At standard temperature and pressure (STP), which of the following is a likely average diffusion rate for a typical gas molecule such as O_2 in air?

Use the kinetic molecular theory formula for the root mean square speed: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(R\) is the gas constant, \(T\) is the temperature in Kelvin, and \(M\) is the molar mass of the gas in kilograms per mole. This speed gives an estimate of how fast molecules move on average.

Recognize that typical rms speeds for oxygen molecules at room temperature (close to STP) are on the order of hundreds of meters per second, but diffusion rates are slower due to collisions and the random walk nature of diffusion, resulting in average diffusion rates on the order of hundreds of centimeters per second.