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.

Understanding the kinetic-molecular theory of gases offers valuable insight into the microscopic behavior of gas particles. One fundamental aspect of this theory is the average kinetic energy of gas molecules. Kinetic energy refers to the energy that a particle has due to its motion, and can be expressed through the equation \( KE = \frac{1}{2}m v^2 \) where \( m \) stands for mass and \( v \) for velocity of a gas molecule.

In a sample of gas at a specific temperature, not all molecules move at the same speed nor do they have the same mass. However, the kinetic theory simplifies this by focusing on the average kinetic energy across all molecules. The key takeaway is that the average kinetic energy is directly proportional to the absolute temperature (measured in Kelvins), not dependent on the mass of the molecules as mistakenly indicated in some statements. This means that as temperature increases, so does the average kinetic energy of the gas molecules.

Gas molecules are in perpetual motion, which results in them frequently colliding with each other and the walls of their container. According to the kinetic-molecular theory, these collisions are perfectly elastic, meaning that no kinetic energy is lost during the collisions. Rather, kinetic energy is transferred between molecules or between molecules and the walls.

During these collisions, there are no lasting intermolecular forces acting; only instantaneous impacts are considered. This simplifies the behavior of gases considerably, allowing predictions about pressure, volume, and temperature relationships. Understanding the nature of these collisions is crucial when studying gas behavior as it explains why gases can expand to fill their containers and how they respond under different conditions.

When discussing gases, several intrinsic properties must be taken into account. These properties, as defined by the kinetic-molecular theory, include the assumption that gas particles are constantly in random motion and the volume occupied by the molecules themselves is minuscule compared to the overall volume of the gas. This gives rise to the 'ideal gas' behavior where the space between particles is so vast that they exert no significant attractive or repulsive forces on one another.

Furthermore, gas molecules are assumed to be point particles, meaning they do not take up space. This is an approximation, but it significantly simplifies calculations. The kinetic-molecular theory also explains that despite individual gas molecules having different velocities and kinetic energies, the overall distribution of speeds follows a recognizable pattern known as the Maxwell-Boltzmann distribution.

The kinetic energy of gas molecules is intimately linked with temperature. The kinetic-molecular theory shows that the temperature of a gas is a measure of its average kinetic energy per particle. This relationship is so critical that it can be used as a thermometer at the molecular level – by measuring the average kinetic energy, you can determine the temperature of the gas.

The temperature is proportional to the average kinetic energy, and the equation often used to express this relationship is \( KE_{avg} = \frac{3}{2} k T \) where \( KE_{avg} \) is the average kinetic energy of the gas molecules, \( k \) is the Boltzmann constant, and \( T \) is the absolute temperature in Kelvins. As the temperature increases, the average speed of the gas molecules increases as well, which results in greater kinetic energy. When working with gases, this concept is essential for understanding the interplay between heat, work, and energy in thermodynamic processes.