NEET · Physics · STD 11 - 12 . kinetic theory of gases

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 After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature \(27^{\circ} C\). The mass of the oxygen withdrawn from the cylinder is nearly equal to:
[Given, \(R=\frac{100}{12} J mol ^{-1} K^{-1}\), and molecular mass of \(O_2=32,1\) atm pressure \(=1.01 \times 10^5 N / m\)]

A \(0.125 \text{ kg}\)
B \(0.144 \text{ kg}\)
C \(0.116 \text{ kg}\)
D \(0.156 \text{kg}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(0.116 \text{ kg}\)

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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