COMEDK · Physics · 14. Kinetic Theory of Gases

Find the mass of oxygen gas with which \(1.882 \times 10^{23}\) degrees of freedom are associated at N.T.P.
Given: Molar mass of diatomic gas, oxygen is \(32\ g\ mol^{-1}\) and oxygen molecule possess three translational and two rotational degrees of freedom.

A \(16\)g
B \(5\)g
C \(2\)g
D \(32\)g

Verified Solution

Answer & Solution

Correct Answer

(C) \(2\)g

Step-by-step Solution

Detailed explanation

Total degrees of freedom of the gas = \(1.882 \times 10^{23}\) Degrees of freedom per oxygen molecule = \(3\) (translational) + \(2\) (rotational) = \(5\) Number of oxygen molecules = \(\dfrac{1.882 \times 10^{23}}{5} = 0.3764 \times 10^{23}\) Number of moles of oxygen gas =…

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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Find the mass of oxygen gas with which \(1.882 \times 10^{23}\) degrees of freedom are associated at N.T.P.Given: Molar mass of diatomic gas, oxygen is \(32\ g\ mol^{-1}\) and oxygen molecule possess three translational and two rotational degrees of freedom.

Step-by-step Solution

Find the mass of oxygen gas with which \(1.882 \times 10^{23}\) degrees of freedom are associated at N.T.P.
Given: Molar mass of diatomic gas, oxygen is \(32\ g\ mol^{-1}\) and oxygen molecule possess three translational and two rotational degrees of freedom.