An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen....

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature

27^{\circ} \mathrm{C}

. The mass of the oxygen withdrawn from the cylinder is nearly equal to : [Given,

R=\frac{100}{12} \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}

, and molecular mass of

O_2=32,1 \mathrm{~atm}

pressure

\left.=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}\right]

Options

A $0.125 \mathrm{~kg}$
B $0.144 \mathrm{~kg}$
C $0.116 \mathrm{~kg}$
D $0.156 \mathrm{~kg}$

Correct answer

C. $0.116 \mathrm{~kg}$

Step-by-step solution

\begin{aligned} & \mathrm{n}_{\mathrm{f}}=\frac{\mathrm{P}_{\mathrm{f}} \mathrm{V}}{\mathrm{RT}} \quad\left[\mathrm{P}_{\mathrm{abs}}=12 \mathrm{ atm}\right] \\ & =\frac{12 \times 1.01 \times 10^5 \times 30 \times 10^{-3}}{\left(\frac{100}{12}\right) \times 300} \\ & =14.544 \\ & \therefore \text{ moles removed }=18.2-14.544=3.656 \\ & \therefore \text{ mass removed }=3.656 \times \frac{32}{1000} \mathrm{ kg}=0.116 \mathrm{ kg}\end{aligned}

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