You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Physics

Ideal Gas Equation

A perfectly c...

Question

A perfectly conducting vessel of volume V = $0.4 m^{3}$ contains an ideal gas constant temperature T = 273 K. A portion of the gas is let our and the pressure of the gas falls by $Δ P = 0.24 a t m$ (Density of the gas at STP is $ρ = 1.2 k g / m^{3}$ ). Find the mass of the gas which excapes from the vessels.

115.2 g

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

215.2 g

No worries! We‘ve got your back. Try BYJU‘S free classes today!

915.2 g

No worries! We‘ve got your back. Try BYJU‘S free classes today!

415.2 g

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $115.2 g$
The molar mass of gas be M.

Hence $ρ = \frac{P M}{R T}$

$1.2 = \frac{10^{5} (M)}{(8.314) (273)}$

$M = 27.24 g$

Also, since temperature and volume are constant,

$V Δ P = \frac{Δ m}{M} R T$

$Δ m = \frac{M V Δ P}{R T} = \frac{27.24 (0.4) (0.24 X 10^{5})}{(8.314) (273)} = 115.22 g$

Answer is $115.2 g$

Suggest Corrections

Similar questions

Q. A vessel of volume V

=

30 l contains ideal gas at the temperature

0^{\circ}

After a portion of the gas has been let out, the pressure in the vessel decreased by

Δ p = 0.78

atm (the temperature remaining constant). Find the mass of the released gas. The gas density under the normal conditions

ρ = 1.3 g / l

Q. A vessel of volume

50000 c m^{3}

contains an ideal gas at

0^{o} C

. After a portion is let out, the pressure in the vessel decreases by 1 atm in constant temperature conditions. If the density under normal conditions is

1.6 k g m^{- 3}

then find the mass of the released gas in decagrams :

Q. A vessel of volume

2 m^{3}

contains an ideal gas at pressure

10^{5} {N/m}^{2}

and temperature

300 K

. The gas is continously pumped out of this vessel at a constant volume rate

\frac{d V}{d t} = 2 \times 10^{- 3} m^{3} / s

, keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find the time taken before half of the original gas is pumped out (in minutes).

A vessel of volume $V$ contains an ideal gas at absolute temperature $T$ and pressure $P$ . The gas is allowed to leak till its pressure falls to $P$ . Assuming that the temperature remains constant during leakage, the number of moles of the gas that have leaked is

A vessel of volume $V_{0}$ contains an ideal gas at pressure $p_{0}$ and temperature T. Gas is continuously pumped out of this vessel at a constant volume -rate dV/dt = r keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find (a) the pressure of the gas as a function of time, (b) the time taken before half the original gas is pumped out.

Join BYJU'S Learning Program

A perfectly conducting vessel of volume V = 0.4m3 contains an ideal gas constant temperature T = 273 K. A portion of the gas is let our and the pressure of the gas falls by ΔP=0.24atm (Density of the gas at STP is ρ=1.2kg/m3). Find the mass of the gas which excapes from the vessels.

The correct option is A 115.2gThe molar mass of gas be M.Hence ρ=PMRT1.2=105(M)(8.314)(273)M=27.24gAlso, since temperature and volume are constant,VΔP=ΔmMRTΔm=MVΔPRT=27.24(0.4)(0.24X105)(8.314)(273)=115.22gAnswer is 115.2g