Molecular Speed Formula

The speed associated to a group of molecules in average. It is valid in ideal gas, where the molecules do not interact with each other.

Average molecular speed = Square root (3 (ideal gas constant) * (Temperature)/m)

The equation is:

v= √ (3 R T/m)

Where:

v: molecular speed

R: Ideal gas constant. (8.314 kg*m²/s²*mol*K)

T: Absolute Temperature in Kelvin.

m: molar mass

Molecular Speed Formula Questions:

1) If the temperature of a box full of particles of m=1gr/mol is 1000 K, what is the speed of those particles if do not interact with each other?

Answer:

The speed is found with the formula:

V= √ ( 3RT/m)

then,

v = √(3 (8.314 kg*m²/s²*mol*K *1000 K/(0.001 Kg/mol ))

v = 2883.4 m/s

2) The same box before, but at temperature of 50 K, what is the value of the speed, larger or shorter?

Answer:

The speed is found with the formula:

V= √ ( 3RT/m)

then,

v = √(3 (8.314 kg*m²/s²*mol*K *50 K/(0.001 Kg/mol ))

v = 644.7 m/s

As temperature is lower, the speed decreases.