Question

Rationalize the temperature dependence of the solubility of a gas in water in terms of the kinetic molecular theory.

Short answer

In summary, the temperature dependence of gas solubility in water can be rationalized through the kinetic molecular theory. As temperature increases, the average kinetic energy of gas molecules also increases, causing them to move more rapidly and overcome the attractive forces between them and water molecules. This results in more gas molecules escaping from their hydration shells and entering the gas phase, consequently decreasing the solubility of the gas in water. This behavior is consistent with Henry's Law, which relates gas solubility to temperature and pressure.

Step-by-step solution

Understand the Relation Between Temperature and Kinetic Energy

According to the kinetic molecular theory, the molecules of a gas are in constant random motion. The temperature of the gas is directly proportional to the average kinetic energy of its molecules. As the temperature increases, the average kinetic energy of the gas molecules also increases, leading them to move more rapidly and collide more often with each other.

Understand Solubility in Terms of Molecular Interactions

Solubility of a gas in water is determined by the balance between two opposing factors: the tendency of molecules to escape into the gas phase (due to their kinetic energy), and the attractive forces between gas molecules and water molecules (which promote solubility). When a gas molecule is surrounded by water molecules, the attractive forces between them form a hydration shell, stabilizing the gas molecule in the water. The gas molecules that have higher kinetic energy are more likely to overcome these attractive forces and escape into the gas phase.

Analyze the Effect of Temperature on Solubility

As the temperature of the system increases, the average kinetic energy of the gas molecules also increases. This results in an increased likelihood for the gas molecules to escape from their hydration shell and move into the gas phase. Consequently, the solubility of the gas decreases, as more gas molecules leave the solution and enter the gas phase. This temperature-dependent behavior can be observed experimentally and is described by Henry's Law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid at a constant temperature.

Conclusion

In summary, according to the kinetic molecular theory, the solubility of a gas in water is determined by the balance between attractive forces between gas and water molecules and the tendency of the gas molecules to escape into the gas phase due to their kinetic energy. As the temperature increases, the average kinetic energy of the gas molecules increases, resulting in a decrease in solubility due to more gas molecules escaping from their hydration shells and entering the gas phase.

Key concepts

Kinetic Molecular Theory

In the context of the solubility of gases in water, the kinetic molecular theory offers vital insights into the molecular level behaviors that affect solubility. At the core of this theory lies the understanding that gas molecules are in a state of continuous and random motion. This motion is central to the theory and provides a framework for interpreting various gas behaviors.

Temperature plays a critical role in this scenario, as it is directly related to the average kinetic energy of the molecules. Higher temperatures correspond to more vigorous molecular movement. This leads to an increased frequency and force of collisions among molecules, which translates to greater kinetic energy. By grasping the relation between temperature and molecular motion, students can begin to understand why gas solubility in water can be temperature dependent.

Temperature Dependence

When it comes to understanding the solubility of gases in water, the temperature dependence is a key factor that cannot be overlooked. As the kinetic energy of molecules increases with temperature, this influences the molecular dynamics to a great extent.

Higher temperatures increase the likelihood of gas molecules escaping from the liquid phase to the gas phase, a process known as desorption. This is because the thermal energy provided to the gas molecules gives them sufficient momentum to break free from their interaction with the surrounding water molecules. Conversely, at lower temperatures, the movement of gas molecules is less vigorous, resulting in a greater number of gas molecules being solvated or dissolved in water. Students should recognize that temperature is a tuning factor for the delicate balance between the solubility and the kinetic motion of gas molecules.

Henry's Law

Henry's Law offers a quantitative glimpse into the behavior of gas solubility by establishing a direct relationship between solubility and pressure at a constant temperature. It states that at a constant temperature, the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid.

The law's formula, \(C = kP\) where \(C\) is the concentration of the gas, \(k\) is Henry's Law constant, and \(P\) is the partial pressure, brings together the topics of pressure and solubility. This means that if the pressure is increased, more gas will dissolve in water up to the point where a new equilibrium is achieved. However, when considering temperature dependence, students must understand that Henry's Law holds true only under the premise of constant temperature. As temperature varies, the constant \(k\) itself may change, reflecting the dynamic nature of molecular interactions in different temperature settings.

Molecular Interactions

Molecular interactions, specifically between gas molecules and water molecules, are at the heart of solubility issues. Water's polarity and ability to form hydrogen bonds make it an excellent solvent for gases. When gas molecules come into contact with water, they are surrounded by water molecules, forming what's referred to as a hydration shell. The strength of this shell, or the solvation process, is a tug-of-war between the kinetic energy that propels molecules to escape into the gas phase and the attractive forces that keep them solvated.

In the scenario of increasing temperature, the intensification of kinetic energy causes more gas molecules to break free from their hydration shells, leading to lower solubility. This concept is crucial for comprehending the dynamic balance that influences the solubility of a gas in water. An appreciation of this balance assists students in understanding not just why gases dissolve, but also why their solubility can alter with changing temperatures.