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?

• A. 20 cm/s
• B. 0.2 cm/s
• C. 200 cm/s
• D. 2 cm/s

Answer: (C)

Verified step by step guidance

1. Recall that the diffusion rate of a gas molecule in air depends on factors such as temperature, pressure, and the molecular properties of the gas, but at STP (standard temperature and pressure), typical diffusion rates for small molecules like O_2 are on the order of hundreds of centimeters per second.
2. Understand that diffusion rate here refers to the average speed at which gas molecules spread out through air, which is related to their root mean square (rms) speed derived from the kinetic molecular theory.
3. 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.
4. 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.
5. Compare the given options with this understanding: 0.2 cm/s and 2 cm/s are too slow, 20 cm/s is somewhat low, and 200 cm/s aligns well with typical diffusion rates for O_2 in air at STP.