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JEE MainPhysicsKinetic Theory of Gases

At a certain temperature, the root mean square (r.m.s) speed of an unknown gas is twice the r.m.s speed of sulphur dioxide ( SO ₂ ) gas at the same temperature. The molar mass of the unknown gas is (Given: Atomic mass of S = 32 u , O = 16 u )

Options

  1. A16 g mol ⁻¹
  2. B32 g mol ⁻¹
  3. C128 g mol ⁻¹
  4. D256 g mol ⁻¹

Correct answer

A. 16 g mol ⁻¹

Step-by-step solution

The root mean square speed of a gas is given by v_ rms = 3RT M . At a constant temperature, v_ rms 1 M . Let the unknown gas be denoted by subscript 1 and SO ₂ by subscript 2 . The molar mass of SO ₂ is M₂ = 32 + 2(16) = 64 g mol ⁻¹ . Taking the ratio of their r.m.s speeds: v₁ v₂ = M₂ M₁ Given that v₁ = 2v₂ , we have: 2 = 64 M₁ Squaring both sides: 4 = 64 M₁ M₁ = 64 4 = 16 g mol ⁻¹ . Answer: 16 g mol ⁻¹

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