Root-Mean-Square Speed

The Molecular Speed of Gaseous Particles calculator uses the root-mean-square speed equation to compute the molecular speed based on the temperature, molar mass and the ideal gas constant.

INSTRUCTIONS: Choose units and enter the following:

• (T) Temperature of the gas
• (M) Molar mass

Molecular Speed (U): The calculator returns the speed in meters per second.  However, this can be automatically converted to compatible units via the pull-down menu.

Related Calculators

• Compute the Temperature of gas based on the Root-Mean-Square formula
• Compute the molecular speed of a gas based on the Root-Mean-Square formula
• Maxwell Molecular Speed
• R-Gas Constant with SI Units

The Math / Science

The Root-Mean-Square Speed formula for the molecular speed of gaseous particles is:

           `U =sqrt((3·R·T)/M)`

where:

• U is the molecular speed of gas particles
• T is the temperature
• M is molar mass
• R is the ideal gas constant (8.314 kg*m² / mol*K*s)

Reference

Whitten, et al. "Chemistry" 10th Edition. Pp. 433

UCDavis ChemWiki: Connecting Gas Properties to Kinetic Theory of Gases

Raymond A. Serway, Jerry S. Faughn, and Chris Vuille (2011). College Physics, Volume 1 (9th ed.). 9780840068484. p. 352.