,no of moles =2/a moles

when pressure 1.5 atm no of moles = $\frac{2}{a}=\frac{3}{b}$ moles

$\Rightarrow \frac{1}{5}=\frac{\frac{1}{a}}{\frac{2}{a}+\frac{3}{b}}\Rightarrow \frac{2}{3}=\frac{\frac{2}{a}}{\frac{2b+3a}{ab}}\Rightarrow \frac{2}{3}=\frac{2b}{2b+3a}\Rightarrow 2(2b+3a)=6b$

$\Rightarrow +b+6a+6b\Rightarrow 6a=6b-4b=2b$

$\frac{a}{b}=\frac{2}{6}1/3$ , so option D