If the r. m.s speed of chlorine molecule is 490 m / s at 27° C, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon =39.9 u, molecular mass of chlorine =70.9 u )

Solution

Physics sir · 3 steps

Same temperature, so only the mass changes: rms speed goes as one over the square root of molar mass.

1. Rms speed formula. For any ideal gas, vᵣₘₛ = √(3RT/M). Both gases are at 27°C, so 3RT is the same for both and cancels when you take a ratio.

   v_(Ar)/v_(Cl₂) = √(M_(Cl₂)/M_(Ar))

2. Put in numbers. Argon is monatomic, so its molar mass is 39.9. The ratio is 70.9/39.9 = 1.777, and √1.777 ≈ 1.33. Argon is lighter, so it moves faster.
3. So. v_(Ar) = 490 × 1.33 ≈ 651.7 m s⁻¹, which is option (d). With more decimal places you get about 653 m s⁻¹, and (d) is still the closest option by far.

The idea to keep. At a fixed temperature, vᵣₘₛ ∝ 1/√M. The lighter gas is always faster, so check which way your answer moves before you calculate.

Answer from the NTA final answer key. Solution by PrepWiser.