A chemistry student relates the following story: I noticed my tires were a bit low and went to the gas station. As I was filling the tires, I thought about the kinetic molecular theory (KMT). I noticed the tires because the volume was low, and I realized that I was increasing both the pressure and volume of the tires. "Hmmm," I thought, "that goes against what I learned in chemistry, where I was told pressure and volume are inversely proportional." What is the fault in the logic of the chemistry student in this situation? Explain why we think pressure and volume to be inversely related (draw pictures and use the KMT).

The Kinetic Molecular Theory describes the behavior of gases in terms of the particles they consist of. According to the KMT, gas particles are in constant motion, and they move in straight lines until they collide with other particles or the walls of their container. When gas particles collide with the container walls, they exert a force on them, which we perceive as pressure. The more particles there are and the faster they move, the more pressure they exert.

Boyle's Law, which is derived from the KMT, states that for a fixed amount of gas at a constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, this can be represented as \(P_1V_1 = P_2V_2 \), where \(P_1\) and \( V_1\) represent the initial pressure and volume, and \(P_2\) and \(V_2\) represent the final pressure and volume. So when the volume of a gas decreases, its pressure increases, and vice versa. This inverse relationship is because, when the volume decreases, the gas particles have less space to move in and will collide more frequently with the walls of the container, thus exerting more pressure.

The chemistry student claims that they were increasing both the pressure and volume of their tires, which contradicts Boyle's Law. The issue in the student's logic lies in the fact that they are not taking into consideration the amount of gas being added to the tires. While adding air to the tires, the student is not just increasing the volume; they are also increasing the amount of gas particles within the tires. As a result, the system is not at a constant temperature and a fixed amount of gas. Therefore, Boyle's Law, which relies on these conditions, does not apply in this situation. In summary, the chemistry student's logic is flawed because they are misapplying Boyle's Law to a situation where the amount of gas is changing. This is why they perceive an inconsistency in their understanding of the pressure-volume relationship as they fill their tires.