Enter the molar mass and the temperature of the gas into the calculator to determine the root mean square molecular speed.

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## Molecular Speed Formula

The following formula is used to calculate molecular speed.

V = SQRT ( 3*R*T / M)

- Where V is the root mean square molecular speed (m/s)
- R is the gas constant (8.3145 J/mol/K)
- T is the temperature (k)
- M is the molar mass kg/mol

To calculate a molecular speed, multiply 3 times the gas constant times the temperature, divide by the molar mass, then take the square root of this result.

## What is molecular speed?

Molecular speed is a measure of the average velocity of a group of particles within a gas.

According to Kinetic Molecular Theory, all gas particles are at a random motion and velocity when their temperature is above 0, so it’s impossible to know any particle’s exact velocity, but the average velocity of all particles can be calculated.

## How to calculate molecular speed?

**Example Problem: **

The following example problem outlines the steps and information required to calculate molecular speed.

First, determine the temperature of the gas. In this example, the gas has a temperature of 500 degrees Kelvin.

Next, determine the molar mass of the gas. In this example, the molar mass is equal to .0023 kg /mol.

Finally, using the formula above, along with the gas constant, calculate the molecular speed.

V = SQRT ( 3*R*T / M)

V = SQRT ( 3*8.3145*500 / .0023)

V = 2328.62 m/s