A container of volume 30 litre is filled with an ideal gas at one atoms pressure and 0° C temperature. Keeping the temperature constant some mass of gas is allowed to escape from the container. Due to this the pressure of the gas decreases to 0.78 atoms from the previous one. If the density of the gas at N.T.P. is 1.3 gm / litre, find the mass (in gram) of the gas remaining.

Question

A container of volume 30 litre is filled with an ideal gas at one atoms pressure and 0° C temperature. Keeping the temperature constant some mass of gas is allowed to escape from the container. Due to this the pressure of the gas decreases to 0.78 atoms from the previous one. If the density of the gas at N.T.P. is 1.3 gm / litre, find the mass (in gram) of the gas remaining. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

PV =( m / M ) RT V , m , T = constant ( P / m )= constant ( P 1/ m 1)=( P 2/ m 2) (1/1.3 × 30)=(0.78/ m ) m =0.78 × 1.3 × 30 =30.42 gm

PV=Mm​RT V,m,T= constant mP​= constant m1​P1​​=m2​P2​​ 1.3×301​=m0.78​ m=0.78×1.3×30 =30.42gm

$P V = \frac{m}{M} RT$
$V, m, T =$ constant
$\frac{P}{m} =$ constant
$\frac{P _{1}}{m _{1}} = \frac{P _{2}}{m _{2}}$
$\frac{1}{1.3 \times 30} = \frac{0.78}{m}$
$m = 0.78 \times 1.3 \times 30$
$= 30.42 g m$