kinetic theory of gases

Meaning: The model explains gas behavior from particle motion. Particles move constantly and randomly, have negligible volume, exert no attractive or repulsive forces on each other, and collide elastically, losing no kinetic energy. Pressure comes from wall collisions. Absolute temperature measures average kinetic energy.

Equation: KEavg = ½mv²rms = (3/2)kBT, so vrms = √(3RT/M). KEavg is average kinetic energy per particle (J), m is particle mass (kg), vrms is root-mean-square speed (m/s), kB is Boltzmann's constant (1.38 × 10⁻²³ J/K), T is temperature (K), R is 8.314 J/(mol·K), and M is molar mass (kg/mol).

On the MCAT: Compare gases at one temperature: average kinetic energy is equal, but lighter gases move faster and effuse faster (Graham's law, rate ∝ 1/√M). On Maxwell-Boltzmann curves, raising T shifts the peak to higher speed and broadens the curve. Raising T at constant volume raises pressure because particles strike the walls harder and more often. Real gases deviate from the model at high pressure and low temperature.

Common confusion: Equal temperature means equal average kinetic energy, not equal speed. At the same T, the heavier gas is slower. Also, use kelvins, not Celsius, in these relations.