Diffusion: Effect of Relative Molecular Mass

Objective

Describe and explain the effect of relative molecular mass on the rate of diffusion of gases.

What is Diffusion?

Diffusion is the net movement of particles from a region of high concentration to a region of low concentration. This movement occurs because of the random motion of particles.

Factors Affecting Diffusion Rate

The rate of diffusion is influenced by several factors, including:

• Concentration Gradient: A steeper concentration gradient leads to a faster rate of diffusion.
• Temperature: Higher temperatures increase the kinetic energy of particles, resulting in faster movement and thus a faster diffusion rate.
• Size of Particles: Smaller particles diffuse faster than larger particles.
• Relative Molecular Mass: Gases with lower relative molecular masses diffuse faster than gases with higher relative molecular masses.

Effect of Relative Molecular Mass

The rate of diffusion of a gas is inversely proportional to the square root of its relative molecular mass (Mr). This means that as the relative molecular mass of a gas increases, its diffusion rate decreases.

Explanation:

Diffusion is driven by the kinetic energy of the particles. Kinetic energy is related to mass by the equation: $$KE = \frac{1}{2}mv^2$$, where KE is kinetic energy, m is mass, and v is velocity. Since velocity is proportional to the square root of mass (v = $\sqrt{\frac{2KE}{m}}$), a heavier molecule will have a lower velocity for the same kinetic energy. Therefore, lighter molecules move faster and diffuse more quickly.

Quantitative Relationship

The relationship between the rate of diffusion (r) and the relative molecular mass (Mr) can be expressed as:

$$r \propto \frac{1}{\sqrt{Mr}}$$

This can also be written as:

$$r = \frac{k}{\sqrt{Mr}}$$

where k is a constant of proportionality.

Example: Comparing Diffusion Rates

Consider the diffusion of nitrogen (N₂), oxygen (O₂), and carbon dioxide (CO₂) at the same temperature and pressure.

N₂ has an Mr of 28 g/mol, O₂ has an Mr of 32 g/mol, and CO₂ has an Mr of 44 g/mol.

Therefore, the rate of diffusion will be:

• CO₂ < O₂ < N₂

Table Summarizing Diffusion Rates

Gas	Relative Molecular Mass (Mr)	Relative Diffusion Rate
Carbon Dioxide (CO2)	44	Lowest
Oxygen (O2)	32	Intermediate
Nitrogen (N2)	28	Highest

Experimental Evidence

Experiments involving the diffusion of gases through porous barriers have demonstrated the effect of relative molecular mass on diffusion rate. The rate of diffusion is faster for gases with lower molecular masses.