Kinetic Theory of an Ideal Gas

A mole is the amount of substance containing the same number of elementary entities as atoms in 12 grams of carbon-12. Avogadro's number, approximately 6.02 × 10²³ mol⁻¹, represents the number of molecules or atoms in one mole. This constant relates the mass of a substance in grams to the number of particles it contains, making it fundamental for converting between macroscopic and molecular scales.

Molar mass is the mass of one mole of a compound, expressed in grams per mole. It numerically equals the sum of atomic masses of all atoms in a molecule. For example, the molar mass of carbon-12 is 12 grams per mole. Molar mass allows chemists to convert between the number of moles and the mass of a substance in laboratory and theoretical calculations.

Kinetic molecular theory assumes gas molecules are identical point particles obeying Newton's laws in random, isotropic motion. The total volume of molecules is negligible compared to the container volume. Collisions between molecules and container walls are perfectly elastic, resulting in no net energy loss. External forces like gravity and intermolecular attractions are negligible, allowing the theory to explain gas behavior at the molecular level.

Gas molecules are treated as point particles because their total volume is extremely small compared to the container volume. This approximation simplifies calculations and is valid because the average distance between molecules far exceeds their individual size. By neglecting molecular volume, kinetic theory can focus on molecular motion and collisions as the primary factors determining gas properties.

Elastic collisions mean that when gas molecules collide with each other or container walls, kinetic energy is conserved with no net energy loss. The total kinetic energy before and after collision remains constant, though energy may be redistributed among molecules. This assumption is crucial for kinetic theory because it ensures gas molecules maintain their motion indefinitely without slowing down due to friction or energy dissipation.

The unified atomic mass unit (u), or dalton, relates molecular mass to molar mass through Avogadro's number. One atomic mass unit is defined such that a carbon-12 atom has a mass of exactly 12 u. When multiplied by Avogadro's number, the atomic mass in daltons numerically equals the molar mass in grams per mole, providing a direct bridge between atomic and macroscopic scales.

Random, isotropic motion means gas molecules move continuously in all directions with no preferred orientation. This assumption ensures that molecular motion is uniform throughout the container and that pressure is exerted equally on all walls. The randomness and isotropy of molecular motion are essential for kinetic theory to predict macroscopic gas properties like pressure and temperature from molecular behavior.