Chemistry - Ideal Gas Question with Solution | TestHub

The root mean square (RMS) velocity of gas molecules is given by the formula:

$$v_{rms}=\sqrt{\frac{3RT}{M}}$$

where $R$ is the ideal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass of the gas.

At STP (Standard Temperature and Pressure), $T$ is constant. Therefore, $v_{rms}\propto \frac{1}{\sqrt{M}}$.

This means that the gas with the smallest molar mass will have the highest RMS velocity.

Let's calculate the molar masses:

H₂: $2\times 1.008=2.016$ g/mol

N₂: $2\times 14.01=28.02$ g/mol

O₂: $2\times 16.00=32.00$ g/mol

HBr: $1.008+79.90=80.908$ g/mol

Arranging them in decreasing order of RMS velocity (increasing order of molar mass):

H₂ (2.016 g/mol) > N₂ (28.02 g/mol) > O₂ (32.00 g/mol) > HBr (80.908 g/mol)

Thus, the decreasing order of root mean square velocity is H₂ > N₂ > O₂ > HBr.