**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.