Question

Two vessels, $A$ and $B$, contain the same gas. If the pressure, volume and absolute temperature of the gas in $A$ are two times as compared with those of gas in $B$, and if mass of the gas in $B$ is $xg$, the mass of the gas in $A$ will be:

• A. $4xg$
• B. $\frac{x}{2}g$
• C. $2xg$
• D. $xg$

Answer 1

Answer: (C)

$2xg$

Both vessels contain same gas $\therefore$molar mass of gas in both the vessels is same.

The mass of the gas in B is $xg$

Let mss of gas in A be $yx$

In vessel B $PV=nRT$

$\frac{PV}{T}=n$ ($R$ is gas constant)

$\frac{PV}{T}=\frac{x}{M}M=x\left(\frac{T}{PV}\right)⟶{eq}^n\left(1\right)$

In vessel A $2P.2V=nR.2T\frac{2P.2V}{2T}=n\frac{2PV}{T}=\frac{y}{M}M=y\left(\frac{T}{2PV}\right)⟶{eq}^n\left(2\right)$

From equation $\left(1\right)$ and equation$\left(2\right)$

$x\left(\frac{T}{PV}\right)=y\left(\frac{T}{2PV}\right)x=\frac{y}{2}2x=y$

Thus, the mass of the gas in A will be $\left(2x\right)g$