Molecular Speed Calculator

Formula

To calculate molecular speed:

\[ V = \sqrt{\frac{3RT}{M}} \]

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)

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 in 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.

Example Calculation

Let's assume the following values:

Temperature (\( T \)) = 300 K
Molar Mass (\( M \)) = 0.028 kg/mol (for nitrogen gas)

Using the formula:

\[ V = \sqrt{\frac{3 \times 8.3145 \times 300}{0.028}} \approx 517.97 \text{ m/s} \]

The molecular speed is approximately 517.97 m/s.