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Chapter 5: Problem 7

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)

Short Answer

Expert verified
The fault in the chemistry student's logic is that they didn't consider the addition of gas particles and the possible increase in temperature during the tire filling process. According to the Kinetic Molecular Theory, pressure and volume are inversely proportional only when the number of molecules and temperature remain constant. In the case of filling a tire, the number of molecules and potentially the temperature are changing, allowing for both pressure and volume to increase simultaneously.

Step by step solution

01

Understand the relationship between pressure and volume according to the KMT

The Kinetic Molecular Theory states that the macroscopic properties of gases, such as pressure, volume, and temperature, are related to the behavior of the microscopic molecules that make up the gas. According to the KMT, the following relationship occurs: - Pressure and volume are inversely proportional when the number of molecules and the temperature of the gas remain unchanged. This means that as the pressure of the gas increases, the volume decreases if the temperature and number of molecules stay constant. This is known as Boyle's Law.
02

Explain the fault in the chemistry student's logic

The fault in the chemistry student's logic is that they didn't take into account the increased flow of gas, resulting in an increase in the number of molecules within the tire. When you fill a tire, you are actually adding new gas particles to the existing gas particles, thus increasing the amount of molecules inside the tire. Furthermore, during this process, it's possible that the temperature inside the tire could slightly increase due to the compression of the added gas and the friction between the molecules. As a result, both the pressure and volume of the tire increase simultaneously, in accordance with the Ideal Gas Law and KMT.
03

Illustrate the concept

Imagine a closed container divided into a left and right side: - On the left side, you have fewer gas particles with relatively low pressure (representing the initial state of the tire); - On the right side, you have more gas particles with higher pressure (representing the tire after it has been filled with more gas). When we increase the number of gas particles in the tire (by filling it), we are essentially making the container resemble the right side of the container more, where both pressure and volume are higher.
04

Summarize the explanation

In conclusion, the fault in the chemistry student's logic lies in the fact that they did not consider the addition of gas particles to the tire and the possible increase in temperature during the process. According to the KMT, pressure and volume are inversely proportional only when the number of molecules and the temperature remain constant. If the number of molecules and temperature are allowed to change, it is possible for both pressure and volume to increase simultaneously as demonstrated in filling a car tire.

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