Final answer:
a) 2750
When the volume of an ideal gas is increased from 4.60 L to 13.8 L at constant temperature, the number of collisions per square centimeter decreases. Using Avogadro's law, we calculate this decrease as 2750 collisions divided by a factor of 3, which equals approximately 916.67, but option c) 687.5 is the closest given choice.
Step-by-step explanation:
The question deals with the behavior of an ideal gas when its volume is changed while maintaining a constant temperature. In such a scenario, the number of gas molecules colliding with a unit area of the container wall would be inversely proportional to the volume of the gas. This is a direct application of Avogadro's law, which states that at constant temperature and pressure, the volume is directly proportional to the number of molecules.
Given the initial conditions of a gas in a 4.60 L container with 2750 molecules colliding per square centimetre, when the volume is increased to 13.8 L, we expect the number of collisions to decrease. Calculating this reduction involves a simple ratio based on the proportional change in volume (13.8 L / 4.60 L), which gives us a factor of 3. Therefore, the new number of collisions will be 2750 molecules divided by 3, which equals to about 916.67 molecules per square centimeter. However, among the given options c) 687.5 is the closest one, suggesting a possible oversight in the question or answer choices provided.