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

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25.2 g

115.2 g

5.2 g

15.2 g

answer is B.

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Detailed Solution

$p_{1} V = n_{1} R T$

$p_{2} V = n_{2} R T$ (T=273 K )

$∴ (p_{1} - p_{2}) V = (n_{1} - n_{2}) R T = (\frac{m_{1} - m_{2}}{M}) R T (Δ p) V = \frac{Δ m}{M} R T$

In the initial condition (at STP)

$\frac{R T}{M} = \frac{p_{0}}{ρ}$

(T=273 K )

From Eqs. (i) and (ii), we get

$Δ m = \frac{ρ V Δ p}{P_{0}} = \frac{1.2 \times 0.4 \times 0.24}{1.0}$

=0.1152 kg =115.2 g

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