Question

A partition divides a container having insulated walls into two compartments. The same gas fills the two compartments (see figure). The ratio of the number of molecules is compartments I and II is

• A. $6:1$
• B. $1:6$
• C. $4:1$
• D. $1:4$

Answer 1

Answer: (B)

$1:6$

Using $pV=nRT$,
We can write,
$p_I{V}_I=n_{I}R{T}_I$
$\Rightarrow pV=n_{I}RT....\left(i\right)$
Similarly, for compartment II
$p_{II}{V}_{II}=n_{II}R{T}_{II}$
$\Rightarrow \left(2p\right)\left(3V\right)=n_{II}R\left(T\right)....\left(ii\right)$
From Eqs. (i) and (ii), we have
$n_{I}RT=\frac{n_{II}RT}{6}$
$\Rightarrow \frac{n_I}{n_{II}}=\frac{1}{6}$
or $n_I:n_{II}=1:6$.