5.6
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision
The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For ex…
While the gas laws summarize the relationships between different properties of ideal gases, the kinetic molecular theory explains why gases follow the laws. The theory is based on a few assumptions or postulates.
The first assumption is that gas particles are negligible in size. A gas is mostly empty space comprised of small particles that are separated at distances far greater than their own dimensions. Their combined volume is negligible relative to the total volume in which the gas is contained.
Contrary to solids and liquids, which are incompressible due to their close interparticle spacing, gases are highly compressible.
Gas particles are in a constant state of motion along straight lines in random directions. Their paths only change when they collide with other particles or with the walls of their container.
The second assumption is that gas particles have perfectly elastic collisions. They collide and bounce off each other without sticking together. This can be compared to the collisions between billiard balls during a game of pool.
When gas particles collide, they exchange energy with each other, but there is no net loss of energy. In other words, the total energy of the system stays constant.
Gas particles are constantly moving; therefore, they possess kinetic energy. Thus, the third assumption states that the average kinetic energy of a gas is proportional to its absolute temperature in kelvin.
This means that kinetic energy increases with temperature, and consequently, the particles move faster. At higher temperatures, their velocity increases.
Conversely, as the temperature decreases, so does the kinetic energy of the particles, and they move more slowly.
At a given temperature, all gases, regardless of their molecular mass, have the same average kinetic energy. Kinetic energy is equal to ½ mass times velocity squared. Thus, for different gases to have the same average kinetic energy, their gas particles must travel at different average velocities. Therefore, heavier gases have lower average velocities, while lighter gases have higher average velocities.
For example, helium and neon, when at the same temperature, have the same average kinetic energy. However, due to the difference in their masses, the neon atoms move much slower than the helium atoms.
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Q1: Why is gas considered mostly empty space?
Gas particles are negligibly small compared to the distances separating them. In argon gas at standard conditions, only 0.01% of volume is occupied by atoms, with average spacing of 3.3 nm between particles versus an atomic radius of 0.097 nm. This vast separation makes the combined volume of all gas particles negligible relative to the container's total volume, explaining why gases are highly compressible unlike solids and liquids.
Q2: What happens to gas particles during elastic collisions?
During elastic collisions, gas particles exchange energy without losing any to the system. Like billiard balls bouncing off each other, particles collide and bounce apart without sticking together. The total kinetic energy remains constant throughout these collisions, and particles change direction only upon impact with other particles or container walls while traveling in straight lines between collisions.
Q3: How does temperature relate to gas particle kinetic energy?
The average kinetic energy of gas particles is directly proportional to absolute temperature in kelvin. As temperature increases, particles move faster and possess greater kinetic energy. Conversely, decreasing temperature reduces kinetic energy and particle velocity. At the same temperature, all gases have identical average kinetic energy regardless of molecular mass, though heavier gases move slower than lighter ones.
Q4: Why do different gases have different average velocities at the same temperature?
Since kinetic energy equals one-half mass times velocity squared, gases with different molecular masses must travel at different velocities to maintain equal average kinetic energy. Heavier gas particles move slower while lighter particles move faster. For example, helium atoms move much faster than neon atoms at identical temperatures because helium has lower mass.
Q5: How does kinetic molecular theory explain gas pressure?
Gas pressure results from collisions between gas molecules and container walls. Since molecules exert no attractive or repulsive forces on each other or walls, their collisions are elastic and transfer momentum to the walls. The constant random motion and frequent wall collisions of gas particles generate the measurable pressure exerted by the gas on its container.
Q6: What is the relationship between gas compressibility and particle spacing?
Gases are highly compressible because particles are separated by distances far greater than their own dimensions, leaving abundant empty space. When external pressure increases, particles can move closer together without significant resistance. In contrast, solids and liquids are incompressible because their particles are already closely spaced with minimal empty space available for compression.
Q7: How do the postulates of kinetic molecular theory connect to observable gas behavior?
The three postulates—negligible particle size, elastic collisions, and temperature-dependent kinetic energy—explain why gases follow empirical gas laws. These postulates, developed from hundreds of experimental observations, provide the microscopic foundation for understanding macroscopic gas properties. Kinetic molecular theory and gas laws explain properties of gas molecules at both molecular and observable levels.