Question

Consider a vessel filled with carbodioxide at ${27}^{\circ }C$ and $5$ atmospheric pressure. A part of the gas is removed at ${27}^{\circ }C$ and it fills a $3L$ container at $1atm$ and the pressure drops to $3.5atm$ in the vessel. The volume of the vessel is:

• A. $1L$
• B. $5.8L$
• C. $3.5L$
• D. $2L$

Answer 1

Answer: (D)

$2L$

Let volume of first $v$ and be $V$ container $n$ moles of $C{O}_2$ initially

Applying ideal gas equation

$PV=nRT$

$\Rightarrow 5\times V=n\times R\times 300$

$\Rightarrow n=\frac{5V}{300R}.....\left(i\right)$

Let $x$ moles from it is transfered to second vessel.

Applying ideal gas eq in second vessel

$PV=nRT$

$\Rightarrow 1\times 3=x\times R=300$

$\Rightarrow n=\frac{3}{300R}....\left(ii\right)$

Now, $(n-x)$ moles are left in first vessel and pressure reduced to $3.5atm$

Applying ideal goa eq first vessel again

$PV=nRT$

$\Rightarrow 3.5\times V=(n-x)R\times 300$

$\Rightarrow (\frac{5V}{300R}-\frac{3}{300R})=\frac{3.5V}{300R}$ from $\left(ii\right)$

$V=2L$