Nitrogen gas is at 300ᵒC temperature. The temperature (in K) at which the rms speed of a H₂ molecule would be equal to the rms speed of a nitrogen molecule, is _______. (Round off to the nearest integer)
(Molar mass of N₂ gas 28 g).

Solution

Physics sir · 4 steps

Equal rms speeds means equal T/M, so convert 300°C to kelvin first and scale by the mass ratio.

1. Set speeds equal. The rms speed is vᵣₘₛ = √(3RT/M). Equal rms speeds means T/M must be the same for both gases.

   T_(H₂)/M_(H₂) = T_(N₂)/M_(N₂)

2. Kelvin first. The gas formula needs absolute temperature: T_(N₂) = 300 + 273 = 573 K. The molar masses are M_(H₂) = 2 g and M_(N₂) = 28 g.
3. Put in numbers. T_(H₂) = 573 × 2/28 = 573/14 = 40.93 K.
4. So. Hydrogen must be at about 40.93 K, which rounds to 41.

The common slip: 21. Using 300 instead of 573 K gives 300 × 2/28 = 21.4, about 21. Temperature must be in kelvin.

The idea to keep. Since vᵣₘₛ ∝ √(T/M), two gases have the same rms speed when T/M matches. A lighter gas needs a proportionally lower temperature, always in kelvin.

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