Question

The number of collisions of \(\mathrm{Ar}\) atoms with the walls of container per unit time (a) increases when the temperature increases. (b) remains the same when \(\mathrm{CO}_{2}\) is added to the container at constant temperature. (c) increases when \(\mathrm{CO}_{2}\) is added to the container at constant temperature. (d) decreases, when the average kinetic energy per molecule is decreased.

Short answer

The number of collisions of \(\text{Ar}\) atoms with the walls per unit time (a) increases when the temperature increases, (b) remains the same when \(\text{CO}_{2}\) is added at constant temperature, (c) does not increase when \(\text{CO}_{2}\) is added at constant temperature (only considering \(\text{Ar}\) atoms), (d) decreases when the average kinetic energy per molecule is decreased.

Step-by-step solution

Understanding the Kinetic Theory of Gases

The key to understanding how the number of collisions of gas atoms with the walls of a container changes is the kinetic theory of gases. This theory tells us that the pressure exerted by a gas in a container is due to collisions of the gas particles with the container walls. The frequency of these collisions, and hence the pressure, is influenced by factors such as temperature and the number of particles in the container.

Analyzing the Effect of Temperature Increase

When the temperature of a gas increases, the average kinetic energy of its particles increases as well. Since the particles are moving faster, they collide more frequently with the container walls. Therefore, the number of collisions per unit time increases with an increase in temperature.

Determining the Impact of Adding \(\text{CO}_{2}\) at Constant Temperature

Adding \(\text{CO}_{2}\) gas to the container at constant temperature does not alter the average speed (and thus the kinetic energy) of the original \(\text{Ar}\) atoms. Although the total number of molecules inside the container increases, this by itself doesn’t affect the frequency of collisions of the \(\text{Ar}\) atoms per unit time with the walls. The collision rate per unit time of \(\text{Ar}\) remains the same. However, the overall collision rate considering both \(\text{Ar}\) and \(\text{CO}_{2}\) would increase.

Evaluating the Effect of Decreasing Kinetic Energy Per Molecule

If the average kinetic energy per molecule decreases, it means that the molecules are moving slower. Slower-moving particles will collide with the container walls less frequently, resulting in fewer collisions per unit time. Consequently, the number of collisions of gas atoms with the walls of the container decreases when the average kinetic energy per molecule is decreased.

Key concepts

Gas Molecules Collisions

The kinetic theory of gases gives us vital insights into the microscopic behavior of gas molecules. According to this theory, gas pressure is the result of countless tiny collisions between the gas molecules and the walls of their container.

Imagine a room full of bouncing balls, each ball representing a molecule. As the balls bounce off the walls, they exert a force, much like how gas molecules do. The number of times these balls hit the walls in a second represents the collision frequency. Naturally, more bouncing balls (gas molecules) or faster balls (higher temperatures) lead to more frequent collisions, thus greater pressure.

Effect of Temperature on Gas Pressure

Temperature plays a crucial role in the behavior of gases. A rise in temperature adds energy to the gas molecules, which makes them move faster. The faster they move, the more often they will hit the container walls.

Think of this in terms of a heated game of ping-pong where players hit the ball harder (increased temperature) causing more frequent hits on the table sides (container walls). This ramp-up in activity corresponds to an increased pressure. It’s a direct reflection of the increased kinetic energy and collision frequency of the molecules.

Impact of Gas Addition on Collision Frequency

When more gas is added to a container, at a constant temperature, you might think that this creates a crowded environment leading to a dramatic increase in collision frequency. However, if we're only interested in the original gas—for instance, Ar in our scenario—their individual collision frequency remains constant. The newcomers, CO2 molecules, will contribute to the total pressure, but won't affect the Ar molecules' behavior unless they change the volume or the temperature of the container.