average kinetic energy
Summary
Average kinetic energy is the mean translational energy of the particles in a sample, equal to (3/2)kBT for an ideal gas. It is proportional to absolute temperature in kelvins and does not depend on the gas's identity or mass, so at the same T lighter molecules move faster.
Detail
Meaning: In kinetic molecular theory, temperature measures the average translational kinetic energy of the particles. Individual molecules have a spread of speeds (the Maxwell-Boltzmann distribution), and the average KE describes the distribution as a whole. Raising T shifts the curve to the right and flattens and broadens it. Different ideal gases at the same temperature have the same average KE, so the lighter gas has the higher typical speed.
Equation: KEavg = (3/2)kBT = ½m(urms)², or (3/2)RT per mole. KEavg is in J, kB is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is absolute temperature in K, m is the mass of one molecule in kg, urms is the root-mean-square speed in m/s, and R = 8.314 J/(mol·K). Also urms = √(3RT/M), with M the molar mass in kg/mol.
On the MCAT: A passage gives Maxwell-Boltzmann curves or a table of gases at one temperature, and you compare speeds, KE, or the fraction of molecules above an activation energy. Doubling the Kelvin temperature doubles KEavg. Going from 300 K to 600 K does this; going from 27 °C to 54 °C does not.
Common confusion: Equal average KE does not mean equal speed. Because KE = ½mv², a lighter gas such as H₂ moves faster than O₂ at the same T. Always convert to kelvins before using ratios.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
- Physical Chemistry (Atkins)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.