Diffusion is the spontaneous dispersal of particles, driven by their random, constant motion. While temperature and physical state are primary factors influencing the rate of this process, the intrinsic mass of the particles themselves plays a critical role. Within the IGCSE 0654 Extended syllabus, it is necessary to explain why lighter gas molecules diffuse faster than heavier ones, utilizing the principles of kinetic energy and molecular velocity.

To understand why mass affects diffusion, we must examine the relationship between temperature and kinetic energy.

Constant Kinetic Energy

At a specific temperature, all gas particles in a mixture—regardless of their identity or mass—possess the same average kinetic energy. Temperature is effectively a macroscopic measure of this microscopic energy.

The Relationship Formula

The kinetic energy ($E_k$) of a moving particle is defined by the equation:

• $m$: Mass of the particle.
• $v$: Velocity (speed) of the particle.

The Statistical Outcome

Because $E_k$ is constant for all particles at a given temperature, the mass ($m$) and velocity ($v$) are inversely proportional.

• Lighter Particles: Have a small mass. To have the same kinetic energy as a heavy particle, they must possess a significantly higher velocity.
• Heavier Particles: Have a larger mass. Consequently, they move at a lower velocity while possessing the same energy.

Since diffusion is the result of particles moving from one location to another, the speed of individual particles directly dictates the speed of the overall dispersal.

• Faster Velocity = Faster Diffusion: Lighter molecules cover more distance per unit time and collide more frequently, leading to a more rapid net movement away from the source of high concentration.

The classic laboratory demonstration of this principle involves the reaction between Ammonia gas ($NH_3$) and Hydrogen Chloride gas ($HCl$).

The Experiment

1. Concentrated ammonia and concentrated hydrochloric acid are placed on cotton wool plugs at opposite ends of a long glass tube.
2. The two gases diffuse toward each other.
3. When they meet, they react to form a white cloud of solid ammonium chloride ($NH_4Cl$).

The Observation and Explanation

The white ring forms closer to the hydrochloric acid end of the tube.

• Ammonia ($NH_3$): Relative Molecular Mass ($M_r$) = 17.
• Hydrogen Chloride ($HCl$): Relative Molecular Mass ($M_r$) = 36.5.
• Conclusion: Ammonia is roughly half the mass of hydrogen chloride. Because it is lighter, ammonia molecules move faster and travel a greater distance down the tube in the same amount of time than the heavier $HCl$ molecules.

The rate of diffusion is a direct physical manifestation of the $E_k = \frac{1}{2}mv^2$ relationship. By recognizing that lower relative molecular mass leads to higher molecular velocity, we can predict the behavior of gaseous mixtures in both industrial processes and biological systems. This principle, known formally as Graham's Law, is a cornerstone of gaseous kinematics.