Problem 78 - Chemistry: The Central Science

Question

Newton had an incorrect theory of gases in which he assumed that all gas molecules repel one another and the walls of their container. Thus, the molecules of a gas are statically and uniformly distributed, trying to get as far apart as possible from one another and the vessel walls. This repulsion gives rise to pressure. Explain why Charles's law argues for the kineticmolecular theory and against Newton's model.

Step-by-Step Solution

Answer

In conclusion, Charles's law supports the kinetic-molecular theory and contradicts Newton's model of gases. This is because the kinetic-molecular theory, which considers the kinetic energy and motion of gas particles, can explain the relationship between the volume of a gas and its temperature, as observed in Charles's law. In contrast, Newton's model, which assumes static and uniformly distributed gas particles without accounting for their kinetic energy, cannot adequately explain this relationship.

Step 1: Understanding Charles's Law

Charles's law states that the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant. Mathematically, it can be represented as: \[V \propto T\] where V is the volume of the gas and T is its temperature in Kelvin.

Step 2: Understanding the Kinetic-Molecular Theory

The kinetic-molecular theory is a model that helps explain the behavior of gases. It is based on the following main assumptions: 1. Gas particles are in constant, random motion. 2. Gas particles are very small compared to the distances between them, so the volume occupied by the particles themselves is negligible. 3. Gas particles interact only through elastic collisions, and there are no other forces acting on them. 4. The average kinetic energy of gas particles is directly proportional to the temperature of the gas.

Step 3: Understanding Newton's Model

In Newton's model of gases, he assumed that all gas molecules repel one another and the walls of their container. Consequently, the molecules of a gas are statically and uniformly distributed, trying to get as far apart as possible from one another and the vessel walls. This repulsion gives rise to pressure but does not consider the kinetic energy or motion of gas particles.

Step 4: Comparing Charles's Law with the Kinetic-Molecular Theory

According to Charles's law, the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant. This is consistent with the kinetic-molecular theory, as the average kinetic energy of gas particles is directly proportional to the temperature of the gas. As the temperature increases, the average kinetic energy of the particles also increases, which results in the expansion of gas and an increase in volume.

Step 5: Comparing Charles's Law with Newton's Model

On the other hand, Newton's model does not explain the relationship between the volume of a gas and its temperature. Since it assumes that gas particles are static and uniformly distributed, it does not account for the effects of temperature on the kinetic energy of the gas molecules. As a result, this model does not adequately explain the phenomena observed in Charles's law.

Step 6: Conclusion

In conclusion, Charles's law supports the kinetic-molecular theory and goes against Newton's model since the kinetic-molecular theory explains the observed relationship between the volume of a gas and its temperature, considering the kinetic energy of gas particles. In contrast, Newton's model cannot adequately explain this relationship, as it assumes the gas particles to be static and uniformly distributed without accounting for their kinetic energy or motion.