Q1. Find the rms speed of oxygen molecules (M = 32 g/mol) at 300 K.
v_rms = √(3RT/M) = √(3 × 8.314 × 300 / 0.032)
v_rms = √(233 831)
v_rms ≈ 484 m/s
Kinetic Theory — Class 11
A gas is just countless tiny particles in motion. Connect pressure and temperature to molecular speeds and compute the rms speed.
Ideal gas equationPV = nRT (R = 8.314 J/mol·K). Real gases obey it well at low pressure and high temperature.
Kinetic interpretationPressure comes from molecular collisions with the walls; temperature is proportional to the average kinetic energy of molecules.
RMS speedThe root-mean-square molecular speed v_rms = √(3RT/M), where M is the molar mass. Lighter/hotter gases move faster.
Degrees of freedomWays a molecule can store energy (translational, rotational…). Each contributes ½kT (law of equipartition).
RMS-speed calculator Interactive
Enter the temperature and molar mass of a gas to find the root-mean-square speed of its molecules.
RMS speed, √(3RT/M)—m/s
At room temperature oxygen molecules zip along at nearly 480 m/s — faster than a passenger jet.
Numericals practice Interactive
RMS-speed and ideal-gas problems with steps.
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Solved numericals
Q2. At what temperature is the average KE of a molecule 6.21×10⁻²¹ J? (k = 1.38×10⁻²³)
KE = (3/2)kT ⇒ T = 2KE/(3k)
T = 2 × 6.21×10⁻²¹ / (3 × 1.38×10⁻²³)
T = 300 K
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Ideal gas equation | P V = n R T | — |
| RMS speed | v_rms = √(3RT/M) | m/s |
| Average KE per molecule | (3/2) k T | J |
| Pressure (kinetic) | P = (1/3) ρ v_rms² | Pa |
Common mistakes & exam wins
- Temperature (in kelvin) is directly proportional to the average kinetic energy of molecules.
- v_rms ∝ √T and v_rms ∝ 1/√M — lighter gases and hotter gases move faster.
- Always use kelvin for T and kg/mol for M in v_rms = √(3RT/M).
- At absolute zero (0 K) molecular motion (kinetic energy) would theoretically stop.
Frequently asked questions
What is the ideal gas equation?
PV = nRT, relating pressure, volume, amount (moles) and temperature of an ideal gas, with R = 8.314 J/mol·K.
What is rms speed?
The root-mean-square speed of gas molecules, v_rms = √(3RT/M); it increases with temperature and decreases with molar mass.
How is temperature related to molecular motion?
The absolute temperature is directly proportional to the average translational kinetic energy of the molecules.