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Calculate Root Mean Square Velocity of Gas Particles

Kinetic Theory of Gases Example

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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

μrms = (3RT/M)½

where
μrms = root mean square velocity in m/sec
R = ideal gas constant = 8.3145 (kg·m2/sec2)/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 (O2) is comprised of two oxygen atoms bonded together. Therefore:

molar mass of O2 = 2 x 16
molar mass of O2 = 32 g/mol

Convert this to kg/mol

molar mass of O2 = 32 g/mol x 1 kg/1000 g
molar mass of O2 = 3.2 x 10-2 kg/mol

Step 3 - Find μrms

μrms = (3RT/M)½
μrms = [3(8.3145 (kg·m2/sec2)/K·mol)(273 K)/3.2 x 10-2 kg/mol]½
μrms = (2.128 x 105 m2/sec2)½
μrms = 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.
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