Question

To which of the following gaseous mixtures is Dalton's law not applicable? (a) \(\mathrm{Ne}+\mathrm{He}+\mathrm{SO}_{2}\) (b) \(\mathrm{NH}_{3}+\mathrm{HCl}\) (c) \(\mathrm{O}_{2}+\mathrm{N}_{2}+\mathrm{CO}_{2}^{2}\) (d) \(\mathrm{N}_{2}+\mathrm{H}_{2}+\mathrm{O}_{2}\)

Short answer

Dalton's law does not apply to option (b), \(\mathrm{NH}_{3}+\mathrm{HCl}\).

Step-by-step solution

Understanding Dalton's Law

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. It assumes gases do not react with each other and are ideal.

Analyzing Option (a)

For the mixture (a) \(\mathrm{Ne}+\mathrm{He}+\mathrm{SO}_{2}\), all gases are inert and do not react with each other. Dalton's law applies here.

Analyzing Option (b)

For the mixture (b) \(\mathrm{NH}_{3}+\mathrm{HCl}\), ammonia (\(\mathrm{NH}_{3}\)) and hydrogen chloride (\(\mathrm{HCl}\)) react with each other to form ammonium chloride (\(\mathrm{NH}_{4}\mathrm{Cl}\)), a chemical reaction occurs preventing the application of Dalton's Law.

Analyzing Option (c)

For the mixture (c) \(\mathrm{O}_{2}+\mathrm{N}_{2}+\mathrm{CO}_{2}\), the gases are inert under normal conditions and do not react with each other. Dalton's law applies here.

Analyzing Option (d)

For the mixture (d) \(\mathrm{N}_{2}+\mathrm{H}_{2}+\mathrm{O}_{2}\), under normal conditions the gases do not react, especially not at room temperature and pressure, allowing Dalton's Law to apply.

Key concepts

Non-reacting gases

Non-reacting gases, as the name suggests, are gases that do not engage in chemical reactions with one another under a given set of conditions. In the context of Dalton's Law of Partial Pressures, the assumption of non-reactivity is crucial.

This is because Dalton's law is based on the idea that each gas in a mixture behaves independently of the others, contributing to the total pressure solely based on its own partial pressure. Under normal conditions, for instance:

• Noble gases like Neon (Ne) and Helium (He) are typically non-reactive due to their complete valence electron shells.
• Inert gases such as Nitrogen (N₂) often do not participate in reactions unless conditions change dramatically, such as under high temperatures or pressures.

Recognizing non-reacting gases is thus fundamental to applying Dalton’s law, as it ensures that no reactions occur to alter the identities or pressures of the gases involved.

Partial pressures

Partial pressures are a fundamental part of Dalton's Law. It describes how each gas in a mixture exerts a pressure independently of the others. The pressure that an individual gas would exert if it alone occupied the entire volume is what we call its partial pressure.

According to Dalton’s Law, the total pressure of a gas mixture is simply the sum of the partial pressures of each component gas. This makes mathematics in gas mixtures quite straightforward since:

• The partial pressure of a gas is directly proportional to its mole fraction in the mixture.
• Mole fraction is the ratio of the number of moles of a gas to the total number of moles of all gases present.

Understanding partial pressures not only applies to theoretical exercises but is also practical in fields like atmospheric science and chemical engineering, where controlling the pressure of gas mixtures is often necessary.

Mixture of gases

A mixture of gases consists of two or more different gases that are combined without reacting with each other. In many scientific and industrial processes, working with gas mixtures is common. The behaviors of these mixtures can be predicted effectively through Dalton’s Law when the gases do not undergo any chemical reactions.

For example:

• A mixture of oxygen (O₂), nitrogen (N₂), and carbon dioxide (CO₂) will follow Dalton's Law as they generally do not interact chemically under normal conditions.
• However, a mixture like ammonia (NH₃) and hydrogen chloride (HCl) does not adhere to Dalton's Law, as these gases react to form ammonium chloride (NH₄Cl).

Understanding whether gases in a mixture will react is vital in applications ranging from laboratory experiments to industrial operations and emergency response situations, where the safety and efficiency of the gas handling processes are paramount.