Here's why:
* Kinetic Molecular Theory: This theory states that gas molecules are in constant random motion and their average kinetic energy is directly proportional to the absolute temperature.
* Kinetic Energy Equation: The kinetic energy (KE) of a gas molecule is given by: KE = (1/2)mv², where m is the mass and v is the velocity.
* Molar Mass and Velocity: Since the kinetic energy of all gas molecules at a given temperature is the same, heavier molecules (higher molar mass) will have a lower velocity to compensate for their greater mass.
Mathematical Representation:
The root-mean-square velocity (vrms) of gas molecules is given by:
vrms = √(3RT/M)
Where:
* R is the ideal gas constant
* T is the absolute temperature
* M is the molar mass
This equation clearly shows the inverse relationship between velocity and molar mass.
Implications:
* Diffusion: Lighter gases diffuse faster than heavier gases because their molecules move faster.
* Effusion: The rate of effusion (the passage of gas molecules through a small hole) is also inversely proportional to the square root of the molar mass. This is known as Graham's law of effusion.
Example:
Hydrogen gas (H2, molar mass = 2 g/mol) will have a higher velocity than oxygen gas (O2, molar mass = 32 g/mol) at the same temperature. This is why hydrogen gas escapes from a container faster than oxygen gas.
