Question

At room temperature the rms speed of the molecules of a certain diatomic gas is found to be 1920 m/s.The gas is
(1) H2
(2)F2
(3) Cl2
(4) O2

Answer 1

Answer on Question #42743, Physics, Molecular Physics — Thermodynamics

At room temperature the rms speed of the molecules of a certain diatomic gas is found to be 1920 m/s.The gas is (1) H2 (2)F2 (3) Cl2 (4) O2

Solution

Let is find the mass of molecula of this gas

$v_{rms}=\sqrt{\frac{3kT}{m}}$

$m=\frac{3kT}{v_{rms}^{2}}$

where $T=293K$ is room temperature, $k=1.38\cdot 10^{-23}J\cdot K^{-1}$ is Boltzmann constant.

$m=\frac{3\cdot 1.38\cdot 10^{-23}\cdot 293}{1920^{2}}\approx 3.29\cdot 10^{-27}\,kg\approx 2u$

This corresponds to molecula of $H_{2}$.