Question

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 $\Delta p=0.78$ atm (the temperature remaining constant). Find the mass of the released gas. The gas density under the normal conditions $\rho =1.3g/l$

• A. 30 g
• B. 40 g
• C. 50 g
• D. None

Answer 1

The correct option is A 30 g

If $m_1$ and $m_2$ be the masses of the gas in the vessel before and after the gas is released, then mass of the gas released, $\Delta m=m_1-m_2$

Using ideal gas equation, $p_{1}V=\frac{m_{1}R{T}_0}{M}$ and $p_{2}V=\frac{m_{2}R{T}_0}{M}$ (as V and T are same before and after release of the gas)

Now, $(p_1-p_2)V=(m_1-m_2)\frac{R{T}_0}{M}$

$\Delta pV=\Delta m\frac{R{T}_0}{M}$

or $\Delta m=\frac{MV\Delta p}{R{T}_0}...\left(1\right)$

We also know that, $p=\rho \frac{R}{M}T$

so , $\frac{M}{R{T}_0}=\frac{\rho }{p_0}....\left(2\right)$ where $p=1atm,$ standard atmospheric pressure and $T_0=273K$

Using (1) & (2), $\Delta m=\rho V\frac{\Delta p}{p_0}=1.3\times 30\times \frac{0.78}{1}=30g$