Question

Which of the following gas mixture is not applicable for Dalton's law of partial pressure? (a) \(\mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2}\) (b) \(\mathrm{CO}_{2}\) and \(\mathrm{N}_{2}\) (c) \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) (d) \(\mathrm{CO}\) and \(\mathrm{N}_{2}\)

Short answer

Mixture (a) is not applicable for Dalton's law of partial pressure because the gases can react with each other.

Step-by-step solution

Understanding Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases. For Dalton's Law to apply, the gases should not react with each other chemically.

Examine Each Gas Mixture

Assess each gas mixture to determine if the gases are likely to react with each other. If any of the gases react, then that mixture does not follow Dalton's Law.

Determining the Applicable Mixture

Mixture (a) contains \(\mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2}\). These gases can react with each other to form chemical compounds, such as sulfur oxychloride \(\mathrm{SOCl}_{2}\) and sulfur dichloride \(\mathrm{SCl}_{2}\), so this mixture does not follow Dalton's Law of Partial Pressures.

Key concepts

Partial Pressures

Understanding the concept of partial pressures is essential in the study of physical chemistry, particularly when dealing with gas mixtures. The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume of the mixture at the same temperature. In a blend of gases, each gas's partial pressure is proportional to its mole fraction, and Dalton's Law of Partial Pressures asserts that the total pressure of the mixture is simply the sum of these individual pressures.To put it in perspective, imagine a room filled with balloons of different colors, each representing a different gas. Each balloon's size corresponds to its partial pressure. Despite their coexistence in the same space, each balloon's size doesn't change because of the others. Similarly, in a gas mixture, each gas exerts pressure independently of the others, and their collective effect contributes to the total pressure we measure.When applying Dalton's Law, it's crucial to assume that the gas particles are non-reactive, meaning they don't form new compounds or change in character upon mixing.

Non-reactive Gas Mixtures

Non-reactive, or inert, gas mixtures are central to the application of Dalton's Law. These mixtures consist of gases that do not undergo chemical reactions when they are in contact with one another. The most common examples include noble gases and mixtures such as nitrogen with carbon dioxide.

Characteristics of Non-reactive Gas Mixtures

• Chemical Stability: The gases in a non-reactive mixture are chemically stable, meaning they retain their individual properties and don't transform into new compounds.
• Physical Mixing: The gases are mixed physically and can be separated by physical means without breaking chemical bonds.
• No Energy Changes: Since there are no chemical reactions, there are no associated energy changes due to bond formation or breaking.

For Dalton's Law to be valid, the requirement of non-reactivity is non-negotiable. If even a minor reaction occurs between the gases in the mixture, the resultant change in the number of moles of gas affects the total pressure, thus invalidating the law's straightforward summation property.

Physical Chemistry

Physical chemistry is the branch of chemistry that deals with the physical properties and phenomena of chemical systems and processes. It includes the study of energy relationships, thermodynamics, kinetics, quantum chemistry, statistical mechanics, and the behavior of gases.Within this discipline, laws such as Dalton's Law of Partial Pressures play a crucial role. They allow us to predict the behavior of gases in mixtures, which is vital in various industrial and research applications like synthesizing materials, environmental monitoring, and even in health industries where gas mixtures are used for anesthesia.The understanding of Dalton's Law and the behavior of gas mixtures reflects the broader goals of physical chemistry: to understand the microscopic mechanisms and derive macroscopic properties from them. It's a fascinating dance between what we cannot see—the individual gas particles—and the pressures we can measure, bringing the invisible to the realm of the quantifiable.