Final answer:
The root mean square (rms) speed of a molecule in a gas is calculated as the square root of the average of the squares of the molecule's speeds, providing an average speed that correlates with the molecule's kinetic energy under standard conditions.
Step-by-step explanation:
The root mean square (rms) speed of a molecule in a gas is a measure of the molecule's average speed. It is calculated as the square root of the average of the squares of the velocities of the molecules in the gas sample. One can determine the rms speed from the kinetic energy K of a molecule in an ideal gas, which is proportional to its mass m, the square of its speed v, and the temperature T of the gas.
The rms speed is typically associated with the Maxwell-Boltzmann distribution, which predicts a distribution of molecular speeds in a gas, where the motion of individual molecules is random but the overall distribution is predictable. The rms speed is important because it is related to a molecule's kinetic energy, helping us understand the thermodynamic properties of gases. This concept is particularly useful under standard conditions of temperature and pressure (STP), which are 273.15 K and 1 atm.