Science, Tech, Math › Science Calculate Root Mean Square Velocity of Gas Particles Kinetic Theory of Gases RMS Example Share Flipboard Email Print Blend Images / Eric Raptosh Photography / Getty Images Science Chemistry Chemical Laws Basics Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate By Todd Helmenstine Todd Helmenstine is a science writer and illustrator who has taught physics and math at the college level. He holds bachelor's degrees in both physics and mathematics. our editorial process Todd Helmenstine Updated January 30, 2020 This example problem demonstrates how to calculate the root mean square (RMS) velocity of particles in an ideal gas. This value is the square root of the average velocity-squared of molecules in a gas. While the value is an approximation, especially for real gases, it offers useful information when studying kinetic theory. Root Mean Square Velocity Problem What is the average velocity or root mean square velocity of a molecule in a sample of oxygen at 0 degrees Celsius? Solution Gases consist of atoms or molecules that move at different speeds in random directions. The root mean square velocity (RMS velocity) is a way to find a single velocity value for the particles. The average velocity of gas particles is found using the root mean square velocity formula: μrms = (3RT/M)½μrms = root mean square velocity in m/secR = ideal gas constant = 8.3145 (kg·m2/sec2)/K·molT = absolute temperature in KelvinM = mass of a mole of the gas in kilograms. Really, the RMS calculation gives you root mean square speed, not velocity. This is because velocity is a vector quantity that has magnitude and direction. The RMS calculation only gives the magnitude or speed. The temperature must be converted to Kelvin and the molar mass must be found in kg to complete this problem. Step 1 Find the absolute temperature using the Celsius to Kelvin conversion formula: T = °C + 273T = 0 + 273T = 273 K Step 2 Find molar mass in kg:From the periodic table, the 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 16molar mass of O2 = 32 g/molConvert this to kg/mol:molar mass of O2 = 32 g/mol x 1 kg/1000 gmolar mass of O2 = 3.2 x 10-2 kg/mol Step 3 Find μrms: μrms = (3RT/M)½μrms = [3(8.3145 (kg·m2/sec2)/K·mol)(273 K)/3.2 x 10-2 kg/mol]½μrms = (2.128 x 105 m2/sec2)½μrms = 461 m/sec Answer The average velocity or root mean square velocity of a molecule in a sample of oxygen at 0 degrees Celcius is 461 m/sec.