Average translational kinetic energy equals three halves kT, depending only on temperature.
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The average translational kinetic energy of a gas molecule is given by KE_avg = (3/2) kB T, or (3/2) RT per mole. This relation shows that the average kinetic energy depends only on the absolute temperature and not on the identity or mass of the gas. Two ideal gases at the same temperature therefore have the same average kinetic energy, even though their molecules move at different speeds. This principle is why temperature is a measure of molecular kinetic energy and why the kelvin scale is tied to an energy scale. The relation follows from the kinetic molecular theory of ideal gases.
Key ideas: Use KE per molecule = (3/2)kT and per mole = (3/2)RT, which is about 3.7 kJ per mole at 298 K. This counts only translation; diatomic and polyatomic molecules have additional rotational and vibrational energy. For monatomic gases, internal energy U = (3/2)nRT, and molar heat capacity Cv = (3/2)R = 12.47 J/(mol K).
Common mistakes and connections: A common mistake is believing heavier gases have more kinetic energy at the same temperature, or that doubling the Celsius temperature doubles the energy. Only kelvin works. Also, molecules in a sample have a range of energies; the formula gives the average. Links to rms speed, heat capacity and equipartition.
Average translational KE = 3/2 RT per mole depends only on temperature, not on the gas identity; 3.74 kJ/mol at 300 K. The interactive lesson shows this as a live animation or chart.
At 300 K the average kinetic energy of a gas molecule is about 6.2 × 10^-21 J.
Average translational kinetic energy equals three halves kT, depending only on temperature.
Average Kinetic Energy of Gas is a intermediate topic in States of Matter & Solutions. It builds on the vocabulary of beginner topics in this area.
Study these earlier topics in States of Matter & Solutions first: Effusion, Root Mean Square Speed, Maxwell-Boltzmann Distribution.
The next topics in States of Matter & Solutions are Molar Volume and Gas Density.
Yes. The interactive lesson includes a self-check question on Average Kinetic Energy of Gas, and the States of Matter & Solutions quiz draws on every topic in this area.
Average Kinetic Energy of Gas is topic 24 of 109 in States of Matter & Solutions.