Indicate which of the following statements regarding the kinetic-molecular theory of gases are correct. (a) The average kinetic energy of a collection of gas molecules at a given temperature is proportional to m^1/2. (b) The gas molecules are assumed to exert no forces on each other. (c) All the molecules of a gas at a given temperature have the same kinetic energy. (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained. (e) All gas molecules move with the same speed if they are at the same temperature.

Verified step by step guidance

1. Identify the key terms in the statement: 'average kinetic energy' and 'proportional to m1>2'.
2. Recall the kinetic-molecular theory of gases, which states that the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.
3. Understand that the average kinetic energy of gas molecules is given by the equation \( KE_{avg} = \frac{3}{2}kT \), where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.
4. Analyze the statement 'proportional to m1>2'. This seems to suggest a dependence on mass, which is incorrect according to the kinetic-molecular theory. The theory states that kinetic energy depends on temperature, not mass.
5. Conclude that the statement is incorrect as it misrepresents the dependence of kinetic energy on mass rather than temperature.

Key Concepts

Kinetic-Molecular Theory

The kinetic-molecular theory explains the behavior of gases in terms of particles in constant motion. It posits that gas molecules are in continuous, random motion and that their collisions with each other and the walls of their container are elastic. This theory helps to understand properties such as pressure, temperature, and volume in gases.

Average Kinetic Energy

The average kinetic energy of gas molecules is directly related to the temperature of the gas. According to the kinetic-molecular theory, as the temperature increases, the average kinetic energy of the molecules also increases. This relationship is expressed mathematically as KE = (3/2)kT, where k is the Boltzmann constant and T is the temperature in Kelvin.

Proportional Relationships

In the context of the kinetic-molecular theory, the average kinetic energy is proportional to the absolute temperature of the gas, not to the mass of the molecules squared. This means that while the kinetic energy depends on temperature, it does not directly depend on the mass of the gas molecules, which is a common misconception.