Determine whether each of the following changes will increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: (a) increasing the volume of the container, \((\mathbf{b})\) increasing the temperature, (c) increasing the molar mass of the gas.

When the volume of the container increases, the gas molecules will have more space to move around. According to the ideal gas law, when the volume increases while the temperature and the number of moles remain constant, the pressure decreases. Since the pressure is the result of collisions of gas molecules with the walls of the container, a decrease in pressure means that the rate of collisions will also decrease. Therefore, increasing the volume of the container will decrease the rate of collisions.

When the temperature of the gas increases, the kinetic energy of the gas molecules increases as well. This increase in kinetic energy means that the gas molecules will move faster, thus colliding with the walls of the container more frequently. Using the ideal gas law, we see that an increase in temperature while keeping the volume and the number of moles constant leads to an increase in pressure. Therefore, increasing the temperature will increase the rate of collisions.

Increasing the molar mass means that the gas has heavier molecules. When we examine the ideal gas law equation, we see that the molar mass (M) is not directly present in the equation. However, we could relate molar mass to the number of moles (n) if we consider the mass (m) of gas constant in the container. If the mass remains constant and the molar mass increases, the number of moles (n) will decrease (n = m/M) since n and M are inversely related. Consequently, from the ideal gas law equation, we can see that decreasing the number of moles while keeping the volume and temperature constant will decrease the pressure. As a result, the rate of collisions will also decrease. Therefore, increasing the molar mass of the gas will decrease the rate of collisions. In conclusion: (a) Increasing the volume of the container decreases the rate of collisions. (b) Increasing the temperature increases the rate of collisions. (c) Increasing the molar mass of the gas decreases the rate of collisions.