Problem 74 - Chemistry 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 kinetic- molecular theory and against Newton's model.

Step-by-Step Solution

Answer

Charles's law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure and amount of gas are held constant, supports the kinetic-molecular theory as it accounts for the motion and interaction of gas molecules. As the temperature increases, the average kinetic energy of the gas molecules increases, leading to a greater occupied volume. This relationship cannot be explained by Newton's static gas model, which assumes a uniform distribution of molecules attempting to maximize their distance from each other and the container walls. Thus, Charles's law argues for the kinetic-molecular theory and against Newton's model, highlighting the importance of understanding the motion and interaction of gas molecules to explain gas behavior.

Step 1: 1. Understanding Charles's Law

Charles's law states that, for a given amount of gas held at a constant pressure, the volume of the gas is directly proportional to its temperature (in Kelvin). Mathematically, this can be represented as: \[ V \propto T \] Or, when represented as an equation with a proportionality constant k: \[ V = kT \] If the temperature of the gas increases, the volume will also increase, and vice versa. This relationship is valid as long as the pressure and amount of gas remain constant.

Step 2: 2. Understanding the Kinetic-Molecular Theory

The kinetic-molecular theory of gases explains the behavior of gases by considering the motion and interaction of gas molecules. The main assumptions of this theory are: 1. Gas molecules are in constant, random motion. 2. The size of gas molecules is negligible compared to the volume of the container. 3. Gas molecules collide with each other and the walls of the container, exerting pressure. 4. No intermolecular forces are acting between gas molecules except during collisions, which are perfectly elastic (no loss of kinetic energy). Based on the kinetic-molecular theory, the temperature of a gas is directly related to the average kinetic energy of its molecules. An increase in temperature leads to an increase in the average kinetic energy, causing gas molecules to move faster and occupy more space, leading to an increase in volume, as stated by Charles's law.

Step 3: 3. Newton's Static Gas Model

Newton's static gas model assumed that gas molecules repel one another and the walls of their container, resulting in a uniform distribution of molecules trying to maximize their distance from each other and the container walls. This repulsion was thought to give rise to the pressure exerted by the gas. However, Newton's model contradicts the concept of the constant motion and interaction of gas molecules, as proposed by the kinetic-molecular theory.

Step 4: 4. Why Charles's Law Supports the Kinetic-Molecular Theory and Refutes Newton's Model

Charles's law demonstrates the relationship between the volume and temperature of a gas while holding pressure and the amount of gas constant. This relationship is supported by the kinetic-molecular theory, which explains the motion and interaction of gas molecules and their relationship to the gas's temperature. An increase in temperature leads to an increase in the average kinetic energy of gas molecules, causing them to move faster, occupy more space, and increase the gas's volume. On the other hand, Newton's static gas model, which postulates a uniform distribution of molecules, does not adequately explain this connection between temperature and volume. The kinetic-molecular theory highlights the importance of understanding the behavior of gas molecules in motion, proving a more plausible explanation for the pressure and volume relationship exhibited by gases. Thus, Charles's law argues for the kinetic-molecular theory by supporting the relationship between volume and temperature as derived from the motion and interaction of gas molecules. It also argues against Newton's model, which cannot account for the relationship between temperature and volume based on its assumption of a static distribution of gas molecules.