This example problem demonstrates how to calculate the root mean square velocity of particles in an ideal gas.**Problem:**

What is the average velocity or root mean square velocity of a molecule in a sample of oxygen at 0 °C?**Solution**

The average velocity of gas particles is found using the root mean square velocity formula

μ_{rms} = (3RT/M)^{½}

where

μ_{rms} = root mean square velocity in m/sec

R = ideal gas constant = 8.3145 (kg·m^{2}/sec^{2})/K·mol

T = absolute temperature in Kelvin

M = mass of a mole of the gas in **kilograms**.

The temperature must be converted to Kelvins and the molar mass must be found in kg to complete this problem.**Step 1** Find absolute temperature

T = °C + 273

T = 0 + 273

T = 273 K**Step 2** Find molar mass in kg

From the periodic table, molar mass of oxygen = 16 g/mol.

Oxygen gas (O_{2}) is comprised of two oxygen atoms bonded together. Therefore:

molar mass of O_{2} = 2 x 16

molar mass of O_{2} = 32 g/mol

Convert this to kg/mol

molar mass of O_{2} = 32 g/mol x 1 kg/1000 g

molar mass of O_{2} = 3.2 x 10^{-2} kg/mol**Step 3** - Find μ_{rms}

μ_{rms} = (3RT/M)^{½}

μ_{rms} = [3(8.3145 (kg·m^{2}/sec^{2})/K·mol)(273 K)/3.2 x 10^{-2} kg/mol]^{½}

μ_{rms} = (2.128 x 10^{5} m^{2}/sec^{2})^{½}

μ_{rms} = 461 m/sec**Answer:**

The average velocity or root mean square velocity of a molecule in a sample of oxygen at 0 °C is 461 m/sec.