Two 112-L tanks are filled with gas at 330 K. One contains 5.00 mol of Kr, and the other contains 5.00 mol of O₂. Considering the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties. (a) Collision frequency

Verified step by step guidance

1. Identify the molecular masses of the gases: Krypton (Kr) has a molecular mass of approximately 83.8 g/mol, and Oxygen (O2) has a molecular mass of approximately 32.0 g/mol.
2. Recall that collision frequency is influenced by the speed of the gas molecules, which is inversely proportional to the square root of their molecular masses (according to the formula for root mean square speed, $v_{rms} = \sqrt{\frac{3RT}{M}}$, where R is the gas constant, T is the temperature, and M is the molar mass).
3. Calculate the root mean square speed for each gas using the formula, substituting the respective molar masses and the given temperature (330 K).
4. Compare the calculated speeds: The gas with the higher speed will have a higher collision frequency because faster-moving molecules collide more frequently.
5. Rank the gases from low to high collision frequency based on the speeds calculated.

Key Concepts

Kinetic-Molecular Theory

Kinetic-molecular theory explains the behavior of gases in terms of particles in constant motion. It posits that gas particles are far apart, move randomly, and collide elastically. This theory helps in understanding properties like pressure, temperature, and volume, as well as how these factors influence the frequency of collisions between gas molecules.

Collision Frequency

Collision frequency refers to the number of collisions that occur between gas molecules in a given volume over a specific time period. It is influenced by factors such as the speed of the molecules, their density, and the size of the molecules. Gases with higher molecular speeds or greater densities will have higher collision frequencies, impacting their behavior in a confined space.

Molecular Mass and Speed

The molecular mass of a gas affects its average speed at a given temperature, as described by the equation for root mean square speed. Lighter gases, like Kr, will generally move faster than heavier gases, like O2, at the same temperature. This difference in speed influences the collision frequency, as faster-moving molecules collide more often.