Question

Two vessels are connected by a valve of negligible volume. One container, $A$ has 2.8 g $N_2$ at $TK$. The other container, $B$ is completely evacuated The container $A$ is heated to $T_{2}K$, while container $B$ is maintained at $T_2/3K$. Volume of $A$ is half that of B. if the valve is opened, then:

• A. $6/70$ moles $of{N}_2$ will be present in $B$
• B. The weight ratio of $N_2$ in $A$ and $B$ vessels in 1 : 6
• C. $N_2$ gas does not enter into $B$ vessel
• D. Number of moles of $N_2$ released into $B$ vessel is less than that in $A$ vessel.

Answer 1

The correct option is B The weight ratio of $N_2$ in $A$ and $B$ vessels in 1 : 6

Let xx mole of $N_2$ present into vessel IIII and PP is final pressure of $N_2$

$P\left(2V\right)=xR\left(\frac{T_2}{3}\right)$ and $P\left(V\right)=(0.1-x)R{T}_2$

$⟹2=\frac{x}{3(0.1-x)}$
$⟹x=\frac{0.6}{7}mole$

So,

$\frac{0.6}{7}\times 28=2.4g{N}_2$

IIII has $2.4g{N}_2$ and II has $0.4g{N}_2$
$\frac{W_1}{W_2}=\frac{0.4}{2.4}=1:6$